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motbob
United States12546 Posts
I am not sure that MLG's extended series provision does a good job of allowing the best player to win. In fact, my simulations show that it does exactly the opposite.
MLG_Lee once told me a story that explained the philosophy behind extended series. At a Halo event, he said, one of the best teams demolished an up-and-coming team 2-0 or 3-0 in the winners' bracket. The two teams met again in the losers' bracket, and the worse team eked out a close win against the favorites. Extended series, Lee said, would have prevented that from happening.
If MLG's goal is to help shepherd the best player to victory, extended series, in some (and perhaps all) cases, do not achieve that goal. If MLG's goal is to help the better player to win just in those matches where they have already played their opponent, extended series, in some (and perhaps all) cases, do not achieve that goal. If MLG's goal isn't either of those two things, what is it?
I made an Excel workbook that simulates a major part of MLG's 2012 tournaments: an 8-player group that features double elimination and extended series. MLG's Spring, Summer, and Fall tournaments each featured these types of groups, and those groups might make a return in Columbus after the fluke formats of 2013 Winter and Spring. I ran Monte Carlo simulations (that is, simulating the group over and over again thousands of times) in this workbook.
Whether the players were close or distant in skill... whether the players were seeded by skill or randomly seeded... whether there was a single dominant player or a more even field... in all these cases, the simulations all came up with the same result: Extended series make it less, not more, likely for the better player to win the bracket.
That's not all. I ran a different set of simulations: If the first- and second-best players in the group met up in the losers' finals, would the best player be more likely to win in a bracket with extended series or one without? Again, the result of the simulations run counter to MLG's wishes: Extended series resulted in the better player being knocked out more often, not less often. Sometimes, the extended series rule worked in the best player's advantage exactly as MLG had designed, allowing them to close out the match against an inferior foe. But other times, the winners' bracket match was a fluke, with the worse player winning -- and in the rematch, that fluke carried over, giving the worse player a better chance to advance! A real world example of this would be ToD vs Ryung in an MLG qualifier, where ToD was probably the worse player of the two. ToD won in the winners' bracket 2-1, and in the rematch managed to finish Ryung off 4-3.
Typically, the difference in the rate of the best player winning the bracket was 0.5% - 1.0%. Fluctuations here were, I assume, due to ELO distribution. The difference in winrate in "would the best player win in this particular matchup" tests was 0.2%-0.8%. In the second case, fluctuations came from how often an extended series match was played: If the first- and second-best players were matched up in the first round, thus guaranteeing that an extended series would be played in a losers' bracket matchup, then the difference between extended series and non-extended series formats was relatively large.
Note that this is NOT definite proof that extended series do not achieve MLG's goals in all situations. I am not going to simulate a 128-player bracket, and I didn't simulate all possible combinations of ELOs or player seeding. However, I'm not sure why things would be much different in a larger bracket, especially since most extended series in MLG events happen near the end of the bracket.
If extended series do not achieve what MLG intends them to achieve, what good are they?
You can see the excel workbook here. (Please don't look at the formula I used to pull ELOs in column B. Yes, I know I could have just used INDEX/MATCH.)
+ Show Spoiler [how the excel spreadsheet works] +Player ELOs are input. Players play winners' bracket matches, and match results are recorded in the table at the top right. Later, in losers' bracket matches, it is determined whether an extended match is appropriate (cell A65, for example, serves this purpose) and, if an extended series needs to be played, an initial score for the match is called. This pattern continues to the grand finals, where MLG's weird grand finals format is appropriately simulated.
  
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So, wait, did you use truly random numbers in the simulation?
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motbob
United States12546 Posts
The RAND function is pseudo-random, but it is fine for my purposes. Older versions of RAND in Excel were not appropriate for Monte Carlo simulations, but Excel 2007 improved it.
http://support.microsoft.com/kb/828795
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Hey, cool stuff.
Im just curious what alternative did you use instead of extended series? Just a normal Bo3?
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motbob
United States12546 Posts
On July 22 2013 23:44 FlubberMan wrote:
Hey, cool stuff.
Im just curious what alternative did you use instead of extended series? Just a normal Bo3?
The alternative was what would have been played under MLG rules if the two players hadn't previously played.
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That's very interesting! Thanks for posting this.
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On July 22 2013 23:51 motbob wrote:Show nested quote +On July 22 2013 23:44 FlubberMan wrote:
Hey, cool stuff.
Im just curious what alternative did you use instead of extended series? Just a normal Bo3? The alternative was what would have been played under MLG rules if the two players hadn't previously played.
Okay thanks for the quick answer. Im not sure what the MLG rules are but I think somehow you have to have some kind of rule that give an advantage to the guy in the winnersbracket playing against someone from the loosers bracket, no matter what makes the best player win the tournament more often.
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Extended series has to be the most overblown, ridiculous controversy in all of StarCraft2.
I understand the argument that the extra matches you have to play to get through the loser bracket is punishment enough but I think the scenario of Player A losing 0-2 the first time and then winning 2-1 the second time and advancing with the 2-3 total is suboptimal.
Excuse me while I go watch NaNiwa vs Flash Game 7.
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Correct me if I'm wrong (I may be missing some complexity or nuance here), but the following is true, and is independent of whether or not the series is continuous or broken into a Bo3 and extended into a Bo7.
If player A is better than B, say having a 51% chance of winning any single game vs. player B, then the more games they play, the law of large numbers will push the winrate of each player towards the projected underlying probability. Which is to say that smaller samples are noisier than large ones.
So, using a simple binomial distribution with the set of binomial parameters:
% chance of success (probability that the better player will win):
# successes needed (required # of wins in a series):
# trials (# of games in a series)
The probability of the better player winning always goes up with a larger set of games.
For example, with the initial binomial parameters (for a Bo3 series with 2 extremely evenly matched players):
% chance of success (probability that the better player will win): 51%
# successes needed (required # of wins in a series): 2
# trials (# of games in a series): 3
The better player wins that series 51.499% of the time.
If the series is extended to 7 games however:
% chance of success (probability that the better player will win): 51%
# successes needed (required # of wins in a series): 4
# trials (# of games in a series): 7
The better player wins 52.19% of the time.
For larger discrepancies between skill level (70% to 30% chance of winning between players), the dichotomy between short and long series increases even further:
% chance of success (probability that the better player will win): 70%
# successes needed (required # of wins in a series): 3 (short), 7 (long)
# trials (# of games in a series): 2 (short), 4 (long)
The better player wins the short series 78.4% of the time, and the long series 87.4% of the time.
This trend is also independent of how the series is broken up. For example, using our 70/30 split again. Here are the chances of certain outcomes in a Bo3 series:
Better player wins Bo3: 78.4%
Better player wins 2-0: 49%---------------------------------->Better player goes on to win Bo7 extended series 96.9% of the time
Better player wins 2-1: 29.4%-------------------------------->Better player goes on to win Bo7 extended series 91.6% of the time
Worse player wins Bo3: 21.6%
Worse player wins 2-0: 9%------------------------------------>Better player goes on to win Bo7 extended series 52.8% of the time
Worse player wins 2-1: 12.6%------------------------------->Better player goes on to win Bo7 extended series 65.2% of the time
Using the % chance of each Bo3 result to weight the Bo7 results:
87.4% chance of the better player winning the Bo7 extended series overall, which is identical to the result for continuous Bo7 series
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motbob this spreadsheet is so big it's hard to figure out what's going on. Isn't is sufficient to just simulate 2 players meeting in the losers bracket? Extended vs not.
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We aren't looking for a continuous Bo7 series though. If Player B beats Player A 2-1, they play again... player B starts as 2-1 so only needs to win 2 games, where Player A has to win 3 games. Compare that to Player B beats player A 2-1, they play again in another Bo3. Either one only needs to win 2 games. So if player A is the better player, he would have a better chance at winning only 2 games, rather than needing to win 3. Simple.
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First let me explain why 'extended series' exists:
Players A and B meet in the winner's bracket and losers bracket.
Scenario 1:
Player A wins 2-0 in winner's bracket. Player B wins 2-1 in loser's bracket rematch. Player A leads 3-2 overall in maps, but Player B advances. I consider this unfair.
Scenario 2;
Player A wins 2-0 in winner's bracket. Player B wins 2-0 in loser's bracket rematch. The series is a tie 2-2 overall in maps, but Player B advances solely based on the order of the matches. A won earlier and B won later, but B advances. Again, I consider this unfair.
Now allow for extended series. This resolves Scenario 1 and 2 by forcing either Player A or B to win in map score. Therefore, if you think Scenario 1 & 2 are unfair, like I do, then there should be a rule to resolve the problem. MLG uses extended series to solve this problem.
With regards to the simulation in the OP:
I think what you are saying is, "Better players lose the extended series when they are playing from the 'behind' position." This is a function of win rates. If you use win rates hovering around 50% for both players (typical Starcraft 2 win rates), then the discreteness of being behind 1 or 2 games entering the extended series will frequently result in an overall loss for the 'better' player.
E.g. Player A and Player B have a 48/52 win rate split. Player A finishes the winner's bracket series up 2-1. Now they meet in an extended series. Player A has to win 2 games and Player B needs to win 3 games. Given the win rates, it is no surprise that once the results of the original series are revealed we can easily predict that Player B will still lose the series more often than Player A loses the series (even though Player B is objectively better!)
TLDR: Better players not coming from behind to survive through extended series has nothing to do with why extended series has been implemented; to resolve unwanted map score advancement scenarios.
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You are ignoring the fact of # of series lost. One player, even with better map score, has lost two series. Player B has only lost one. We aren't looking for the best player vs player B, but the best player, which takes into account all of the matches. The same thing happens in GSL.
Player A 2-0 Player B
C 2-0 D
C > A
B > D
B 2-1 A
Does A still deserve to advance just because he has a better map score vs player B? He still lost one more series than B did, therefore as an overall player he is not as skilled on that day.
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Hong Kong9151 Posts
On July 23 2013 01:15 KissMeRed wrote:
With regards to the simulation in the OP:
I think what you are saying is, "Better players lose the extended series when they are playing from the 'behind' position." This is a function of win rates. If you use win rates hovering around 50% for both players (typical Starcraft 2 win rates), then the discreteness of being behind 1 or 2 games entering the extended series will frequently result in an overall loss for the 'better' player.
E.g. Player A and Player B have a 48/52 win rate split. Player A finishes the winner's bracket series up 2-1. Now they meet in an extended series. Player A has to win 2 games and Player B needs to win 3 games. Given the win rates, it is no surprise that once the results of the original series are revealed we can easily predict that Player B will still lose the series more often than Player A loses the series (even though Player B is objectively better!)
TLDR: Better players not coming from behind to survive through extended series has nothing to do with why extended series has been implemented; to resolve unwanted map score advancement scenarios.
it's not observable win rates, but an inference based on Elo values
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On July 23 2013 01:15 KissMeRed wrote:
First let me explain why 'extended series' exists:
Players A and B meet in the winner's bracket and losers bracket.
Scenario 1:
Player A wins 2-0 in winner's bracket. Player B wins 2-1 in loser's bracket rematch. Player A leads 3-2 overall in maps, but Player B advances. I consider this unfair.
Scenario 2;
Player A wins 2-0 in winner's bracket. Player B wins 2-0 in loser's bracket rematch. The series is a tie 2-2 overall in maps, but Player B advances solely based on the order of the matches. A won earlier and B won later, but B advances. Again, I consider this unfair.
Now allow for extended series. This resolves Scenario 1 and 2 by forcing either Player A or B to win in map score. Therefore, if you think Scenario 1 & 2 are unfair, like I do, then there should be a rule to resolve the problem. MLG uses extended series to solve this problem.
With regards to the simulation in the OP:
I think what you are saying is, "Better players lose the extended series when they are playing from the 'behind' position." This is a function of win rates. If you use win rates hovering around 50% for both players (typical Starcraft 2 win rates), then the discreteness of being behind 1 or 2 games entering the extended series will frequently result in an overall loss for the 'better' player.
E.g. Player A and Player B have a 48/52 win rate split. Player A finishes the winner's bracket series up 2-1. Now they meet in an extended series. Player A has to win 2 games and Player B needs to win 3 games. Given the win rates, it is no surprise that once the results of the original series are revealed we can easily predict that Player B will still lose the series more often than Player A loses the series (even though Player B is objectively better!)
TLDR: Better players not coming from behind to survive through extended series has nothing to do with why extended series has been implemented; to resolve unwanted map score advancement scenarios.
well said.
on a different note i never actually thought that extended series was used to resolve potential map score issues. The rules makes a little more sense now. However, I still dislike it from a spectator point of view.
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Hong Kong9151 Posts
On July 23 2013 02:05 Theberlinwall wrote:Show nested quote +On July 23 2013 01:15 KissMeRed wrote:
First let me explain why 'extended series' exists:
Players A and B meet in the winner's bracket and losers bracket.
Scenario 1:
Player A wins 2-0 in winner's bracket. Player B wins 2-1 in loser's bracket rematch. Player A leads 3-2 overall in maps, but Player B advances. I consider this unfair.
Scenario 2;
Player A wins 2-0 in winner's bracket. Player B wins 2-0 in loser's bracket rematch. The series is a tie 2-2 overall in maps, but Player B advances solely based on the order of the matches. A won earlier and B won later, but B advances. Again, I consider this unfair.
Now allow for extended series. This resolves Scenario 1 and 2 by forcing either Player A or B to win in map score. Therefore, if you think Scenario 1 & 2 are unfair, like I do, then there should be a rule to resolve the problem. MLG uses extended series to solve this problem.
