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On November 18 2014 02:33 Sn0_Man wrote:
Nobody is saying that Tom Ross isn't a ridiculously good magic player. He certainly is, that much is clear. But even if he played every game perfectly for however many straight tournaments, it is pretty likely that Tom Ross is running above expected value.
Running well doesn't make you a bad player, and being an amazing player doesn't mean that you don't need to catch a few breaks to have a streak like Tom's. Basically, these things aren't mutually exclusive.
I think it's impressive that he can win with weenie aggro decks so consistently, so more power to him.
This is exactly what I'm trying to say.
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I suppose. It is just that when you call someone lucky, it usually means you're insinuate that they're not as skilled as people think. From my point of view, there is no point in calling someone lucky because it is understood that you have to run well to win a tournament.
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Everyone is equally lucky
Not everyone is equally good
The pros though, play enough where the random bad streaks are outnumbered by the random good streaks.
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United States24768 Posts
On November 18 2014 08:26 Thieving Magpie wrote:
The pros though, play enough where the random bad streaks are outnumbered by the random good streaks.
I'm not sure where the asymmetry is coming from...
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Player A has a higher winrate than player B
Player A goes on X number of win streaks (on average)
Player B goes on Y number of win streaks (on average)
Being that X is higher than Y, player A seems to "get lucky win streaks" more often than player B does.
Player B also sees that player A has less losing streaks than Player B does.
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On November 18 2014 02:09 Tarias wrote:
You guys seem to forget that there is a random element in this game. Even if you always play the perfect lines, assuming your opponents aren't complete retards, you'll probably still only get a match win percentage of around 70%(which is extremely high afaik). Kai Budde for example is around 64% afaik. Given such a win percentage the chance of winning for example 4 matches in a row is already below 25%. So just because Tom Ross has been succesful in a lot of different events doesn't mean he hasn't been lucky throughout those events. Of course if you suck you will probably never be able to win a tournament, but no matter how good you are, you need some luck. Tom has had plenty of it.
...Again which is a fallacy once you take into account multiple events/tournaments. Also, you guys are misusing the hell out of statistics. That win rate is extremely misleading when trying to attribute to luck or not luck; and your example specifically violates quite a few assumptions that is necessary for you to calculate that <25%. I am not saying luck isn't part of the equation, it always is, but in my opinion, it isn't as high as some of you like to believe.
Preparation is huge for events like this, Kai Budde I would say is still at a disadvantage compared to modern Magic players (MTGO prevalence, teams, the raw amount of information available), Tom arguably has better preparation available than Kai. Then it comes down the games/matches themselves, except you can ask a very simple question here if you can attribute results to luck or skill/preparation provided that the players are of at least some skill (PT level - which everyone here is in agreement of for Tom): if luck is a huge factor, is it more likely for Tom to be contending (let's say at least top 16/32) in multiple events and formats or is it more likely for Tom to be exhibit random results? I think we all know the answer to that one and I think players tend to over-attribute certain situations to luck without context.
The biggest reason for this (imo) is that players tend to think of the given specific moment (the over-emphasis on the top deck), "if I just draw this card now, I'll win/be advantaged". Then we tend to attribute luck to that single draw, oh he/she got what they needed, gg lucky, or oh he/she didn't get what they needed, gg unlucky. That's reasonable, except for the fact that we would be ignoring the game as a whole and imo over-valued that singular draw, basically ignoring the more important question of could I have won if I played differently? That question is much harder to answer. This is how formerly terrible match ups can get turned on their heads when the decks themselves have changed very little, i.e. - UB versus Frites or UB versus Burning Vengeance back a few standard cycles ago, both of those UB match ups were terrible at first until UB players figured out what actually matters and what doesn't.
The only game I caught of Tom's this past weekend was his G3 against Landstill in the playoffs where playing through 3 Pyroclasms early on should have resulted in a loss for Tom in most scenarios, but instead Tom won off the back off of a very patient resolution (and impatience on his opponent's part) of Sylvan Library where he setup for the resolution off of multiple turns.
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On November 18 2014 10:50 Judicator wrote:Show nested quote +On November 18 2014 02:09 Tarias wrote:
You guys seem to forget that there is a random element in this game. Even if you always play the perfect lines, assuming your opponents aren't complete retards, you'll probably still only get a match win percentage of around 70%(which is extremely high afaik). Kai Budde for example is around 64% afaik. Given such a win percentage the chance of winning for example 4 matches in a row is already below 25%. So just because Tom Ross has been succesful in a lot of different events doesn't mean he hasn't been lucky throughout those events. Of course if you suck you will probably never be able to win a tournament, but no matter how good you are, you need some luck. Tom has had plenty of it.