With regards to the simulation in the OP:
I think what you are saying is, "Better players lose the extended series when they are playing from the 'behind' position." This is a function of win rates. If you use win rates hovering around 50% for both players (typical Starcraft 2 win rates), then the discreteness of being behind 1 or 2 games entering the extended series will frequently result in an overall loss for the 'better' player.
E.g. Player A and Player B have a 48/52 win rate split. Player A finishes the winner's bracket series up 2-1. Now they meet in an extended series. Player A has to win 2 games and Player B needs to win 3 games. Given the win rates, it is no surprise that once the results of the original series are revealed we can easily predict that Player B will still lose the series more often than Player A loses the series (even though Player B is objectively better!)
TLDR: Better players not coming from behind to survive through extended series has nothing to do with why extended series has been implemented; to resolve unwanted map score advancement scenarios. well said.
except he's wrong.
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On July 23 2013 02:11 itsjustatank wrote:Show nested quote +On July 23 2013 02:05 Theberlinwall wrote:On July 23 2013 01:15 KissMeRed wrote:
First let me explain why 'extended series' exists:
Players A and B meet in the winner's bracket and losers bracket.
Scenario 1:
Player A wins 2-0 in winner's bracket. Player B wins 2-1 in loser's bracket rematch. Player A leads 3-2 overall in maps, but Player B advances. I consider this unfair.
Scenario 2;
Player A wins 2-0 in winner's bracket. Player B wins 2-0 in loser's bracket rematch. The series is a tie 2-2 overall in maps, but Player B advances solely based on the order of the matches. A won earlier and B won later, but B advances. Again, I consider this unfair.
Now allow for extended series. This resolves Scenario 1 and 2 by forcing either Player A or B to win in map score. Therefore, if you think Scenario 1 & 2 are unfair, like I do, then there should be a rule to resolve the problem. MLG uses extended series to solve this problem.
With regards to the simulation in the OP:
I think what you are saying is, "Better players lose the extended series when they are playing from the 'behind' position." This is a function of win rates. If you use win rates hovering around 50% for both players (typical Starcraft 2 win rates), then the discreteness of being behind 1 or 2 games entering the extended series will frequently result in an overall loss for the 'better' player.
E.g. Player A and Player B have a 48/52 win rate split. Player A finishes the winner's bracket series up 2-1. Now they meet in an extended series. Player A has to win 2 games and Player B needs to win 3 games. Given the win rates, it is no surprise that once the results of the original series are revealed we can easily predict that Player B will still lose the series more often than Player A loses the series (even though Player B is objectively better!)
TLDR: Better players not coming from behind to survive through extended series has nothing to do with why extended series has been implemented; to resolve unwanted map score advancement scenarios. well said. except he's wrong.
thanks for the explanation
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On July 23 2013 02:11 itsjustatank wrote:Show nested quote +On July 23 2013 02:05 Theberlinwall wrote:On July 23 2013 01:15 KissMeRed wrote:
First let me explain why 'extended series' exists:
Players A and B meet in the winner's bracket and losers bracket.
Scenario 1:
Player A wins 2-0 in winner's bracket. Player B wins 2-1 in loser's bracket rematch. Player A leads 3-2 overall in maps, but Player B advances. I consider this unfair.
Scenario 2;
Player A wins 2-0 in winner's bracket. Player B wins 2-0 in loser's bracket rematch. The series is a tie 2-2 overall in maps, but Player B advances solely based on the order of the matches. A won earlier and B won later, but B advances. Again, I consider this unfair.
Now allow for extended series. This resolves Scenario 1 and 2 by forcing either Player A or B to win in map score. Therefore, if you think Scenario 1 & 2 are unfair, like I do, then there should be a rule to resolve the problem. MLG uses extended series to solve this problem.
With regards to the simulation in the OP:
I think what you are saying is, "Better players lose the extended series when they are playing from the 'behind' position." This is a function of win rates. If you use win rates hovering around 50% for both players (typical Starcraft 2 win rates), then the discreteness of being behind 1 or 2 games entering the extended series will frequently result in an overall loss for the 'better' player.
E.g. Player A and Player B have a 48/52 win rate split. Player A finishes the winner's bracket series up 2-1. Now they meet in an extended series. Player A has to win 2 games and Player B needs to win 3 games. Given the win rates, it is no surprise that once the results of the original series are revealed we can easily predict that Player B will still lose the series more often than Player A loses the series (even though Player B is objectively better!)
TLDR: Better players not coming from behind to survive through extended series has nothing to do with why extended series has been implemented; to resolve unwanted map score advancement scenarios. well said. except he's wrong.
Country A plays Country B in world cup pool play. Country A beats Country B 2-0. They meet again in knockout stages, Country A starts with 2-0 advantage having already beaten Country B by that margin. This sounds fair right?
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On July 23 2013 01:15 KissMeRed wrote:
First let me explain why 'extended series' exists:
Players A and B meet in the winner's bracket and losers bracket.
Scenario 1:
Player A wins 2-0 in winner's bracket. Player B wins 2-1 in loser's bracket rematch. Player A leads 3-2 overall in maps, but Player B advances. I consider this unfair.
Scenario 2;
Player A wins 2-0 in winner's bracket. Player B wins 2-0 in loser's bracket rematch. The series is a tie 2-2 overall in maps, but Player B advances solely based on the order of the matches. A won earlier and B won later, but B advances. Again, I consider this unfair.
Now allow for extended series. This resolves Scenario 1 and 2 by forcing either Player A or B to win in map score. Therefore, if you think Scenario 1 & 2 are unfair, like I do, then there should be a rule to resolve the problem. MLG uses extended series to solve this problem.
With regards to the simulation in the OP:
I think what you are saying is, "Better players lose the extended series when they are playing from the 'behind' position." This is a function of win rates. If you use win rates hovering around 50% for both players (typical Starcraft 2 win rates), then the discreteness of being behind 1 or 2 games entering the extended series will frequently result in an overall loss for the 'better' player.
E.g. Player A and Player B have a 48/52 win rate split. Player A finishes the winner's bracket series up 2-1. Now they meet in an extended series. Player A has to win 2 games and Player B needs to win 3 games. Given the win rates, it is no surprise that once the results of the original series are revealed we can easily predict that Player B will still lose the series more often than Player A loses the series (even though Player B is objectively better!)
TLDR: Better players not coming from behind to survive through extended series has nothing to do with why extended series has been implemented; to resolve unwanted map score advancement scenarios.
Why would games from a diferent stage in the tournament matter? It doesn't matter if you won 2-0 or 2-1 in the groups stage, if you had an easy win or a hard win, if you won in 50mins of 15mins, if you meet the guy again in a later part of the tourney, it's a diferent match that should start from scratch.
A Bo3 is a single match, done in this way to avoid some of the randomness of the game. If you were to count every game as a single match, you would have to always play the 3 games of the series, else you would be giving an advantage to whoever wins earlier, the exact thing you are saying is bad. The odds of winning O-X-O and winning O-O-X should be very similar. By how much you win a match has never been important in any kind of sport, except for tiebreakers.
It's like counting goals scored in football. It can be used as a tiebreaker, the same way games won is used as a tiebreaker, but it is absolutelly never used in diferent stages of the tournament. If Arsenal beats Barça 3-0 in the groups stage and they meet again in the finals, it will obviously start from scratch. Saying that match should start 3-0, or that Barça doesn't deserve the win if they win 1-0 make zero sense.
There's also the issue that you are saying that's the reason it exists, when the MLG guys who implemented it said otherwise.
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Imagine a tournament with double elimination Bo1, and another tournament with double elimination Bo1 extended into Bo3 in rematches.
Now take two players who meet in the first round and will always meet each other in the loser's bracket regardless of who wins the initial game. In the first tournament, the better player will have x chance to advance, where x is his chance of winning a Bo1 against the worse player.
In the second tournament, if the better player wins the first match, he has (1 - (1-x)^2) chance of advancing. (1 minus the chance of losing 2 Bo1s in a row) If the worse player wins the first match, the better player has x^2 chance of winning the extended series (2 Bo1s in a row)
So for the second tournament, the better player has x*(1 - (1-x)^2) + (1-x)*x^2 chance to advance, based on simple conditional probability. This is larger than x for all x between 0.5 and 1, as seen here:
http://www.wolframalpha.com/input/?i=x*(1 - (1-x)^2) + (1-x)*x^2 = x
It really looks like extended series benefits the better player to me, and I don't see why this would change with Bo3 extended to Bo7.
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On July 23 2013 00:17 Quoonit wrote:
Correct me if I'm wrong (I may be missing some complexity or nuance here), but the following is true, and is independent of whether or not the series is continuous or broken into a Bo3 and extended into a Bo7.
If player A is better than B, say having a 51% chance of winning any single game vs. player B, then the more games they play, the law of large numbers will push the winrate of each player towards the projected underlying probability. Which is to say that smaller samples are noisier than large ones.
So, using a simple binomial distribution with the set of binomial parameters:
% chance of success (probability that the better player will win):
# successes needed (required # of wins in a series):
# trials (# of games in a series)
The probability of the better player winning always goes up with a larger set of games.
For example, with the initial binomial parameters (for a Bo3 series with 2 extremely evenly matched players):
% chance of success (probability that the better player will win): 51%
# successes needed (required # of wins in a series): 2
# trials (# of games in a series): 3
The better player wins that series 51.499% of the time.
If the series is extended to 7 games however:
% chance of success (probability that the better player will win): 51%
# successes needed (required # of wins in a series): 4
# trials (# of games in a series): 7
The better player wins 52.19% of the time.
For larger discrepancies between skill level (70% to 30% chance of winning between players), the dichotomy between short and long series increases even further:
% chance of success (probability that the better player will win): 70%
# successes needed (required # of wins in a series): 3 (short), 7 (long)
# trials (# of games in a series): 2 (short), 4 (long)
The better player wins the short series 78.4% of the time, and the long series 87.4% of the time.
This trend is also independent of how the series is broken up. For example, using our 70/30 split again. Here are the chances of certain outcomes in a Bo3 series:
Better player wins Bo3: 78.4%
Better player wins 2-0: 49%---------------------------------->Better player goes on to win Bo7 extended series 96.9% of the time
Better player wins 2-1: 29.4%-------------------------------->Better player goes on to win Bo7 extended series 91.6% of the time
Worse player wins Bo3: 21.6%
Worse player wins 2-0: 9%------------------------------------>Better player goes on to win Bo7 extended series 52.8% of the time
Worse player wins 2-1: 12.6%------------------------------->Better player goes on to win Bo7 extended series 65.2% of the time
Using the % chance of each Bo3 result to weight the Bo7 results:
87.4% chance of the better player winning the Bo7 extended series overall, which is identical to the result for continuous Bo7 series
Given a simple statistical model, this is the best answer.
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Katowice25012 Posts
On July 23 2013 02:05 Theberlinwall wrote:
well said.
on a different note i never actually thought that extended series was used to resolve potential map score issues. The rules makes a little more sense now. However, I still dislike it from a spectator point of view.
This is what motbob's anecdote from Lee gets at but is a bit muddled, the basic idea here is that a player cannot be knocked out while still having a positive record against another player due to the format being double elim. It's a fine enough ideal and if you talk to most players they love it, but it tends to make spectating kind of lame which is why people on TL rally against it.
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On July 23 2013 02:32 Heyoka wrote:Show nested quote +On July 23 2013 02:05 Theberlinwall wrote:
well said.
on a different note i never actually thought that extended series was used to resolve potential map score issues. The rules makes a little more sense now. However, I still dislike it from a spectator point of view. This is what motbob's anecdote from Lee gets at but is a bit muddled, the basic idea here is that a player cannot be knocked out while still having a positive record against another player due to the format being double elim. It's a fine enough ideal and if you talk to most players they love it, but it tends to make spectating kind of lame which is why people on TL rally against it.
Weird, I thought most players hated it with spectators being more split, at least in polls. The anti-extended-series people are much more vocal though.
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Right at least I'm polls, you are much more likely to get self-selection bias with strong negative opinions being overrepresented to some degree.
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A few random notes from calculating probabilities:
If Player A and Player B were on equal ground (50/50 chance of winning a game)...
There is a 50% chance for A to eliminate B in two unweighted series.
There is a 50% chance for A to eliminate B under extended series.
There is a 6.25% chance that, without extended series, A can be eliminated by B in two series but have a better overall map score between them.
There is a 75% chance for A to win in an extended series given a win previously.
There is a 25% chance for A to win in an extended series given a loss previously.
If Player A were slightly better than Player B (51/49)...
There is a 51.5% chance for A to eliminate B in two unweighted series.
There is a 52.19% chance for A to eliminate B under extended series.
There is a 6.37% chance that, without extended series, A can be eliminated by B in two series but have a better overall map score between them.
There is a 76.42% chance for A to win in an extended series given a win previously.
There is a 26.46% chance for A to win in an extended series given a loss previously.
If Player A were significantly better than Player B (70/30)...
There is a 78.4% chance for A to eliminate B in two unweighted series.
There is a 87.4% chance for A to eliminate B under extended series.
There is a 6.17% chance that, without extended series, A can be eliminated by B in two series but have a better overall map score between them.
There is a 94.94% chance for A to win in an extended series given a win previously.
There is a 60.03% chance for A to win in an extended series given a loss previously.
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motbob
United States12546 Posts
Upon further review, I reported the results of the second type of test I ran correctly, but it's actually a useless test in regards to whether extended series are good or bad. Can you spot why?