...Again which is a fallacy once you take into account multiple events/tournaments. Also, you guys are misusing the hell out of statistics. That win rate is extremely misleading when trying to attribute to luck or not luck; and your example specifically violates quite a few assumptions that is necessary for you to calculate that <25%. I am not saying luck isn't part of the equation, it always is, but in my opinion, it isn't as high as some of you like to believe. Preparation is huge for events like this, Kai Budde I would say is still at a disadvantage compared to modern Magic players (MTGO prevalence, teams, the raw amount of information available), Tom arguably has better preparation available than Kai. Then it comes down the games/matches themselves, except you can ask a very simple question here if you can attribute results to luck or skill/preparation provided that the players are of at least some skill (PT level - which everyone here is in agreement of for Tom): if luck is a huge factor, is it more likely for Tom to be contending (let's say at least top 16/32) in multiple events and formats or is it more likely for Tom to be exhibit random results? I think we all know the answer to that one and I think players tend to over-attribute certain situations to luck without context. The biggest reason for this (imo) is that players tend to think of the given specific moment (the over-emphasis on the top deck), "if I just draw this card now, I'll win/be advantaged". Then we tend to attribute luck to that single draw, oh he/she got what they needed, gg lucky, or oh he/she didn't get what they needed, gg unlucky. That's reasonable, except for the fact that we would be ignoring the game as a whole and imo over-valued that singular draw, basically ignoring the more important question of could I have won if I played differently? That question is much harder to answer. This is how formerly terrible match ups can get turned on their heads when the decks themselves have changed very little, i.e. - UB versus Frites or UB versus Burning Vengeance back a few standard cycles ago, both of those UB match ups were terrible at first until UB players figured out what actually matters and what doesn't. The only game I caught of Tom's this past weekend was his G3 against Landstill in the playoffs where playing through 3 Pyroclasms early on should have resulted in a loss for Tom in most scenarios, but instead Tom won off the back off of a very patient resolution (and impatience on his opponent's part) of Sylvan Library where he setup for the resolution off of multiple turns.
Please tell me what the fallacy is. You make it sound like there is no random factor if your sample size is a bit larger, which is obviously wrong. By luck I also don't only mean "he topdecks well". I'll try to illustrate my point in a different way:
Let's say that instead of one Tom Ross, 100 Tom Ross clones, playing exactly the same deck with exactly the same skill, enter this tournament. Probably 1 one them makes top 8, maybe another one makes top 16, maybe two more make top 32 etc. The large majority of these Tom Ross clones, however, will due to the random variance in magic not make it that far. Now if we were to take a random magic player, me for example, and do the same thing, non of my clones would make the top 8, most of them probably wouldn't even make day 2. The reason is that Tom Ross is a much better player obviously. Tom Ross however, will still need to end up on the right end of the variance spectrum to get this top 8. So while him being a great player is exactly what enables him to do this, he still needs variance on his side.
Now contrary to what you seem to believe, the fact that he manages to do this consistently means he has variance on his side consistently, not that top 8 is the average expected result for him. Now this, and not a topdeck, is what I call lucky.
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On November 18 2014 21:01 Tarias wrote:Show nested quote +On November 18 2014 10:50 Judicator wrote:On November 18 2014 02:09 Tarias wrote:
You guys seem to forget that there is a random element in this game. Even if you always play the perfect lines, assuming your opponents aren't complete retards, you'll probably still only get a match win percentage of around 70%(which is extremely high afaik). Kai Budde for example is around 64% afaik. Given such a win percentage the chance of winning for example 4 matches in a row is already below 25%. So just because Tom Ross has been succesful in a lot of different events doesn't mean he hasn't been lucky throughout those events. Of course if you suck you will probably never be able to win a tournament, but no matter how good you are, you need some luck. Tom has had plenty of it.