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On July 23 2013 02:55 motbob wrote:
Upon further review, I reported the results of the second type of test I ran correctly, but it's actually a useless test in regards to whether extended series are good or bad. Can you spot why?
Because extended series are bad! No math required.
I think we should tell the NFL about the extended series. So regular season results carry over into the Superbowl! A terrible comparison? Certainly.
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United States47024 Posts
On July 23 2013 01:15 KissMeRed wrote:
Scenario 1:
Player A wins 2-0 in winner's bracket. Player B wins 2-1 in loser's bracket rematch. Player A leads 3-2 overall in maps, but Player B advances. I consider this unfair.
Scenario 2;
Player A wins 2-0 in winner's bracket. Player B wins 2-0 in loser's bracket rematch. The series is a tie 2-2 overall in maps, but Player B advances solely based on the order of the matches. A won earlier and B won later, but B advances. Again, I consider this unfair.
If tournaments were simply about number of games won/head-to-head, then we would always run round robin tournaments with no bracket stage and decide the winner by the player with the most wins/best head-to-head in ties.
The nature of a bracket tournament is that it ascribes particular importance to specific games/series'. In this case, a match deeper in a tournament is considered more important. Losses in the loser's finals are considered more severe than losses in an earlier stage, perhaps because the match carries more importance and you are expected to bring more of your skill to bear.
You could actually have a similar discrepancy in head-to-head results vs. match winner in a Group Stage->Single Elim tournament, but we don't consider this a problem because bracket stage games are considered more important than Group Stage games and losing them is supposed to be more consequential.
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Technically, if we're talking about loser's bracket rematch, MLG Lee is right, it does benefit the more skilled player. It does so at the expense of other players at the same level of the bracket, though, and is primarily based on the luck of the bracket placement.
The problem isn't extended series, it's the circumstances under which it comes into play.
I do think that extended series is a good alternative to traditional double elimination for the Winner bracket vs Loser bracket match, because it gives a slight advantage to the underdog without being unfair to the winner of the first series, doesn't give an unfair advantage to one part of the bracket over another, ensures that all games actually matter, and is more interesting/easy to follow for the spectator.
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On July 23 2013 00:17 Quoonit wrote:
Correct me if I'm wrong (I may be missing some complexity or nuance here), but the following is true, and is independent of whether or not the series is continuous or broken into a Bo3 and extended into a Bo7.
If player A is better than B, say having a 51% chance of winning any single game vs. player B, then the more games they play, the law of large numbers will push the winrate of each player towards the projected underlying probability. Which is to say that smaller samples are noisier than large ones.
So, using a simple binomial distribution with the set of binomial parameters:
% chance of success (probability that the better player will win):
# successes needed (required # of wins in a series):
# trials (# of games in a series)
The probability of the better player winning always goes up with a larger set of games.
For example, with the initial binomial parameters (for a Bo3 series with 2 extremely evenly matched players):
% chance of success (probability that the better player will win): 51%
# successes needed (required # of wins in a series): 2
# trials (# of games in a series): 3
The better player wins that series 51.499% of the time.
If the series is extended to 7 games however:
% chance of success (probability that the better player will win): 51%
# successes needed (required # of wins in a series): 4
# trials (# of games in a series): 7
The better player wins 52.19% of the time.
For larger discrepancies between skill level (70% to 30% chance of winning between players), the dichotomy between short and long series increases even further:
% chance of success (probability that the better player will win): 70%
# successes needed (required # of wins in a series): 3 (short), 7 (long)
# trials (# of games in a series): 2 (short), 4 (long)
The better player wins the short series 78.4% of the time, and the long series 87.4% of the time.
This trend is also independent of how the series is broken up. For example, using our 70/30 split again. Here are the chances of certain outcomes in a Bo3 series:
Better player wins Bo3: 78.4%
Better player wins 2-0: 49%---------------------------------->Better player goes on to win Bo7 extended series 96.9% of the time
Better player wins 2-1: 29.4%-------------------------------->Better player goes on to win Bo7 extended series 91.6% of the time
Worse player wins Bo3: 21.6%
Worse player wins 2-0: 9%------------------------------------>Better player goes on to win Bo7 extended series 52.8% of the time
Worse player wins 2-1: 12.6%------------------------------->Better player goes on to win Bo7 extended series 65.2% of the time
Using the % chance of each Bo3 result to weight the Bo7 results:
87.4% chance of the better player winning the Bo7 extended series overall, which is identical to the result for continuous Bo7 series
This is correct. Then extend the logic thusly:
The odds of winning a Bo3 from your binomial math listed above, using 51% as the chance of the "better" player winning to demonstrate his edge, (51.499%) and the odds of him winning an extended Bo7 (52.19%).
Now, consider a player that must win either both Bo3 matches, or the second Bo3. That leaves us with:
•AA -win
•BA -win
•AB -loss
•BB -loss
write probability of A winning as p(A):
=> 2C2*p(A)^2 + 2C1*p(A)*(1-p(A))/2
=>1*p(A)^2 + 2/2*p(A)*(1-p(A))
=>p(A) * (p(A) + 1 - p(A))
=>p(A)
=> .51499
51.499% is the chance of a better player winning two Bo3 in double elim format (where second winner wins).
52.19% is the chance of that same player winning a Bo7.
We can do this again to the 70/30 split then too and say:
Chance of winning Bo7 (as above): 87.4%
Chance of winning the correct two Bo3's is the same as winning one of them: 78.4%
The better player always has the advantage, but his advantage is greater in a Bo7 than two Bo3 series. Flukes or not, one can fluke any game in any situation and these must be considered independent events.
Therefore Bo7 is the better format (in purely mathematical theory, excluding maps and map choice).
QED unless I'm mistaken. Feel free to point it out if so 
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First of all, excuse me, but I always thought that winning games is what determines the better player, not the other way around.
The fact that player agreed to participate in a tournament under specific conditions means he has to reconcile himself with a possibility of paradoxes like those mentioned in this thread. I never liked or supported the whole 'Loser/Winner brackets' format, but I can see the point behind their existence: to give defeated players/teams bigger margin of error and extend their tournament experience by granting them chances for a comeback.
But 'extended series' format - apart from OP's point of not really letting better player through - is absurd itself. Imagine Greece playing Euro 2004 soccer championship final from the 2-1 goal advantage their earned against Portugal in a group stage game - total nonsense. In Starcraft under those rules, there will be evantually tournaments with one matchup of players who didn't met before, and other match, with players who did met. Two matches at the same stage of tournament played under different rules - only because of random luck. Something is really wrong.
For years, instead of going for such complications, events had 1-game advantage for winners' bracket comptetitor, winner picks maps/ map order or some other handicaps (Day[9] once even mentioned 1 Bo5 advantage for winners' bracket player, but to me it's way too extreme). Everyone seemed happy with those simple conditions, so why MLG bothers to confuse them?
(Yet still, as I said, you participate ---> you can't complain about the format of shit you got into -- so it all comes down to us, fans complaining about the fact that math sort of disproves the logic background of this format.)
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TL;DR: Setting up a test where it's already known who the better player is is flawed since the premise of the competition itself is to determine who the better player is. The better player is defined as the player who wins the most number of games in an odd number of sets/games; the better player ALWAYS advances in ES because the better player is defined by who wins the most games in a Best of X series.
Assuming the data is correct, I find the arguments on either side of the aisle regarding "does the better player have a better shot of advancing" flawed in the definition of "better player".
I thought the point of having competition is that we don't know who the "better player" between a set of two players is. The "better player" isn't something that's a definitive, ELO-like thing; such an objective way of telling us who is a "better player" does not exist and may even come to be rejected if it did. We have tournaments and leagues so when someone says "you're considered a better player than that other guy...so prove it".
I think the premise behind the old MLG reasoning regarding the top team and up-and-comer team works more like this:
"Well, that team won 3-0 and the other won 3-2. They've each won a Bo5, so we actually don't know who the better team is. In fact, we have the tricky situation where, cumulatively, the team that's set for elimination actually won more maps than the other team, but the other team can argue that they won a series and better teams are determined by defined sets of games. To see who's better we need to have another set to see who's better (like how tennis or volleyball operate) or we can instead just make the one set longer."
If, in the MLG example given in the OP, MLG thought that the lesser team advanced then they're wrong.They'd also be wrong if they thought the better team did advance. The fact of the matter is that we may think we know who the better team/player going into the tournament is, but the point of having the competition is to actually find out since we don't know for certain.
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On July 23 2013 02:32 Heyoka wrote:Show nested quote +On July 23 2013 02:05 Theberlinwall wrote:
well said.
on a different note i never actually thought that extended series was used to resolve potential map score issues. The rules makes a little more sense now. However, I still dislike it from a spectator point of view. This is what motbob's anecdote from Lee gets at but is a bit muddled, the basic idea here is that a player cannot be knocked out while still having a positive record against another player due to the format being double elim. It's a fine enough ideal and if you talk to most players they love it, but it tends to make spectating kind of lame which is why people on TL rally against it.
What?????? Who
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On July 23 2013 04:39 wingpawn wrote:
But 'extended series' format - apart from OP's point of not really letting better player through - is absurd itself. Imagine Greece playing Euro 2004 soccer championship final from the 2-1 goal advantage their earned against Portugal in a group stage game - total nonsense. In Starcraft under those rules, there will be evantually tournaments with one matchup of players who didn't met before, and other match, with players who did met. Two matches at the same stage of tournament played under different rules - only because of random luck. Something is really wrong.
For years, instead of going for such complications, events had 1-game advantage for winners' bracket comptetitor, winner picks maps/ map order or some other handicaps (Day[9] once even mentioned 1 Bo5 advantage for winners' bracket player, but to me it's way too extreme). Everyone seemed happy with those simple conditions, so why MLG bothers to confuse them?
These are two separate issues.
I don't think there can be a very convincing argument for extended series within the loser's bracket of a tournament, because both players should go into that series as equals and it introduces an extra luck factor into the bracket for the players.
It's pretty standard, however, for double elimination formats to force the loser's bracket to beat the winner's bracket player in two matches before the winner's bracket player wins one. In that specific case, extended series has an effect that isn't innately unfair, just different. I don't think it's any more complicated than the alternative either, since you can display the score in X-Y and get a clear picture of what each player must do to win. In double elimination, you have to know which series is which to understand what's going on.
Suppose the bracket is Bo3 throughout. Player X beat Player Y 2-0 and put him in the loser's bracket and they now meet in the Grand Finals.
Player X wins game 1, but loses game 2 and 3. In traditional double elimination, Player Y won the first series and forced a second Bo3. In extended series, the score is now 3-2 in favor of Player X.
Player Y wins game 4 and Player X wins game 5.
In traditional double elimination, we have a 1-1 going into a deciding game. In extended series, Player X wins the tournament after game 5.
Now consider the same situation after a 2-1 first meeting in both cases. In standard double elimination, the result is the same. In extended series, Player Y wins the tournament after game 4.
You can look at this a few ways, 1) you have more games so it's more fair and there's more content in the tournament 2) each game really mattered in this case, so you have to be at your best throughout the whole tournament.
I don't think either are clearly better and I don't think extended series is inherently worse, provided it's only in the above situation.
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On July 23 2013 05:27 TrippSC2 wrote:+ Show Spoiler +On July 23 2013 04:39 wingpawn wrote:
But 'extended series' format - apart from OP's point of not really letting better player through - is absurd itself. Imagine Greece playing Euro 2004 soccer championship final from the 2-1 goal advantage their earned against Portugal in a group stage game - total nonsense. In Starcraft under those rules, there will be evantually tournaments with one matchup of players who didn't met before, and other match, with players who did met. Two matches at the same stage of tournament played under different rules - only because of random luck. Something is really wrong.
For years, instead of going for such complications, events had 1-game advantage for winners' bracket comptetitor, winner picks maps/ map order or some other handicaps (Day[9] once even mentioned 1 Bo5 advantage for winners' bracket player, but to me it's way too extreme). Everyone seemed happy with those simple conditions, so why MLG bothers to confuse them?
These are two separate issues. I don't think there can be a very convincing argument for extended series within the loser's bracket of a tournament, because both players should go into that series as equals and it introduces an extra luck factor into the bracket for the players. It's pretty standard, however, for double elimination formats to force the loser's bracket to beat the winner's bracket player in two matches before the winner's bracket player wins one. In that specific case, extended series has an effect that isn't innately unfair, just different. I don't think it's any more complicated than the alternative either, since you can display the score in X-Y and get a clear picture of what each player must do to win. In double elimination, you have to know which series is which to understand what's going on. Suppose the bracket is Bo3 throughout. Player X beat Player Y 2-0 and put him in the loser's bracket and they now meet in the Grand Finals. Player X wins game 1, but loses game 2 and 3. In traditional double elimination, Player Y won the first series and forced a second Bo3. In extended series, the score is now 3-2 in favor of Player X. Player Y wins game 4 and Player X wins game 5. In traditional double elimination, we have a 1-1 going into a deciding game. In extended series, Player X wins the tournament after game 5. Now consider the same situation after a 2-1 first meeting in both cases. In standard double elimination, the result is the same. In extended series, Player Y wins the tournament after game 4. You can look at this a few ways, 1) you have more games so it's more fair and there's more content in the tournament 2) each game really mattered in this case, so you have to be at your best throughout the whole tournament. I don't think either are clearly better and I don't think extended series is inherently worse, provided it's only in the above situation.
What I feel after thinking those rules through:
Okay, so long story short, instead of no odds/1 game odds in Bo3 or Bo5, winner bracket guy gets 1 game/2 game odds in Bo7, depending on his previous performance against that rival, right? Strange, but might be acceptable for many, I guess.