...Again which is a fallacy once you take into account multiple events/tournaments. Also, you guys are misusing the hell out of statistics. That win rate is extremely misleading when trying to attribute to luck or not luck; and your example specifically violates quite a few assumptions that is necessary for you to calculate that <25%. I am not saying luck isn't part of the equation, it always is, but in my opinion, it isn't as high as some of you like to believe. Preparation is huge for events like this, Kai Budde I would say is still at a disadvantage compared to modern Magic players (MTGO prevalence, teams, the raw amount of information available), Tom arguably has better preparation available than Kai. Then it comes down the games/matches themselves, except you can ask a very simple question here if you can attribute results to luck or skill/preparation provided that the players are of at least some skill (PT level - which everyone here is in agreement of for Tom): if luck is a huge factor, is it more likely for Tom to be contending (let's say at least top 16/32) in multiple events and formats or is it more likely for Tom to be exhibit random results? I think we all know the answer to that one and I think players tend to over-attribute certain situations to luck without context. The biggest reason for this (imo) is that players tend to think of the given specific moment (the over-emphasis on the top deck), "if I just draw this card now, I'll win/be advantaged". Then we tend to attribute luck to that single draw, oh he/she got what they needed, gg lucky, or oh he/she didn't get what they needed, gg unlucky. That's reasonable, except for the fact that we would be ignoring the game as a whole and imo over-valued that singular draw, basically ignoring the more important question of could I have won if I played differently? That question is much harder to answer. This is how formerly terrible match ups can get turned on their heads when the decks themselves have changed very little, i.e. - UB versus Frites or UB versus Burning Vengeance back a few standard cycles ago, both of those UB match ups were terrible at first until UB players figured out what actually matters and what doesn't. The only game I caught of Tom's this past weekend was his G3 against Landstill in the playoffs where playing through 3 Pyroclasms early on should have resulted in a loss for Tom in most scenarios, but instead Tom won off the back off of a very patient resolution (and impatience on his opponent's part) of Sylvan Library where he setup for the resolution off of multiple turns. Please tell me what the fallacy is. You make it sound like there is no random factor if your sample size is a bit larger, which is obviously wrong. By luck I also don't only mean "he topdecks well". I'll try to illustrate my point in a different way: Let's say that instead of one Tom Ross, 100 Tom Ross clones, playing exactly the same deck with exactly the same skill, enter this tournament. Probably 1 one them makes top 8, maybe another one makes top 16, maybe two more make top 32 etc. The large majority of these Tom Ross clones, however, will due to the random variance in magic not make it that far. Now if we were to take a random magic player, me for example, and do the same thing, non of my clones would make the top 8, most of them probably wouldn't even make day 2. The reason is that Tom Ross is a much better player obviously. Tom Ross however, will still need to end up on the right end of the variance spectrum to get this top 8. So while him being a great player is exactly what enables him to do this, he still needs variance on his side. Now contrary to what you seem to believe, the fact that he manages to do this consistently means he has variance on his side consistently, not that top 8 is the average expected result for him. Now this, and not a topdeck, is what I call lucky.
You are as likely to be unlucky as lucky. For every lucky topdeck Tom had, he also had a bad topdeck. Same with the opponent. If there were 100 Tom Ross' playing in 100 tournaments an infinite number of times each tournament--all 100 Tom Ross' would rank the same being that no factors are different in all 100 tournaments. Tom Ross simply plays more featured matches than the average joe schmoe and so his win streaks are more public than the average joe schmoe.
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On November 19 2014 00:31 Thieving Magpie wrote:Show nested quote +On November 18 2014 21:01 Tarias wrote:On November 18 2014 10:50 Judicator wrote:On November 18 2014 02:09 Tarias wrote:
You guys seem to forget that there is a random element in this game. Even if you always play the perfect lines, assuming your opponents aren't complete retards, you'll probably still only get a match win percentage of around 70%(which is extremely high afaik). Kai Budde for example is around 64% afaik. Given such a win percentage the chance of winning for example 4 matches in a row is already below 25%. So just because Tom Ross has been succesful in a lot of different events doesn't mean he hasn't been lucky throughout those events. Of course if you suck you will probably never be able to win a tournament, but no matter how good you are, you need some luck. Tom has had plenty of it.
...Again which is a fallacy once you take into account multiple events/tournaments. Also, you guys are misusing the hell out of statistics. That win rate is extremely misleading when trying to attribute to luck or not luck; and your example specifically violates quite a few assumptions that is necessary for you to calculate that <25%. I am not saying luck isn't part of the equation, it always is, but in my opinion, it isn't as high as some of you like to believe. Preparation is huge for events like this, Kai Budde I would say is still at a disadvantage compared to modern Magic players (MTGO prevalence, teams, the raw amount of information available), Tom arguably has better preparation available than Kai. Then it comes down the games/matches themselves, except you can ask a very simple question here if you can attribute results to luck or skill/preparation provided that the players are of at least some skill (PT level - which everyone here is in agreement of for Tom): if luck is a huge factor, is it more likely for Tom to be contending (let's say at least top 16/32) in multiple events and formats or is it more likely for Tom to be exhibit random results? I think we all know the answer to that one and I think players tend to over-attribute certain situations to luck without context. The biggest reason for this (imo) is that players tend to think of the given specific moment (the over-emphasis on the top deck), "if I just draw this card now, I'll win/be advantaged". Then we tend to attribute luck to that single draw, oh he/she got what they needed, gg lucky, or oh he/she didn't get what they needed, gg unlucky. That's reasonable, except for the fact that we would be ignoring the game as a whole and imo over-valued that singular draw, basically ignoring the more important question of could I have won if I played differently? That question is much harder to answer. This is how formerly terrible match ups can get turned on their heads when the decks themselves have changed very little, i.e. - UB versus Frites or UB versus Burning Vengeance back a few standard cycles ago, both of those UB match ups were terrible at first until UB players figured out what actually matters and what doesn't. The only game I caught of Tom's this past weekend was his G3 against Landstill in the playoffs where playing through 3 Pyroclasms early on should have resulted in a loss for Tom in most scenarios, but instead Tom won off the back off of a very patient resolution (and impatience on his opponent's part) of Sylvan Library where he setup for the resolution off of multiple turns. Please tell me what the fallacy is. You make it sound like there is no random factor if your sample size is a bit larger, which is obviously wrong. By luck I also don't only mean "he topdecks well". I'll try to illustrate my point in a different way: Let's say that instead of one Tom Ross, 100 Tom Ross clones, playing exactly the same deck with exactly the same skill, enter this tournament. Probably 1 one them makes top 8, maybe another one makes top 16, maybe two more make top 32 etc. The large majority of these Tom Ross clones, however, will due to the random variance in magic not make it that far. Now if we were to take a random magic player, me for example, and do the same thing, non of my clones would make the top 8, most of them probably wouldn't even make day 2. The reason is that Tom Ross is a much better player obviously. Tom Ross however, will still need to end up on the right end of the variance spectrum to get this top 8. So while him being a great player is exactly what enables him to do this, he still needs variance on his side. Now contrary to what you seem to believe, the fact that he manages to do this consistently means he has variance on his side consistently, not that top 8 is the average expected result for him. Now this, and not a topdeck, is what I call lucky. You are as likely to be unlucky as lucky. For every lucky topdeck Tom had, he also had a bad topdeck. Same with the opponent. If there were 100 Tom Ross' playing in 100 tournaments an infinite number of times each tournament--all 100 Tom Ross' would rank the same being that no factors are different in all 100 tournaments. Tom Ross simply plays more featured matches than the average joe schmoe and so his win streaks are more public than the average joe schmoe.
I'm not sure if you really don't understand what I'm trying to say or if you are just being obtuse. Off course I am not saying we redo the same thing 100 times without changing everything, and assume that everyone draws exactly the same. That would just be utterly pointless.
What I'm proposing is an alternate version of GP NJ in which 100 exact clones of Tom Ross all play infect. These 100 clones then get paired up against other players and make their way through the tournament. They all make the choices the actual Tom Ross would make in any given situation. Since Tom Ross has played a lot of matches we have a metric we can use to get an idea how likely it is he will beat a random opponent in a best of 3; his match win percentage. Let's be very generous for the purpose of this example and say it is 75%. This means that against any random opponent Tom Ross has a 75% chance to win. Now let's simplify a little bit and say this tournament has 15 rounds, and any player that is 13-2 or better makes top 8. Using math I find that 75% winrate Tom Ross has a 23% chance to go 13-2 or better. I guess if Tom Ross has an actual win percentage of 75%, 23 of the 100 clones would make it into the top 8 on average, so my original guess was wrong. The point remains that far more of the Tom Ross clones don't make the top 8 (77% chance not top 8). So the actual Tom Ross did a lot better in GP NJ than the average Tom Ross would.