It's largely a matter of taste, but I always felt that 'the underdog' shouldn't be punished with any point disadvantage at all. After all, he is so often punished for 1-2 defeat in super-close series that could've gone either way. Maybe the losers' brackets should merge with winners' at earlier stage of the tournament? Or, perhaps, to compensate for having 'weaker' players in their bracket, losers should make some sort of group stage between each other to increase the number of games and difficulty of getting through the bracket, so it could match the difficulty of winners?
Nauseating issue. Just copy/paste old BW OSL format people and live happily ever after 
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On July 23 2013 02:38 jalstar wrote:Show nested quote +On July 23 2013 02:32 Heyoka wrote:On July 23 2013 02:05 Theberlinwall wrote:
well said.
on a different note i never actually thought that extended series was used to resolve potential map score issues. The rules makes a little more sense now. However, I still dislike it from a spectator point of view. This is what motbob's anecdote from Lee gets at but is a bit muddled, the basic idea here is that a player cannot be knocked out while still having a positive record against another player due to the format being double elim. It's a fine enough ideal and if you talk to most players they love it, but it tends to make spectating kind of lame which is why people on TL rally against it. Weird, I thought most players hated it with spectators being more split, at least in polls. The anti-extended-series people are much more vocal though.
That has proven to be false on these forums. I already posted the old data where it was 2/3 opposed and I wonder which players Heyoka is talking about because I've seen quite a number opposed to it. Maybe he's talking about TL players like Tyler & possibly Jos. Keep the math blogs coming on extended series. Weeeeeeeeeeeee.
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The result in the original post might surprise people, but it makes sense when you consider the implications of player skill in a broader bracket. Consider the following:
Suppose we have two players that I shall name GOOD and BAD. Further suppose that I am omnipotent and can determine with full accuracy that GOOD beats BAD exactly 70% of the time. We place these two players into a double elimination tournament with extended series, each round being best of 3.
Scenario 1: GOOD beats BAD in the winner's bracket (expected result). BAD drops to lowers. Because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players as well. Because GOOD is favored against BAD, it is extremely likely that GOOD is also favored against other players as well. As a result, BAD has a high probability to be knocked out of the tournament in lowers long before he ever meets GOOD again. The simple conclusion is thus: is GOOD beats BAD in the winner's bracket, there is a low probability that an extended series will even happen. For the sake of argument, lets say there is a 5% chance that GOOD meets BAD again. When this does occur, GOOD has a very high chance to beat BAD as a result of the extended series setup (GOOD begins with a lead).
Scenario 2: BAD beats GOOD in the winner's bracket (unexpected result / the "fluke"). GOOD drops to lowers. As we said before, because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players in the tournament. Consequently, BAD has a high probability of falling to lowers sooner rather than later. Similarly, since GOOD is favored against BAD, GOOD has a high probability of advancing through lowers. Therefore, there is a much higher probability that GOOD will meet BAD an extended series will happen. Lets suppose there is a 20% that GOOD meets BAD again. When this does occur, BAD has quite an edge due to the extended series setup (BAD begins with a lead). So, although GOOD is favored in an individual match against BAD, BAD still has a higher probability of winning in an extended series.
Based upon these (somewhat winged) numbers, we see that, when an extended series DOES occur, MUCH more often it is a bad player starting with a lead against a good player. So, "worse players" will win more often in an extended series double elimination bracket.
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
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On July 23 2013 02:32 Heyoka wrote:Show nested quote +On July 23 2013 02:05 Theberlinwall wrote:
well said.
on a different note i never actually thought that extended series was used to resolve potential map score issues. The rules makes a little more sense now. However, I still dislike it from a spectator point of view. This is what motbob's anecdote from Lee gets at but is a bit muddled, the basic idea here is that a player cannot be knocked out while still having a positive record against another player due to the format being double elim. It's a fine enough ideal and if you talk to most players they love it, but it tends to make spectating kind of lame which is why people on TL rally against it.
it would be a fine enough ideal if MLGs format (the way brackets feed in to one another) didnt cause players to meet each other more often than you would expect through random chance. because at most mlg events to date the way brackets had been preformed rather than having randomized group selections it was specifically designed to make people play the same people over and over. this is bad from a purely "we want our bracket to be good sense" but also undermines any argument that they dont want players to go out with positive win rates vs people. because the easiest step to stopping that happening is to stop players meeting twice before the final.
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It's bad either way. Tournaments are not meant to determine (let alone aid) better players, they're meant to determine winners. The format doesn't matter in that context.
Extended series is just a tunnel vision solution to the inherent ugliness of double elimination systems when it comes higher-lower bracket interaction. There's really no better alternative to extended series - they're all terrible, because the underlying format (double elimination) is terrible.
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On July 23 2013 06:12 Day[9] wrote:
Scenario 2: BAD beats GOOD in the winner's bracket (unexpected result / the "fluke"). GOOD drops to lowers. As we said before, because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players in the tournament. Consequently, BAD has a high probability of falling to lowers sooner rather than later. Similarly, since GOOD is favored against BAD, GOOD has a high probability of advancing through lowers. Therefore, there is a much higher probability that GOOD will meet BAD an extended series will happen. Lets suppose there is a 20% that GOOD beats BAD again. When this does occur, BAD has quite an edge due to the extended series setup (BAD begins with a lead). So, although GOOD is favored in an individual match against BAD, BAD still has a higher probability of winning in an extended series.
Based upon these (somewhat winged) numbers, we see that, when an extended series DOES occur, MUCH more often it is a bad player starting with a lead against a good player. So, "worse players" will win more often in an extended series double elimination bracket.
If you suppose the part the I just bolded, doesn't that assumption defeat the previous assumption based on which GOOD player is GOOD and BAD is BAD (namely: 70-30 win odds of GOOD beating BAD)?
That being said, I see your point - BAD player gets good edge. It's comparable to soccer - I heard that statistically, teams that score 1-0 goal in a match are winning games in like 70% of cases, regardless whether they were favourites or not. The impact of those extra points is usually bigger than people think.
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On July 23 2013 06:25 Talin wrote:
It's bad either way. Tournaments are not meant to determine (let alone aid) better players, they're meant to determine winners. The format doesn't matter in that context.
Extended series is just a tunnel vision solution to the inherent ugliness of double elimination systems when it comes higher-lower bracket interaction. There's really no better alternative to extended series - they're all terrible, because the underlying format (double elimination) is terrible.
Wow, you sound like me. Talin am I your evil twin, or is it the other way around?
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On July 23 2013 05:59 wingpawn wrote:
Okay, so long story short, instead of no odds/1 game odds in Bo3 or Bo5, winner bracket guy gets 1 game/2 game odds in Bo7, depending on his previous performance against that rival, right? Strange, but might be acceptable for many, I guess.
Not exactly, which is why I gave the example in the way that I did.
In double elimination, there are two separate series with no scoring overlap and no influence from the previous meeting. If the winner's bracket player wins, it's over. If the loser's bracket player wins, the scores don't carry over and there is a second series where winner takes all. Think of it as the loser's bracket player has to eliminate the winner's bracket player twice, since he hasn't been eliminated at all yet.
Extended series has a starting score from their winner's bracket meeting and both players are playing to a set number of wins. One player starts down 1-2 games, but you can display the score and say they're playing to 4 and it makes sense. Whereas, if I put a 1-1 score up during a normal double elimination, you don't know if it's the first series or second series.
There are only really two important differences (aside from the clarity of showing the score):
1) If the Loser's bracket player lost 1-2 in the first meeting, that 1 win counts in the finals in extended series, but not in double elimination.
2) If the Loser's bracket player wins 2-1 in the first series of the finals, the 1 win for the Winner's bracket player counts in the second series in extended series, but not in the double elimination.
On July 23 2013 05:59 wingpawn wrote:It's largely a matter of taste, but I always felt that 'the underdog' shouldn't be punished with any point disadvantage at all. After all, he is so often punished for 1-2 defeat in super-close series that could've gone either way. Maybe the losers' brackets should merge with winners' at earlier stage of the tournament? Or, perhaps, to compensate for having 'weaker' players in their bracket, losers should make some sort of group stage between each other to increase the number of games and difficulty of getting through the bracket, so it could match the difficulty of winners?
Being the underdog and coming from the loser's bracket of a double elimination are two different things.
If you make it all the way through a tournament without losing a match, why should you be on an even playing field with someone who lost once already? That holds true whether the loser's bracket player is Goody or Innovation. It has nothing to do with weaker players vs stronger players and everything to do with having a bracket that rewards you for your performance.
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On July 23 2013 06:33 wingpawn wrote:Show nested quote +On July 23 2013 06:12 Day[9] wrote:
Scenario 2: BAD beats GOOD in the winner's bracket (unexpected result / the "fluke"). GOOD drops to lowers. As we said before, because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players in the tournament. Consequently, BAD has a high probability of falling to lowers sooner rather than later. Similarly, since GOOD is favored against BAD, GOOD has a high probability of advancing through lowers. Therefore, there is a much higher probability that GOOD will meet BAD an extended series will happen. Lets suppose there is a 20% that GOOD beats BAD again. When this does occur, BAD has quite an edge due to the extended series setup (BAD begins with a lead). So, although GOOD is favored in an individual match against BAD, BAD still has a higher probability of winning in an extended series.
Based upon these (somewhat winged) numbers, we see that, when an extended series DOES occur, MUCH more often it is a bad player starting with a lead against a good player. So, "worse players" will win more often in an extended series double elimination bracket. If you suppose the part the I just bolded, doesn't that assumption defeat the previous assumption based on which GOOD player is GOOD and BAD is BAD (namely: 70-30 win odds of GOOD beating BAD)? That being said, I see your point - BAD player gets good edge. It's comparable to soccer - I heard that statistically, teams that score 1-0 goal in a match are winning games in like 70% of cases, regardless whether they were favourites or not. The impact of those extra points is usually bigger than people think.
The one behind receives mental discomfort from the very knowledge that he or she is behind. Mental discomfort can lead to worse play, demoralization, etc. On the flip side, the one ahead gains mental comfort from knowing he or she is ahead, and in games where you accumulate points through various methods of scoring (e.g. soccer), the winner after scoring one point just has to sit back, defend, and let the clock run out.
This is why I've never agreed with double elimination brackets, nor the extended series, because it unnecessarily complicates determining who is the winner, and throws in factors other than player skill in determining the winner as well. IMO pool play based on seeding + single elimination brackets are the best way to go, but that could just be my bias talking.
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@TrippSC2 - Understood. Somehow, I screwed up the logic of double elimination format. Guess I'm just tired. Or dumb. 
My new proposition that just crossed my mind: losers bracket dude has no game disadvantage, but has to offrace in the exact number of games he previously lost to his winners' bracket opponent. Wouldn't this provide even more games and fun?
@Day[9] - ohhh, I see. Actually, I should've figured that out earlier lol (GOOD player can't beat BAD again, cause in your example, he was beaten by BAD before, so there's no point of saying again). By the way, I'm quite sure that in this case, psychology backs up pure statistics even more.
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On July 23 2013 06:33 wingpawn wrote:Show nested quote +On July 23 2013 06:12 Day[9] wrote:
Scenario 2: BAD beats GOOD in the winner's bracket (unexpected result / the "fluke"). GOOD drops to lowers. As we said before, because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players in the tournament. Consequently, BAD has a high probability of falling to lowers sooner rather than later. Similarly, since GOOD is favored against BAD, GOOD has a high probability of advancing through lowers. Therefore, there is a much higher probability that GOOD will meet BAD an extended series will happen. Lets suppose there is a 20% that GOOD beats BAD again. When this does occur, BAD has quite an edge due to the extended series setup (BAD begins with a lead). So, although GOOD is favored in an individual match against BAD, BAD still has a higher probability of winning in an extended series.
Based upon these (somewhat winged) numbers, we see that, when an extended series DOES occur, MUCH more often it is a bad player starting with a lead against a good player. So, "worse players" will win more often in an extended series double elimination bracket. If you suppose the part the I just bolded, doesn't that assumption defeat the previous assumption based on which GOOD player is GOOD and BAD is BAD (namely: 70-30 win odds of GOOD beating BAD)? That being said, I see your point - BAD player gets good edge. It's comparable to soccer - I heard that statistically, teams that score 1-0 goal in a match are winning games in like 70% of cases, regardless whether they were favourites or not. The impact of those extra points is usually bigger than people think.
Fuck!! I mistyped! I meant to type "meets" but I typed "beats"
Fixed!
[edit]
I completely understand where your confusion came from, but just in case anyone else is still a bit confused: there is literally 0 psychology in what I've typed. It's just straight statistics.
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I think Day[9] is onto what is happening here. Here is a simplified example with numbers. I made these simplifications: regular series are BO1. There is one Noob in the tournament, he has a 10% winning chance against all the pros. Suppose the brackets are such that he plays pro1 in WR2, and the only time they ever meet again is LR4. (I skipped WR1 because LR1 acts a little differently than other loser rounds).
WR2 pro1>noob 0.9
WR3 prox<pro1 0.5
LR2 noob>prox 0.1
LR3 noob>prox 0.1
LR4 pro1 vs noob 0.9*0.5*0.1*0.1 = 0.0045
No extended (BO1) : pro1 0.90 * 0.0045 = 0.004050
Extended (pro up 1-0): pro1 0.99 * 0.0045 = 0.004455
WR2 noob>pro1 0.1
WR3 prox>noob 0.9
LR2 pro1>prox 0.5
LR3 pro1>prox 0.5
LR4 noob vs pro1 P=0.1*0.9*0.5*0.5 = 0.0225
No extended (BO1) : pro1 0.90 * 0.0225 = 0.020250
Extended (noob up 1-0): pro1 0.81 * 0.0225 = 0.018225
No extended 0.004050 + 0.020250 = 0.02430
Extended 0.004455 + 0.018225 = 0.02268
No extended series gives pro1 a 0.02430 chance to advance.