Also statements like "You are as likely to be unlucky as lucky." are just meaningless crap to be honest. What lucky and unlucky are depends on the situation. Sometimes being "lucky" is topdecking a one-off with like a 2% chance to draw it, and other times being unlucky is drawing a spell when you needed any land (probably more around 30% chance to be "unlucky")
Edit: Corrected bad math
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I'm not sure I want to wade into this but "consistently has variance on his side" easily falls into the meaningless crap category imho.
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On November 19 2014 01:46 Tarias wrote:Show nested quote +On November 19 2014 00:31 Thieving Magpie wrote:On November 18 2014 21:01 Tarias wrote:On November 18 2014 10:50 Judicator wrote:On November 18 2014 02:09 Tarias wrote:
You guys seem to forget that there is a random element in this game. Even if you always play the perfect lines, assuming your opponents aren't complete retards, you'll probably still only get a match win percentage of around 70%(which is extremely high afaik). Kai Budde for example is around 64% afaik. Given such a win percentage the chance of winning for example 4 matches in a row is already below 25%. So just because Tom Ross has been succesful in a lot of different events doesn't mean he hasn't been lucky throughout those events. Of course if you suck you will probably never be able to win a tournament, but no matter how good you are, you need some luck. Tom has had plenty of it.
...Again which is a fallacy once you take into account multiple events/tournaments. Also, you guys are misusing the hell out of statistics. That win rate is extremely misleading when trying to attribute to luck or not luck; and your example specifically violates quite a few assumptions that is necessary for you to calculate that <25%. I am not saying luck isn't part of the equation, it always is, but in my opinion, it isn't as high as some of you like to believe. Preparation is huge for events like this, Kai Budde I would say is still at a disadvantage compared to modern Magic players (MTGO prevalence, teams, the raw amount of information available), Tom arguably has better preparation available than Kai. Then it comes down the games/matches themselves, except you can ask a very simple question here if you can attribute results to luck or skill/preparation provided that the players are of at least some skill (PT level - which everyone here is in agreement of for Tom): if luck is a huge factor, is it more likely for Tom to be contending (let's say at least top 16/32) in multiple events and formats or is it more likely for Tom to be exhibit random results? I think we all know the answer to that one and I think players tend to over-attribute certain situations to luck without context. The biggest reason for this (imo) is that players tend to think of the given specific moment (the over-emphasis on the top deck), "if I just draw this card now, I'll win/be advantaged". Then we tend to attribute luck to that single draw, oh he/she got what they needed, gg lucky, or oh he/she didn't get what they needed, gg unlucky. That's reasonable, except for the fact that we would be ignoring the game as a whole and imo over-valued that singular draw, basically ignoring the more important question of could I have won if I played differently? That question is much harder to answer. This is how formerly terrible match ups can get turned on their heads when the decks themselves have changed very little, i.e. - UB versus Frites or UB versus Burning Vengeance back a few standard cycles ago, both of those UB match ups were terrible at first until UB players figured out what actually matters and what doesn't. The only game I caught of Tom's this past weekend was his G3 against Landstill in the playoffs where playing through 3 Pyroclasms early on should have resulted in a loss for Tom in most scenarios, but instead Tom won off the back off of a very patient resolution (and impatience on his opponent's part) of Sylvan Library where he setup for the resolution off of multiple turns. Please tell me what the fallacy is. You make it sound like there is no random factor if your sample size is a bit larger, which is obviously wrong. By luck I also don't only mean "he topdecks well". I'll try to illustrate my point in a different way: Let's say that instead of one Tom Ross, 100 Tom Ross clones, playing exactly the same deck with exactly the same skill, enter this tournament. Probably 1 one them makes top 8, maybe another one makes top 16, maybe two more make top 32 etc. The large majority of these Tom Ross clones, however, will due to the random variance in magic not make it that far. Now if we were to take a random magic player, me for example, and do the same thing, non of my clones would make the top 8, most of them probably wouldn't even make day 2. The reason is that Tom Ross is a much better player obviously. Tom Ross however, will still need to end up on the right end of the variance spectrum to get this top 8. So while him being a great player is exactly what enables him to do this, he still needs variance on his side. Now contrary to what you seem to believe, the fact that he manages to do this consistently means he has variance on his side consistently, not that top 8 is the average expected result for him. Now this, and not a topdeck, is what I call lucky. You are as likely to be unlucky as lucky. For every lucky topdeck Tom had, he also had a bad topdeck. Same