Extended series gives pro1 a 0.02258 chance to advance.
The issue is that without considering the rest of the tournament, you would expect pro1 to be up 1-0 against noob with a probability 0.9. But since noob usually fails in the loser rounds:
If the players meet in LR4, probability pro1 will be up 1-0:
0.0045 / (0.0045+0.0225) = .167
In fact if they meet in LR4, it's overwhelmingly likely that this happened because noob got lucky in WR2 by beating pro1 1-0. And on top of that you extend the series. Pro1 also benefits from this in the reverse case, but that case is far less likely to actually happen.
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On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
That's a pretty good point. However, I don't think we should start Series#2 ignoring GOOD's mistakes. GOOD flubbed Series#1. Why should we give him more of a chance to overthrow BAD if BAD legitimately won Series#1? I mean, it's not like BAD cheated to beat GOOD.
The concept that BAD drops out of the bracket a lot more commonly than GOOD is true. But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around?
The conclusion is that Bo3 makes for a more volatile tournament. That's may be good for spectators. But saying that we should give the GOOD player an advantage by giving him/her a second Bo3 is not convincing to me. His/her chances are better in a Bo7. It's not like players never come back from the disadvantage (cough Soulkey cough).
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...or just forget it all and set up a rule that by shamefully dropping to the losers bracket through losing to BAD, GOOD himself becomes BAD and BAD becomes GOOD - as he just proved himself better than a GOOD player. Problem solved 
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The part I identify with in Day[9]'s idea is that I also want GOOD to win. But I don't think GOOD deserves any advantages against BAD if he/she already lost to BAD once. BAD took maps. BAD should get credit for those maps and GOOD should have to fight for them back. Hopefully GOOD took a map in series 1. That means GOOD has to deliver 3 maps to BAD's 1, which would prove that GOOD can win more maps.
Somewhere I saw it suggested that BAD should go to a Bo5 with a +1. That means GOOD has to win 3 maps to BAD's 1, which is exactly what happens if GOOD takes 1 map in series#1 and it goes to an Extended Bo7. All shortening the Extended series does is give the losing player an advantage by ignoring lost maps.
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On July 23 2013 07:15 wingpawn wrote:...or just forget it all and set up a rule that by shamefully dropping to the losers bracket through losing to BAD, GOOD himself becomes BAD and BAD becomes GOOD - as he just proved himself better than a GOOD player. Problem solved
I like you. Let's be friends.
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On July 23 2013 07:07 kingNothing42 wrote:Show nested quote +On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
That's a pretty good point. However, I don't think we should start Series#2 ignoring GOOD's mistakes. GOOD flubbed Series#1. Why should we give him more of a chance to overthrow BAD if BAD legitimately won Series#1? I mean, it's not like BAD cheated to beat GOOD. The concept that BAD drops out of the bracket a lot more commonly than GOOD is true. But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? The conclusion is that Bo3 makes for a more volatile tournament. That's may be good for spectators. But saying that we should give the GOOD player an advantage by giving him/her a second Bo3 is not convincing to me. His/her chances are better in a Bo7. It's not like players never come back from the disadvantage (cough Soulkey cough).
That usually happens if they're really, really good players with a strong playbook. You know who also came back in extended series? Leenock. He was on fire that time though. If someone gets red hot at a LAN good luck taking them out.
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On July 23 2013 07:07 kingNothing42 wrote:Show nested quote +On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around?
BAD has a statistical advantage if they meet again. Bad begins a best of 7 leading 2-0. So, although he has a 30% chance to win each individual game, he has a much higher percentage (greater than 30%) of winning the best of 7 since he only has to win 2 games while his opponent has to win 4.
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On July 23 2013 07:04 KillerDucky wrote:I think Day[9] is onto what is happening here. Here is a simplified example with numbers. I made these simplifications: regular series are BO1. There is one Noob in the tournament, he has a 10% winning chance against all the pros. Suppose the brackets are such that he plays pro1 in WR2, and the only time they ever meet again is LR4. (I skipped WR1 because LR1 acts a little differently than other loser rounds).
WR2 pro1>noob 0.9
WR3 prox<pro1 0.5
LR2 noob>prox 0.1
LR3 noob>prox 0.1
LR4 pro1 vs noob 0.9*0.5*0.1*0.1 = 0.0045
No extended (BO1) : pro1 0.90 * 0.0045 = 0.004050
Extended (pro up 1-0): pro1 0.99 * 0.0045 = 0.004455
WR2 noob>pro1 0.1
WR3 prox>noob 0.9
LR2 pro1>prox 0.5
LR3 pro1>prox 0.5
LR4 noob vs pro1 P=0.1*0.9*0.5*0.5 = 0.0225
No extended (BO1) : pro1 0.90 * 0.0225 = 0.020250
Extended (noob up 1-0): pro1 0.81 * 0.0225 = 0.018225
No extended 0.004050 + 0.020250 = 0.02430
Extended 0.004455 + 0.018225 = 0.02268
No extended series gives pro1 a 0.02430 chance to advance. Extended series gives pro1 a 0.02258 chance to advance. The issue is that without considering the rest of the tournament, you would expect pro1 to be up 1-0 against noob with a probability 0.9. But since noob usually fails in the loser rounds: If the players meet in LR4, probability pro1 will be up 1-0: 0.0045 / (0.0045+0.0225) = .167 In fact if they meet in LR4, it's overwhelmingly likely that this happened because noob got lucky in WR2 by beating pro1 1-0. And on top of that you extend the series. Pro1 also benefits from this in the reverse case, but that case is far less likely to actually happen.
Yes! This exactly!
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On July 23 2013 07:27 Day[9] wrote:Show nested quote +On July 23 2013 07:07 kingNothing42 wrote:On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? BAD has a statistical advantage if they meet again. Bad begins a best of 7 leading 2-0. So, although he has a 30% chance to win each individual game, he has a much higher percentage (greater than 30%) of winning the best of 7 since he only has to win 2 games while his opponent has to win 4.
BAD has a statistical advantage to win because he already won games. I don't see how that makes for a poor format when the goal of a tournament is to determine who wins the most games. Right? Why wipe out the 2-0 map score so that GOOD has a better chance when he already screwed up hard (indicating he's actually kinda bad)?
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On July 23 2013 01:58 Alryk wrote:
You are ignoring the fact of # of series lost. One player, even with better map score, has lost two series. Player B has only lost one. We aren't looking for the best player vs player B, but the best player, which takes into account all of the matches. The same thing happens in GSL.
Player A 2-0 Player B
C 2-0 D
C > A
B > D
B 2-1 A
Does A still deserve to advance just because he has a better map score vs player B? He still lost one more series than B did, therefore as an overall player he is not as skilled on that day.
Yes, GSL groups have the same map score issue, and I think the 2nd advancement match isn't fair. In my opinion, GSL style groups should have extended series.
It's easy to see how GSL groups map directly to a 4 person double-elim bracket w/o a Grand Final (just draw it on paper really fast if you can't see it).
Player B won two series, but he/she has not beaten Player A.
Here is how I see it. Take all of the information prior to the last match. What do we know? We know Player C won the Winner's Bracket. Player D lost in the Loser's Bracket with no rematches. These two are removed from the problem. Player C advances from the group, and Player D is out.
Now consider A and B. They are meeting in the Loser's Bracket final. This match determines who 'deserves' to be in the Grand Final (i.e. advance from the group). If B bests A 2-1, then overall map scores are A: 3 maps, B: 2 maps. Why does B deserve to be in the Grand Final?
In my opinion, B doesn't deserve to be in the Grand Final until B proves he/she is better than A. Hence invoke the extended series rule so B can prove this to me. If B wins the extended series, then B will be 2:1 in group series and have the overall better map score 4:2 when compared to A.
TLDR: It's the same argument from my first post. If you think head to head map scores are important (like I do and I think MLG does) then you are in favor of extended series. If you don't care about map scores and order of series wins (some kind of argument like later rounds are more important) then you probably think extended series is a useless or hurtful rule.
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On July 23 2013 07:43 kingNothing42 wrote:Show nested quote +On July 23 2013 07:27 Day[9] wrote:On July 23 2013 07:07 kingNothing42 wrote:On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? BAD has a statistical advantage if they meet again. Bad begins a best of 7 leading 2-0. So, although he has a 30% chance to win each individual game, he has a much higher percentage (greater than 30%) of winning the best of 7 since he only has to win 2 games while his opponent has to win 4. BAD has a statistical advantage to win because he already won games. I don't see how that makes for a poor format when the goal of a tournament is to determine who wins the most games. Right? Why wipe out the 2-0 map score so that GOOD has a better chance when he already screwed up hard (indicating he's actually kinda bad)?
I have made no statements on whether the format is poor or good (or any opinions for that matter). I'm simply providing an explanation for the counter intuitive results that OP presented.
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On July 23 2013 08:11 Day[9] wrote:Show nested quote +On July 23 2013 07:43 kingNothing42 wrote:On July 23 2013 07:27 Day[9] wrote:On July 23 2013 07:07 kingNothing42 wrote:On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? BAD has a statistical advantage if they meet again. Bad begins a best of 7 leading 2-0. So, although he has a 30% chance to win each individual game, he has a much higher percentage (greater than 30%) of winning the best of 7 since he only has to win 2 games while his opponent has to win 4. BAD has a statistical advantage to win because he already won games. I don't see how that makes for a poor format when the goal of a tournament is to determine who wins the most games. Right? Why wipe out the 2-0 map score so that GOOD has a better chance when he already screwed up hard (indicating he's actually kinda bad)? I have made no statements on whether the format is poor or good (or any opinions for that matter). I'm simply providing an explanation for the counter intuitive results that OP presented.
That is fair. What you've stated could definitely explain the difference between a statistical calculation of the entire tournament vs a mathematical representation of the outcome of only the second match. Agreed!
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i already did the conditional probability stuff back on page 1, read the whole thread guys.
On July 23 2013 02:21 jalstar wrote:Imagine a tournament with double elimination Bo1, and another tournament with double elimination Bo1 extended into Bo3 in rematches. Now take two players who meet in the first round and will always meet each other in the loser's bracket regardless of who wins the initial game. In the first tournament, the better player will have x chance to advance, where x is his chance of winning a Bo1 against the worse player. In the second tournament, if the better player wins the first match, he has (1 - (1-x)^2) chance of advancing. (1 minus the chance of losing 2 Bo1s in a row) If the worse player wins the first match, the better player has x^2 chance of winning the extended series (2 Bo1s in a row) So for the second tournament, the better player has x*(1 - (1-x)^2) + (1-x)*x^2 chance to advance, based on simple conditional probability. This is larger than x for all x between 0.5 and 1, as seen here: http://www.wolframalpha.com/input/?i=x*(1 - (1-x)^2) + (1-x)*x^2 = xIt really looks like extended series benefits the better player to me, and I don't see why this would change with Bo3 extended to Bo7.
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On July 23 2013 08:52 jalstar wrote:i already did the conditional probability stuff back on page 1, read the whole thread guys. Show nested quote +On July 23 2013 02:21 jalstar wrote:Imagine a tournament with double elimination Bo1, and another tournament with double elimination Bo1 extended into Bo3 in rematches. Now take two players who meet in the first round and will always meet each other in the loser's bracket regardless of who wins the initial game. In the first tournament, the better player will have x chance to advance, where x is his chance of winning a Bo1 against the worse player. In the second tournament, if the better player wins the first match, he has (1 - (1-x)^2) chance of advancing. (1 minus the chance of losing 2 Bo1s in a row) If the worse player wins the first match, the better player has x^2 chance of winning the extended series (2 Bo1s in a row) So for the second tournament, the better player has x*(1 - (1-x)^2) + (1-x)*x^2 chance to advance, based on simple conditional probability. This is larger than x for all x between 0.5 and 1, as seen here: http://www.wolframalpha.com/input/?i=x*(1 - (1-x)^2) + (1-x)*x^2 = xIt really looks like extended series benefits the better player to me, and I don't see why this would change with Bo3 extended to Bo7.
This analysis is spot on if you assume that the extended series happens immediately following the first match. However, this analysis doesn't account for either player being eliminated from the tournament in other ways. This is what I posted about above: if the good player wins in the upper bracket, it's unlikely that the players will meet again. If the bad player wins in the upper bracket, it's more likely that the players will meet again.
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jalstar I agree with your math except that it is ignoring too many things. What do you think about the example I posted?
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I really wish i hadn't been used as an example here
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Honestly, I just don't like any scenario where one player starts with an advantage. Extended series and/or double elimination (where the final is upper vs lower with a second set if lower bracket wins the first one) take away a lot of the value when one player can throw away games.
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I've written a highly stylized story to convince everyone that Extended Series is the best rule ever implemented in tournament play.
We're at the 2014 MLG Winter Championship in Detroit, Michigan where 128 SC2 players from around the world are competing in the open bracket. At the request of a vocal internet minority, MLG has decided to conduct the tournament without the standard extended series rules.
The player pool in uncharacteristically weak featuring only two Koreans. However, fans are still excited since they will get to witness some epic foreigner beatdowns coming from the hands of KT Rolster's  Flash and Samsung Khan's  Shine!