with the opponent. If there were 100 Tom Ross' playing in 100 tournaments an infinite number of times each tournament--all 100 Tom Ross' would rank the same being that no factors are different in all 100 tournaments. Tom Ross simply plays more featured matches than the average joe schmoe and so his win streaks are more public than the average joe schmoe. I'm not sure if you really don't understand what I'm trying to say or if you are just being obtuse. Off course I am not saying we redo the same thing 100 times without changing everything, and assume that everyone draws exactly the same. That would just be utterly pointless. What I'm proposing is an alternate version of GP NJ in which 100 exact clones of Tom Ross all play infect. These 100 clones then get paired up against other players and make their way through the tournament. They all make the choices the actual Tom Ross would make in any given situation. Since Tom Ross has played a lot of matches we have a metric we can use to get an idea how likely it is he will beat a random opponent in a best of 3; his match win percentage. Let's be very generous for the purpose of this example and say it is 75%. This means that against any random opponent Tom Ross has a 75% chance to win. Now let's simplify a little bit and say this tournament has 15 rounds, and any player that is 13-2 or better makes top 8. Using math I find that 75% winrate Tom Ross has a 23% chance to go 13-2 or better. I guess if Tom Ross has an actual win percentage of 75%, 23 of the 100 clones would make it into the top 8 on average, so my original guess was wrong. The point remains that far more of the Tom Ross clones don't make the top 8 (77% chance not top 8). So the actual Tom Ross did a lot better in GP NJ than the average Tom Ross would. Also statements like "You are as likely to be unlucky as lucky." are just meaningless crap to be honest. What lucky and unlucky are depends on the situation. Sometimes being "lucky" is topdecking a one-off with like a 2% chance to draw it, and other times being unlucky is drawing a spell when you needed any land (probably more around 30% chance to be "unlucky") Edit: Corrected bad math
While you are at it, correct some bad statistics and understanding of probability. The matches are not independent of each other. The probability of Tom winning also changes from round to round. You are also making the assumption that you know what the true win rate of Tom is which is completely not true.
So before you totally reduce sabermetrics and sports statistics into intro to college stats, understand those fallacies. Just because you make the assumptions does not make it a good or even reasonable.
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He isn't incorrect that a 75% in a match does not mean a 75% chance to top 8
Where he is wrong is mainly at the conclusion of his work--it's still an incomplete analysis for the most part and with a bit more effort he could probably piece something substantive if he doesn't make conclusions before engaging the argument.
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On November 19 2014 02:57 mordek wrote:
I'm not sure I want to wade into this but "consistently has variance on his side" easily falls into the meaningless crap category imho.
You are right. I was merely trying to say that the fact Tom top 8's a lot more than would perhaps be expected from any player at the top level, given the nature of variance in magic can be at least partially attributed to variance being on his side. I think that point isn't meaningless crap
On November 19 2014 03:05 Judicator wrote:
While you are at it, correct some bad statistics and understanding of probability. The matches are not independent of each other. The probability of Tom winning also changes from round to round. You are also making the assumption that you know what the true win rate of Tom is which is completely not true.
So before you totally reduce sabermetrics and sports statistics into intro to college stats, understand those fallacies. Just because you make the assumptions does not make it a good or even reasonable.
While I agree that the statistics aren't perfect, I think they are good enough to get at least a decent estimate. I'm curious why you think the matches are not independent. I'll concede that since they have some influence on the mental state of the player etc. they won't be 100% independent. I think that for a player of Tom's caliber, however, who probably plays his decks near perfectly anyways, these effects are negligible. I'll agree that the probability of him winning changes, on average it will be higher in early rounds and lower in later rounds. I'm quite confident however that my 75% estimate is high enough that the actual top 8 probability will be lower. Now if you know more about statistics and probability than I do, which is very likely (Or maybe not. I don't know enough about the demographics of this website, or about probability, to calculate this.) since I've indeed only seen probability once as a topic in a math course, I would love to see you do a similar analysis with more advanced methods.
The overall point I'm trying to make is that even for extremely skilled players like Tom, Top 8 is not the expected result. I think that a more advanced analysis will find the same result. He needs some luck to get there. This is also not a criticism of Tom in particular, I think this goes for any player in any event. BBD also needed some luck to get to the top 8 and later win the event.