Fast forwarding through the E-sports massacre, we are in Winner's Round 6 featuring none other than our two Korean heroes, Flash and Shine! Now Shine knows he can't possibly beat Flash in a standard game (0% win rate on ladder T.T), but he's been saving two of his most devious Zerg cheeses specifically for MLG Detroit! These cheeses are guaranteed wins for Shine!
Since there is no extended series, and because he's smarter than Flash, Shine realizes the only way he can win this tournament is to purposely lose in Winner's Round 6 and save his cheeses for the impending Semifinals rematch. Once Flash sees the build orders, they will become useless. Shine executes two of his drones in Game 1 to go for a 4 pool and attempts a mass overlord 'blinding' strategy in Game 2, both of which end in losses. Flash take the series 2-0.
Shine makes quick work of a non-Korean chump in Loser's Round 10 and gets ready for the semifinals rematch. Remember, Shine has two cheeses that are 100%, guaranteed map wins against Flash. Shine goes for his first cheese on Newkirk Redevelopment Precinct (yes, it's still in the map pool). MLG cuts the video feed halfway through the match, it's too much for the audience to handle. Shine wins Game 1. Game 2, Flash suffers the most horrifying loss of his career on Red (Sick) City and instead of typing the customary 'gg', he plunges his ruler into the face of the monitor in a fit of rage. Shine wins the series 2-0 and advances to the Grand Final! Flash is eliminated!
The Grand Finals are about to begin, but there is one more twist. Shine and his competitor, ID: STXUncleDrew, shake hands. UncleDrew begins peeling back professional grade makeup to reveal that Shine's opponent is actually INnoVation in disguise!
Men, women, and children all weep uncontrollably since they don't get to see a Flash vs Innovation finals. Then they log-on to Teamliquid.net to comment on a thread about why MLG should have upheld their extended series policy.
The end.
(Disclaimer: This is not a true story or vision of a real future. No disrespect to any players, maps, or tournaments referenced above.)
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I'm not sure what I think of extended series to be honest. I dislike the idea going too late into a tournament, especially occurring in the finals of a tournament, but I think it's a decent idea somewhat early on. Here's an example of a situation where I feel extended series help make a tournament more fair:
We have a GSL Ro32 group featuring:
Innovation
-Massive favorite, should crush everyone else in the group
Minigun
Vibe
-Two decent players who are likely 50% against each other, very unlikely they beat innovation, very unlikely they lose to the last player
MarineMan
-random bronze player who should lose to everyone here
With the matchups being:
Innovation vs. MarineMan
Minigun vs. Vibe
Scenario A:
Innovation 2-0 MarineMan
Minigun 2-1 Vibe
Innovation 2-0 Minigun
Vibe 2-0 MarineMan
Vibe 2-1 Minigun
Innovation and Vibe advance.
Scenario B:
Innovation 2-0 MarineMan
Vibe 2-1 Minigun
Innovation 2-0 Vibe
Minigun 2-0 MarineMan
Minigun 2-1 Vibe
Innovation and Minigun advance.
Now, what's the difference between the two? In both cases, Minigun and Vibe are 1-1 (3-3 games) against each other. The only difference? In both cases the player who won the first match picked up a second loss against innovation, and was therefore eliminated. However, is it really fair to say that because Minigun beat MarineMan, and Vibe lost to Innovation, that Minigun > Vibe and should therefore advance?
With extended series in the circumstance, whoever advances in second place is the one who wins the overall series between the two players, rather than who won the more recent series.
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On July 23 2013 09:08 KillerDucky wrote:
jalstar I agree with your math except that it is ignoring too many things. What do you think about the example I posted?
Yeah I dunno how to do the complete simulation like you did without plugging in specific values. I think when you look at our posts together it becomes clear that what causes the discrepancy in results is that the better player isn't as likely to be sent to the loser's bracket in the first place. So if, as in your example, the worse player wins 10% of the time in the initial series, he'll actually have the extended series advantage more than 10% of the time because he's likely to be sent to the loser's bracket right away.
So you and motbob are right, for 8 person tournaments. In a 128-player bracket things get much more complicated, and there's less likely to be an extended series in the first place. I'd still like to see the 8-player model done rigorously the way I did the 2-player model, I'm not really sure how to do that though.
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motbob
United States12546 Posts
[00:12] <motbob> i did a test: let's say the two best players play each other in the first round. If they meet in the losers' finals, does the better of the two have a greater advantage over the other in a bracket where extended series exists, or one where it doesn't exist?
[00:12] <motbob> so i ran a bunch of simulations, took all the runs where there was a rematch, and saw who won the rematch
[00:13] <motbob> it turned out that in the extended series universe, the better player had a lower winrate than in the non-extended universe
[00:14] <motbob> but this didn't actually have anything to do with extended series! at least, not directly.
[00:14] <motbob> let's say player 1 is better than player 2
[00:14] <motbob> if player 1 wins first round, player 2 has an x chance of making it through the loser's bracket to maybe get a rematch
[00:15] <motbob> if player 2 wins the first round, player 1 has a greater than x chance of making it through, since he's a better player
[00:15] <motbob> so rematches where player 2 has an advantage in an extended series happen more often
[00:16] <motbob> explaning the difference
So my second result has no meaning. I asked the wrong question of my workbook.
Also Day9 explained what I was going to explain better than I could, thanks Day9.
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Extended series makes brackets even more luck-based, since it's an advantage that only triggers if you happen to get lucky with the brackets. If you knock someone into the loser's bracket and then later fall to the loser's bracket yourself, you get a bonus if you're lucky enough to get matched with that person again. You do not get that bonus if you are not lucky enough to get matched with that person again.
It does not reward skill, merit, guts, or any other positive feature in the player. It rewards the passive attribute of being matched by the tournament with someone you'd beaten earlier, and the passive attribute of being lucky enough not to be matched against the person who beat you earlier (since Extended Series don't apply if you're still in the winner's bracket).
So, we're explicitly rewarding players for bracket luck, and claiming this favors the better player? Better players aren't better at rolling bracket dice. C'mon.
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People using figurative examples to prove their points, eek. You know since that rule has been implemented you should go back and see exactly how many players came back to win a set when they were either favored prior to meeting the given player or at least 50-50. The results might surprise you. Very few comebacks.
On July 23 2013 11:34 jalstar wrote:Show nested quote +On July 23 2013 09:08 KillerDucky wrote:
jalstar I agree with your math except that it is ignoring too many things. What do you think about the example I posted?
Yeah I dunno how to do the complete simulation like you did without plugging in specific values. I think when you look at our posts together it becomes clear that what causes the discrepancy in results is that the better player isn't as likely to be sent to the loser's bracket in the first place. So if, as in your example, the worse player wins 10% of the time in the initial series, he'll actually have the extended series advantage more than 10% of the time because he's likely to be sent to the loser's bracket right away. So you and motbob are right, for 8 person tournaments. In a 128-player bracket things get much more complicated, and there's less likely to be an extended series in the first place. I'd still like to see the 8-player model done rigorously the way I did the 2-player model, I'm not really sure how to do that though.
That's part of the problem because for the guys who weren't originally favored in those matches and then they manage to pull off the upset are more susceptible to lose early on. Thus setting up the extended series to come into play a lot sooner. It happens very often. Extended series are very potent in the later stages as well. It happens very often when the Koreans meet too because they're always on the same war path.
It's not so much luck Severedevil once you look at how the brackets are actually set-up. These players are going to keep running into one another.
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On July 23 2013 09:58 KissMeRed wrote:I've written a highly stylized story to convince everyone that Extended Series is the best rule ever implemented in tournament play. We're at the 2014 MLG Winter Championship in Detroit, Michigan where 128 SC2 players from around the world are competing in the open bracket. At the request of a vocal internet minority, MLG has decided to conduct the tournament without the standard extended series rules. The player pool in uncharacteristically weak featuring only two Koreans. However, fans are still excited since they will get to witness some epic foreigner beatdowns coming from the hands of KT Rolster's Flash and Samsung Khan's Shine! Fast forwarding through the E-sports massacre, we are in Winner's Round 6 featuring none other than our two Korean heroes, Flash and Shine! Now Shine knows he can't possibly beat Flash in a standard game (0% win rate on ladder T.T), but he's been saving two of his most devious Zerg cheeses specifically for MLG Detroit! These cheeses are guaranteed wins for Shine! Since there is no extended series, and because he's smarter than Flash, Shine realizes the only way he can win this tournament is to purposely lose in Winner's Round 6 and save his cheeses for the impending Semifinals rematch. Once Flash sees the build orders, they will become useless. Shine executes two of his drones in Game 1 to go for a 4 pool and attempts a mass overlord 'blinding' strategy in Game 2, both of which end in losses. Flash take the series 2-0. Shine makes quick work of a non-Korean chump in Loser's Round 10 and gets ready for the semifinals rematch. Remember, Shine has two cheeses that are 100%, guaranteed map wins against Flash. Shine goes for his first cheese on Newkirk Redevelopment Precinct (yes, it's still in the map pool). MLG cuts the video feed halfway through the match, it's too much for the audience to handle. Shine wins Game 1. Game 2, Flash suffers the most horrifying loss of his career on Red (Sick) City and instead of typing the customary 'gg', he plunges his ruler into the face of the monitor in a fit of rage. Shine wins the series 2-0 and advances to the Grand Final! Flash is eliminated! The Grand Finals are about to begin, but there is one more twist. Shine and his competitor, ID: STXUncleDrew, shake hands. UncleDrew begins peeling back professional grade makeup to reveal that Shine's opponent is actually INnoVation in disguise! Men, women, and children all weep uncontrollably since they don't get to see a Flash vs Innovation finals. Then they log-on to Teamliquid.net to comment on a thread about why MLG should have upheld their extended series policy. The end. (Disclaimer: This is not a true story or vision of a real future. No disrespect to any players, maps, or tournaments referenced above.)
How did Flash wind up in the losers bracket?
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On July 23 2013 11:01 Kovaz wrote:
I'm not sure what I think of extended series to be honest. I dislike the idea going too late into a tournament, especially occurring in the finals of a tournament, but I think it's a decent idea somewhat early on. Here's an example of a situation where I feel extended series help make a tournament more fair:
We have a GSL Ro32 group featuring:
Innovation
-Massive favorite, should crush everyone else in the group
Minigun
Vibe
-Two decent players who are likely 50% against each other, very unlikely they beat innovation, very unlikely they lose to the last player
MarineMan
-random bronze player who should lose to everyone here
With the matchups being:
Innovation vs. MarineMan
Minigun vs. Vibe
Scenario A:
Innovation 2-0 MarineMan
Minigun 2-1 Vibe
Innovation 2-0 Minigun
Vibe 2-0 MarineMan
Vibe 2-1 Minigun
Innovation and Vibe advance.
Scenario B:
Innovation 2-0 MarineMan
Vibe 2-1 Minigun
Innovation 2-0 Vibe
Minigun 2-0 MarineMan
Minigun 2-1 Vibe
Innovation and Minigun advance.
Now, what's the difference between the two? In both cases, Minigun and Vibe are 1-1 (3-3 games) against each other. The only difference? In both cases the player who won the first match picked up a second loss against innovation, and was therefore eliminated. However, is it really fair to say that because Minigun beat MarineMan, and Vibe lost to Innovation, that Minigun > Vibe and should therefore advance?
With extended series in the circumstance, whoever advances in second place is the one who wins the overall series between the two players, rather than who won the more recent series.
Now, what's the difference between the two? In the first case, Vibe wins the relevant game, in case two, Minigun does. If you falter when it matters most, you should be knocked out.
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So what for the other options?
You have 2 options on where you'll meet up with your opponent again:
1) Loser's Bracket
2) Grand Finals
With fighting games, if you meet up in the loser's bracket, the game is treated like any other game.
If you meet up in the grand final, you have to beat the guy in the winner's bracket in 2 Best of X games. However, this is the case whether you have played them or not.
Personally, I think this is a great system, as it always gives an advantage to the "better" player.
In any system where you have to play the same player twice, there'll always be a disadvantage to someone.
Even in GSL format, you can get knocked out of your group after playing someone twice, even if you, effectively, beat them 3-2.
This may have been said before, though. There's a lot of great stats here!
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On July 23 2013 18:23 ZeroPageX wrote:Show nested quote +On July 23 2013 09:58 KissMeRed wrote:I've written a highly stylized story to convince everyone that Extended Series is the best rule ever implemented in tournament play. We're at the 2014 MLG Winter Championship in Detroit, Michigan where 128 SC2 players from around the world are competing in the open bracket. At the request of a vocal internet minority, MLG has decided to conduct the tournament without the standard extended series rules. The player pool in uncharacteristically weak featuring only two Koreans. However, fans are still excited since they will get to witness some epic foreigner beatdowns coming from the hands of KT Rolster's Flash and Samsung Khan's Shine! Fast forwarding through the E-sports massacre, we are in Winner's Round 6 featuring none other than our two Korean heroes, Flash and Shine! Now Shine knows he can't possibly beat Flash in a standard game (0% win rate on ladder T.T), but he's been saving two of his most devious Zerg cheeses specifically for MLG Detroit! These cheeses are guaranteed wins for Shine! Since there is no extended series, and because he's smarter than Flash, Shine realizes the only way he can win this tournament is to purposely lose in Winner's Round 6 and save his cheeses for the impending Semifinals rematch. Once Flash sees the build orders, they will become useless. Shine executes two of his drones in Game 1 to go for a 4 pool and attempts a mass overlord 'blinding' strategy in Game 2, both of which end in losses. Flash take the series 2-0. Shine makes quick work of a non-Korean chump in Loser's Round 10 and gets ready for the semifinals rematch. Remember, Shine has two cheeses that are 100%, guaranteed map wins against Flash. Shine goes for his first cheese on Newkirk Redevelopment Precinct (yes, it's still in the map pool). MLG cuts the video feed halfway through the match, it's too much for the audience to handle. Shine wins Game 1. Game 2, Flash suffers the most horrifying loss of his career on Red (Sick) City and instead of typing the customary 'gg', he plunges his ruler into the face of the monitor in a fit of rage. Shine wins the series 2-0 and advances to the Grand Final! Flash is eliminated! The Grand Finals are about to begin, but there is one more twist. Shine and his competitor, ID: STXUncleDrew, shake hands. UncleDrew begins peeling back professional grade makeup to reveal that Shine's opponent is actually INnoVation in disguise! Men, women, and children all weep uncontrollably since they don't get to see a Flash vs Innovation finals. Then they log-on to Teamliquid.net to comment on a thread about why MLG should have upheld their extended series policy. The end. (Disclaimer: This is not a true story or vision of a real future. No disrespect to any players, maps, or tournaments referenced above.) How did Flash wind up in the losers bracket?
He never goes to the losers bracket. I followed the most recent MLG format: http://wiki.teamliquid.net/starcraft2/2013_MLG_Spring_Championship
When you lose in the semis coming from the winners bracket, you are just out.
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On July 23 2013 09:12 ToD wrote:
I really wish i hadn't been used as an example here
Hehe
Also, good read. A lot of it goes over my head sadly, since I should actually be following it. But I get the concepts, and I must agree (Day9's example was awesome) with the OP. Extended series seem to be detrimental.
Also, lets not forget the actual effort going into winning an extended series if you are down actually adds onto the amount of games played vs your next opponent in the loser's bracket. If one player plays 0 extended series and another plays 1, that's an extra 2 minimum games that the other has had to play over the former.
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Alot of nonsensical bs in this thread.
Extended series was made so the better player was the one who advances, and it is already explained here by KissMeRed but somehow ppl still keep on putting useless math into this.
If player A wins 2-0 then loses 3-2 in loser bracket HOW CAN you HONESTLY say that B is the better player when he lost more games than he won vs A?? madness
This whole thread is flawed because you suppose player A is better than B before they even played.
Guess what, the better player is the ONE WHO WINS the match not the one who was given some random % pre-game win rate.
If you want to reduce fluke the only way to do it is by making the 2 players play more games. BO1 has obviously more flukes, BO3 has less, BO7 has even lesser and so on. Theres no other way to reduce fluke.
What extended series does is put the 2 players in a BO7 instead of BO3 thus reducing the chances of happening fluke.
If your "GOOD" player loses in a BO7 vs the "BAD" maybe he isnt so GOOD after all.
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Are you going to address the criticism of your tiebreaker analysis?
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On July 24 2013 02:37 siri wrote:
If your "GOOD" player loses in a BO7 vs the "BAD" maybe he isnt so GOOD after all.
So, it's like this:
The analysis presented in this thread is based on an assumption:
Tournaments are tools for determining which players are better than other players.
In this context, the "better" player is the one who, if the two players played infinity matches against one another, would win the majority of those matches. That's a pretty intuitive definition of being the better player, right?
Tournaments have to exist because, since we live in the real world, we can't have our players play infinity matches. Instead, we have to infer which player is better from the imperfect evidence we can derive from the finite number of games they actually play. That evidence is imperfect because there's no guarantee that the better player will win any given game (or any given BoX series).
Tournament organizers and spectators already intuitively understand this logic, even if they don't think about the statistics behind it. This is why we consider series with more games (Bo5's and Bo7's) to be more reliable indicators of who the better player is than those with less games. Everybody knows that a weak player can knock out a strong player in a Bo1; this is why.
Motbob's analysis, and Day[9]'s explanation of why it works that way, demonstrate that tournaments with extended series rules are won by the player who would win a Best of Infinity series less often than tournaments without extended series rules. Given the assumptions the analysis is based on, that's equivalent to saying compared to non-extended series tournaments, extended series tournaments are worse tools for determining which players are better than other players.
-----
It's possible you disagree with some of the assumptions here. It's possible, for instance, that you think it's more important for tournaments to be sources of entertainment than it is for them to be inferential tools about player skill, and it's possible you find underdog stories more entertaining than the better player winning all the time. If that's the case, it makes sense for you to like extended series. But, for the purpose of determining which of two players would win in a Best of Infinity series, the analysis in the OP really does demonstrate that extended series are counter-productive. No nonsensical bs whatsoever. Just truth.
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On July 24 2013 04:40 ASoo wrote:Show nested quote +On July 24 2013 02:37 siri wrote:
If your "GOOD" player loses in a BO7 vs the "BAD" maybe he isnt so GOOD after all. ...
ok, lets change the tournament format for a bit.
Lets say instead of 2 brackets theres 3:
-winners
-middle
-losers
And player A and B face each other in those 3 and the scores were 2-0, 2-0, 1-2
Its 5-2 between A and B but player B (without ES) will go on to the next round.
Now lets put 4 brackets, now its 7-2 and A will still get eliminated.
Now lets make it BO5, its 11-3 and again, B advances.
Do you think this is the best and fair way to determine the best between two players?
Because what i see, is B getting a few fluke wins in the last BOx and because of that, eliminating A, who was smashing him the whole tournment. This is what mlg_LEE is trying to protect against.
You said it yourself, the only way to determine the best player minimizing flukes is by increasing the number of games they play. This is what ES does. Instead of deciding who the best player is on a BO3 forgetting all that just happened in the tournment, they increase it to a BO5/7 thus reducing flukes.
Extended series is about protecting the best player between 2 people. Not the one who won the last bo3.
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On July 23 2013 07:19 StarStruck wrote:Show nested quote +On July 23 2013 07:07 kingNothing42 wrote:On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
That's a pretty good point. However, I don't think we should start Series#2 ignoring GOOD's mistakes. GOOD flubbed Series#1. Why should we give him more of a chance to overthrow BAD if BAD legitimately won Series#1? I mean, it's not like BAD cheated to beat GOOD. The concept that BAD drops out of the bracket a lot more commonly than GOOD is true. But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? The conclusion is that Bo3 makes for a more volatile tournament. That's may be good for spectators. But saying that we should give the GOOD player an advantage by giving him/her a second Bo3 is not convincing to me. His/her chances are better in a Bo7. It's not like players never come back from the disadvantage (cough Soulkey cough). That usually happens if they're really, really good players with a strong playbook. You know who also came back in extended series? Leenock. He was on fire that time though. If someone gets red hot at a LAN good luck taking them out.
if you're referring to him winning the finals from the lower bracket, that wasn't coming back in extended series, because he had no prior history there. that was him benefiting from the one time in MLG where extended series favors the lower bracket. normal double elimination would reset the score after the first series, extended series in the finals does not.
I guess this could be an argument in favor of extended series since it makes things more even in the finals. sometimes. unless you drop 2 games at the start. but only at the start, dropping 2 games in the middle is still okay.
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How about an expanded version:
Since there is 3 races, a players performance and understanding usually varies depending on the opponents race.
Supose we have 2 Terran players:
Player 1) vP Godly, vZ Amazingly, vT Good
Player 2) vP Poor, vZ Awful, vT Good
They meet up in a TvT with 50-50 for either to advance.
1) Given player 1 wins, they probably won't meet again.
2) Given player 2 wins, it is many times more likely for them to meet again (As for Day9's explaination; the good player will crush lower bracket, the bad will probably lose in upper bracket.
2.1) Given they meet again, extended series gives Player 2 an advantage.
Now I ask, what is the goal of the tournament?
-To find the Best player overall?, or
-To give interesting matches?, or
-To create frontpage news, of a storyline of a 'lesser' player knocking out a 'stronger' opponent?
Whether one feels for storylines or fairness two-players in-between, extended series only satisfy the last goal and counteract the first two.
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On July 24 2013 09:30 renlynn wrote:Show nested quote +On July 23 2013 07:19 StarStruck wrote:On July 23 2013 07:07 kingNothing42 wrote:On July 23 2013 06:12 Day[9] wrote:
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
That's a pretty good point. However, I don't think we should start Series#2 ignoring GOOD's mistakes. GOOD flubbed Series#1. Why should we give him more of a chance to overthrow BAD if BAD legitimately won Series#1? I mean, it's not like BAD cheated to beat GOOD. The concept that BAD drops out of the bracket a lot more commonly than GOOD is true. But by the same point as above, why should BAD get an advantage against GOOD if they happen to meet again (albeit less likely than the converse) just because he stuck around? The conclusion is that Bo3 makes for a more volatile tournament. That's may be good for spectators. But saying that we should give the GOOD player an advantage by giving him/her a second Bo3 is not convincing to me. His/her chances are better in a Bo7. It's not like players never come back from the disadvantage (cough Soulkey cough). That usually happens if they're really, really good players with a strong playbook. You know who also came back in extended series? Leenock. He was on fire that time though. If someone gets red hot at a LAN good luck taking them out. if you're referring to him winning the finals from the lower bracket, that wasn't coming back in extended series, because he had no prior history there. that was him benefiting from the one time in MLG where extended series favors the lower bracket. normal double elimination would reset the score after the first series, extended series in the finals does not. I guess this could be an argument in favor of extended series since it makes things more even in the finals. sometimes. unless you drop 2 games at the start. but only at the start, dropping 2 games in the middle is still okay.
Are we talking about the same thing? DRG beat Leenock 2-0 in Winners Round 2 of MLG Providence in 2011. They would later meet in the losers Final where Leenock beat him 4-3. -_-
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oh, sorry. forgot about that.
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lets all be honest here, as a "viewer". Not taking to account all the factors say: Players condition, MLG's Budget and all that jazz. We can all agree that the more games we can watch the happier we are. Do we all agree with this?
So with that even if more games would result to some shitty games of cheese,giving changes to prove ones worth or just giving a statement by providing quality games from a player, we as viewers are still all in favor in more games.
The advantages (as far as I can only remember and list down:
1. More games, more replays more material more fun?
2. Will prove a player is indeed worthy of the bout (self worth and bragging rights, makes the person really prove he is better than the other player)
3 ? Will give a chance to the early lossing player (well only advantage was for him) - he might be just nervous and needs more time to cope with tounament fright? Can still prove himself? Can recover from cheesy stuff? Can learn and become better in the next encounters?
The disadvantages:
1. Could result to some games to cheese ( but still can happen to shorter bouts)
2. Will tire players ( we can do a week long tourney which results to number 3)
3. Budget ( higher tickets? More sponsors? less price money? It is MLG's problem?)
Therefore I can say, the more bouts, lossers bracket/ extended series etc = better event. Viewers wins!
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On July 24 2013 23:36 woreyour wrote:
lets all be honest here, as a "viewer". Not taking to account all the factors say: Players condition, MLG's Budget and all that jazz. We can all agree that the more games we can watch the happier we are. Do we all agree with this?
...
Therefore I can say, the more bouts, lossers bracket/ extended series etc = better event. Viewers wins!
More games != more fun
Better games = more fun and better viewer experience
Look at my example, last post page 4.
If the BAD player ends up winning the extended series (knocking out the GOOD player)
He will very likely soon meet an opponent of a race he is bad against, giving really really bad games forward.
(Assuming games between GOOD players are more fun to watch)
Best example of getting far through one good matchup is the GSL season were Inca reached the finals vs Nestea (Through only playing PvP's iirc).
Hopefully we can all agree, that was one of the worst finals ever played,
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I would say more games are a disadvantage if it doesn't help us determine the objectively best player (if there is such a thing). Making the format more entertaining isn't a bad thing, but if we're going to put more games played into a tournament, is it really a good idea to stuff these extra games into the lower bracket? The lower braket is already a bottleneck when it comes to scheduling. If we wanted more games, why not make the upper bracket games BO5 instead of BO3? That would give us more games with people who are actually winning while making it less likely better players fall into the lower bracket on fluke results.
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I don't understand the big fuss about all this anyways. If MLG believes that in order to win their tournament, they must win the majority of games against everybody they play, that's absolutely their perogative. It's OK for two tournaments to have two different philosophies on this matter. If Dreamhack or IEM or ESL or NASL has a different philosophy, that doesn't mean MLG is wrong, just different. It's their tournament, they're spending the money to run it and stream it, they get to say how a player advances.
It's just an excuse for people to hate on MLG more. We all know how much people love that.
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On July 23 2013 06:12 Day[9] wrote:
The result in the original post might surprise people, but it makes sense when you consider the implications of player skill in a broader bracket. Consider the following:
Suppose we have two players that I shall name GOOD and BAD. Further suppose that I am omnipotent and can determine with full accuracy that GOOD beats BAD exactly 70% of the time. We place these two players into a double elimination tournament with extended series, each round being best of 3.
Scenario 1: GOOD beats BAD in the winner's bracket (expected result). BAD drops to lowers. Because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players as well. Because GOOD is favored against BAD, it is extremely likely that GOOD is also favored against other players as well. As a result, BAD has a high probability to be knocked out of the tournament in lowers long before he ever meets GOOD again. The simple conclusion is thus: is GOOD beats BAD in the winner's bracket, there is a low probability that an extended series will even happen. For the sake of argument, lets say there is a 5% chance that GOOD meets BAD again. When this does occur, GOOD has a very high chance to beat BAD as a result of the extended series setup (GOOD begins with a lead).
Scenario 2: BAD beats GOOD in the winner's bracket (unexpected result / the "fluke"). GOOD drops to lowers. As we said before, because BAD is unfavored against GOOD, it is extremely likely that BAD is also unfavored against other players in the tournament. Consequently, BAD has a high probability of falling to lowers sooner rather than later. Similarly, since GOOD is favored against BAD, GOOD has a high probability of advancing through lowers. Therefore, there is a much higher probability that GOOD will meet BAD an extended series will happen. Lets suppose there is a 20% that GOOD meets BAD again. When this does occur, BAD has quite an edge due to the extended series setup (BAD begins with a lead). So, although GOOD is favored in an individual match against BAD, BAD still has a higher probability of winning in an extended series.
Based upon these (somewhat winged) numbers, we see that, when an extended series DOES occur, MUCH more often it is a bad player starting with a lead against a good player. So, "worse players" will win more often in an extended series double elimination bracket.
To clarify, we are not saying that worse players have a statistical advantage overall. Rather, in a double elimination bracket, most of the extended series will be a worse player beginning with a lead over a better player.
This totally changed my mind on this subject and IMHO should be added to the OP. I was (and still am) a huge proponent of the extended series. Mostly because I think it is more fair. And there is just the added drama of the Bo7 when the better player is behind (one of my favorites to bring up is MC vs Idra).
It just seems unfair to me that someone GOOD could lose 2-0, then come back and win 2-1 in the loser bracket and advance over BAD with a total map score of 2-3.
Reading your analysis has convinced me that the extended series is putting GOOD at a disadvantage to BAD, which probably should be enough to get the whole system scrapped.
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On July 23 2013 22:53 KissMeRed wrote:Show nested quote +On July 23 2013 18:23 ZeroPageX wrote:On July 23 2013 09:58 KissMeRed wrote:I've written a highly stylized story to convince everyone that Extended Series is the best rule ever implemented in tournament play. We're at the 2014 MLG Winter Championship in Detroit, Michigan where 128 SC2 players from around the world are competing in the open bracket. At the request of a vocal internet minority, MLG has decided to conduct the tournament without the standard extended series rules. The player pool in uncharacteristically weak featuring only two Koreans. However, fans are still excited since they will get to witness some epic foreigner beatdowns coming from the hands of KT Rolster's Flash and Samsung Khan's Shine! Fast forwarding through the E-sports massacre, we are in Winner's Round 6 featuring none other than our two Korean heroes, Flash and Shine! Now Shine knows he can't possibly beat Flash in a standard game (0% win rate on ladder T.T), but he's been saving two of his most devious Zerg cheeses specifically for MLG Detroit! These cheeses are guaranteed wins for Shine! Since there is no extended series, and because he's smarter than Flash, Shine realizes the only way he can win this tournament is to purposely lose in Winner's Round 6 and save his cheeses for the impending Semifinals rematch. Once Flash sees the build orders, they will become useless. Shine executes two of his drones in Game 1 to go for a 4 pool and attempts a mass overlord 'blinding' strategy in Game 2, both of which end in losses. Flash take the series 2-0. Shine makes quick work of a non-Korean chump in Loser's Round 10 and gets ready for the semifinals rematch. Remember, Shine has two cheeses that are 100%, guaranteed map wins against Flash. Shine goes for his first cheese on Newkirk Redevelopment Precinct (yes, it's still in the map pool). MLG cuts the video feed halfway through the match, it's too much for the audience to handle. Shine wins Game 1. Game 2, Flash suffers the most horrifying loss of his career on Red (Sick) City and instead of typing the customary 'gg', he plunges his ruler into the face of the monitor in a fit of rage. Shine wins the series 2-0 and advances to the Grand Final! Flash is eliminated! The Grand Finals are about to begin, but there is one more twist. Shine and his competitor, ID: STXUncleDrew, shake hands. UncleDrew begins peeling back professional grade makeup to reveal that Shine's opponent is actually INnoVation in disguise! Men, women, and children all weep uncontrollably since they don't get to see a Flash vs Innovation finals. Then they log-on to Teamliquid.net to comment on a thread about why MLG should have upheld their extended series policy. The end. (Disclaimer: This is not a true story or vision of a real future. No disrespect to any players, maps, or tournaments referenced above.) How did Flash wind up in the losers bracket? He never goes to the losers bracket. I followed the most recent MLG format: http://wiki.teamliquid.net/starcraft2/2013_MLG_Spring_ChampionshipWhen you lose in the semis coming from the winners bracket, you are just out.
...Except you would not. You took out extended series but then you forgot how normal double elimination works. Without extended series, Shine would immediately have to rematch against Flash in a brand new best of 3 (And get owned). That's the advantage from making into the finals of a standard double elimination bracket (which is what the semis are in this case).
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On July 25 2013 22:54 sertman wrote:
I don't understand the big fuss about all this anyways. If MLG believes that in order to win their tournament, they must win the majority of games against everybody they play, that's absolutely their perogative. It's OK for two tournaments to have two different philosophies on this matter. If Dreamhack or IEM or ESL or NASL has a different philosophy, that doesn't mean MLG is wrong, just different. It's their tournament, they're spending the money to run it and stream it, they get to say how a player advances.
It's just an excuse for people to hate on MLG more. We all know how much people love that.
It's been a while since I've checked this thread and I found this comment rather odd considering how much praise people gave MLG for hosting an American Invitational and people criticizing Geoff for making a hasty tweet about the thought of SC2 having a smaller stage. Not sure how you missed that, but the responses were overwhelming positive. As for your spiel about tournaments. The CEOs have commented on that matter saying they like having different formats. That's great and all but when it comes down to a global like Blizzard is trying to implement.. I'd make every major offline and implement a World Tour Circuit where you'd get the same format and usual suspects coming to a city near you for unison. I don't mind more games when it comes to Ro8, Ro4 and Finals, but you would have to trim that production time from somewhere. First thing on my list to cut would most likely be double elimination if there was one. That would save a ton of time.
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On July 23 2013 08:03 KissMeRed wrote:
TLDR: It's the same argument from my first post. If you think head to head map scores are important (like I do and I think MLG does) then you are in favor of extended series. If you don't care about map scores and order of series wins (some kind of argument like later rounds are more important) then you probably think extended series is a useless or hurtful rule.
I just want to note that the reason I prefer non extended series, though I'm not extremely opposed apart from in finals, is that to me fairness of all players is more important than fairness between two players. In my opinion, just because a player is lucky/unlucky enough to play against a player that they have already played should not give them an advantage/disadvantage over players who do not meet any players they have already played against. So for me it's not really about the order of series, but the number of full series.
As far as I am concerned, the winner got his advantage by continuing on in the winners bracket and having a better opportunity to win the tournament, once the initial winner loses both players should be on an even field. In the case of a Winner vs Loser, I would favour playing a regular series and a second series if the winner loses, this would mean a minimum of 6 games and a maximum of 9 which is more games than extended series and it also guarantees that whoever advances has at least an even score (2-1, 0-2, 2-1 = 4-4 being the closest possible outcome)
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On July 25 2013 02:19 Goolpsy wrote:
Look at my example, last post page 4.
If the BAD player ends up winning the extended series (knocking out the GOOD player)
He will very likely soon meet an opponent of a race he is bad against, giving really really bad games forward.
But if he is really a "Good Player" he should not have problems with opponents of a race he is bad against, unless he is not thet "good".
If he is really good he is going to have problems with his opponents and would just take them like a boss.
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[note: final math conclusions at bottom of post]
MLG's extended series rule is and always has been a mediocre solution to a very real problem. The issue MLG faces (along with most other major tournaments) is that in a double elimination bracket, a player (or team in the case of dota2, etc) must lose two series to be eliminated. This should be quite obvious from the name. If you look at the recent example of Evo2013, this results in the Grand Final being either a single series won by the Winner's Bracket player, or a two-series final that could be won by either player. Neither player gets a game advantage within a single series, but the player who came from the Winner's Bracket still must lose two full series to drop out of the tournament (as does everyone else).
Let's take some examples from the previous posts and see how they turn out with Evo-style rules. (Disclaimer: I'm no total expert in probability so I'm not 100% sure I handled win probabilities perfectly in bo3/7 format but I think the results will be quite accurate still relative to each other).
Day9 mentions the players GOOD and BAD, where GOOD beats BAD 70% of the time. I'll use P(G) to refer to GOOD winning over and P(~G) to GOOD losing to BAD. All of these probabilities will occur within the sample space of an extended series rematch actually happening.
In a best of 3...
P(G) = (3 choose 2)(.7^2)(.3^1) + (3 choose 3)(.7^3)(.3^0)
P(G) = (3)(.49)(.3) + (1)(.343)
P(G) = .441 + .343
P(G) = .784
Case 1: GOOD wins in WB, is met by BAD in Grand Final.
Extended Series: Given GOOD won, GOOD won the WB meetup 2-0 with probability .4375 and 2-1 with probability .5625.
P(GOOD wins grand final) = (.4375)(GOOD wins with 2-0 lead) + (.5625)(GOOD wins with 2-1 lead)
P(G) = (.4375)((5 choose 2)(.7^2)(.3^3) + (5 choose 3)(.7^3)(.3^2) + (5 choose 4)(.7^4)(.3) + (5 choose 5)(.7^5)) + (.5625)((4 choose 2)(.7^2)(.3^2) + (4 choose 3)(.7^3)(.3) + (4 choose 4)(.7^4))
P(G) = (.4375)(.09261 + .3087 + .36015 + .16807) + (.5625)(.2646+ .4116 + .2401)
P(G) = (.4375)(.92953) + (.5625)(.9163)
P(G) = .9221
GOOD will win the extended series with probability ~92.21%, which is a good ~14% higher than his chances of winning a regular bo3. It is worth noting that GOOD's chances of winning a simple bo7 vs BAD would actually be 87.40%.
Evo-style rules: GOOD has no game advantage but must lose twice (lose two bo3s) in order to lose the grand final against BAD.
P(GOOD wins grand final) = P(GOOD wins first bo3) + P(GOOD loses first bo3)*P(GOOD wins second bo3)
P(G) = (.784) + (.216)(.784)
P(G) = .95334
GOOD has a 95.33% chance to win the grand finals with Evo-style rules (WB player must lose 2 bo3s)
While GOOD still has a very good chance of winning in either format, Evo-style rules increase GOOD's chances of winning by about 3%. Both formats still give GOOD a nice advantage over both a regular bo3 or bo7.
Case 2: BAD wins in WB, meets GOOD in grand final.
Extended Series: Given BAD won in WB, there was a .875 probability it was 2-1 and .125 probability it was 2-0.
P(G) = (.875)((4 choose 3)(.7^3)(.3) + (4 choose 4)(.7^4)) + (.125)((5 choose 4)(.7^4)(.3) + (5 choose 5)(.7^5))
P(G) = (.875)(.4116 + .2401) + (.125)(.36015 + .08235)
P(G) = .5702375 + .0553125
P(G) = .6256
GOOD will have a 62.56% chance of winning the extended series if he is coming from the loser's bracket. Obviously, this is lower than his chance of winning a bo3 or bo7 as he has already lost two games in this scenario.
Evo-style: GOOD must win two straight bo3s to win the grand final.
P(G) = (.784)(.784)
P(G) = .6147
GOOD will only have a 61.47% chance of winning two best of threes in a row, which is actually about 1% lower than in an extended series! Maybe we were wrong about you after all, MLG.
Summary & Conclusion
So, we've found out two major things thus far.
1. Extended series gives the better player a slightly better chance to win the full series IF he has already lost the first bo3 to a worse player.
2. Extended series gives the worse player a slightly better chance to win the full series IF he has already lost the first bo3 to a better player.
People have been saying that the "worse" player gets a better chance statistically with extended series when the rematch comes around, but the truth is that whoever lost first gets a very slightly better chance for a "comeback" in a potential rematch. Now, let's calculate overall winrates in both cases.
Evo-style rules:
P(G) = P(GOOD wins first bo3 and grand final) + P(GOOD loses first bo3, wins grand final)
P(G) = (.784)(.9533) + (.216)(.6147)
P(G) = .8801
Extended Series:
P(G) = P(GOOD wins first bo3 and extended series) + P(GOOD loses first bo3, wins extended series)
P(G) = (.784)(.9221) + (.216)(.6256)
P(G) = .8581
Therefore, GOOD will win his overall series against BAD 88.01% of the time with dual elim Evo-style rules, and 85.81% of the time with Extended Series. It looks like we were right about MLG, and extended series does in fact give GOOD a 2.2% lower chance of winning his series against BAD! This percentage would change if GOOD's bo1 win chance against BAD was different.
Addendum: KissMeRed's scenario is a bit unique in the way it was set up but I will say this in favor of extended series. If Shine was to purposefully lose to Flash, and then Flash was knocked into Lower Bracket to play Shine again (say in LB finals), an extended series would result in Flash winning while a simple bo3 (the regular Evo-style rule) would have him lose to Shine's perfected cheeses. I don't find this scenario particularly realistic (nor do I wish or need to do math with 100% winrates) so I skipped doing any calculations on it.
(edit:typos)
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The problem with extended series (as I see it?) isn't, the probability for the finals (It is a special case altogether)
But that you insert an inherited disadvange somewhere in the middle of the bracket, with claims of 'fairness' players between, but not taking note, that the competition is between 512 og 1024 players and not just two, and furthermore doesn't take into consideration that the player from the lower bracket has already played a fair deal more opponents than the player from the upper bracket.
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EPT