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Straight outta Johto18973 Posts
On November 19 2014 04:29 Tarias wrote:
While I agree that the statistics aren't perfect, I think they are good enough to get at least a decent estimate. I'm curious why you think the matches are not independent.
In between rounds players can learn from their friends and team members what other people are playing and what lines of plays they should be looking out for, or any hidden tech they should be aware of. Or if someone finishes a round early they can go watch someone else's game.
The possible increase in information for the participants involved in a game is sufficient to come to the conclusion that each game is not independent of each other. For example, when you flip a coin the coin doesn't care what happened 30 minutes ago. When you play a game of magic the players do care what happened 30 minutes ago.
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Not only that, but as you progress through the rounds, the possibility of variant decks decreases allowing for better predictability and metagame knowledge. For example: in legacy you can expect ANY deck in round 1 but chances are there's only the top 3-5 decks around in rounds 8-10. That's when sideboard choices, metagame choices, and deck choices really start to come into play.
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Good points. Although I'm not sure I agree with you completely MoonBear. I agree that as the tournament goes on, players will have access to more information about what their opponents could be doing. I'm not sure that is an argument against independence though. It's not the outcome of round x that effects round x+1, it's the fact that players have time to acquire helpful information between the two rounds that has an effect.
I think it's more so just another factor influencing the change of win rates between every round, and I guess there are a lot of other factors. Intuitively I'd say that the average win rate of a pro player should decrease as the rounds get later, because the average opponent will be better, but obviously if you meta-gamed everyone that doesn't really apply either.
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Straight outta Johto18973 Posts
On November 19 2014 05:49 Tarias wrote:
Good points. Although I'm not sure I agree with you completely MoonBear. I agree that as the tournament goes on, players will have access to more information about what their opponents could be doing. I'm not sure that is an argument against independence though. It's not the outcome of round x that effects round x+1, it's the fact that players have time to acquire helpful information between the two rounds that has an effect.
If you can't guarantee that between two events there is 0 probability of an increase in information that could affect the outcome then the two events are not independent. That's basically the definition of independence.
In practise, you can say "well I observed that nothing changed therefore I'm going to treat the two events as independent because it's more convenient when I'm trying to do the math and ultimately the answer won't change". But that's more you making a convenient shortcut to save yourself time and effort rather than saying that these real world events are actually independent. In a perfect lab where you set everything up, sure you can make sure there's no communication in-between rounds. But that's not what happens at tournaments so it's a bit disingenuous to say so.
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ah, I see. The way I knew independence was more about the outcomes. "If the outcome of a does not affect P(b) than a and b are independent". I thought an event in probability theory basically meant outcome. The way I see it is that the outcome of round one (win or lose) doesn't change the players chances in the next round. However due to the fact that the next round is round two, and players have exchanged some information before it etc. the probability of winning round 2 is different from the probability of winning round 1.
So I could say that P(win round two) doesn't change based on the outcome of round one, but because stuff happened between round one and round two P(win round one) is just different from P(win round two). Not sure if I'm making sense, let alone if I'm correct, but this was my thought process.
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Straight outta Johto18973 Posts
On November 19 2014 06:35 Tarias wrote:
ah, I see. The way I knew independence was more about the outcomes. "If the outcome of a does not affect P(b) than a and b are independent". I thought an event in probability theory basically meant outcome. The way I see it is that the outcome of round one (win or lose) doesn't change the players chances in the next round. However due to the fact that the next round is round two, and players have exchanged some information before it etc. the probability of winning round 2 is different from the probability of winning round 1.
So I could say that P(win round two) doesn't change based on the outcome of round one, but because stuff happened between round one and round two P(win round one) is just different from P(win round two). Not sure if I'm making sense, let alone if I'm correct, but this was my thought process.
Basically. A simpler way of thinking about it goes a bit like this:
- Whether a player wins Game 2 doesn't really depend on whether they won Game 1
(Assuming that they're not on tilt or something)
- But it does depend on several other factors
(e.g. whether players talk to each other, the fact that weird decks tend not to make it to later rounds, etc.)
- So you can't guarantee that Game 2 is completely independent from Game 1
(Unless you can guarantee that every possible factor that could have a potential impact on Game 2 is exactly the same as it was before Game 1)
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Honestly, my view of Magic skill is that X% of the time you pretty much always win, Y% of the time, you lose, and Z% of the time, the game balances on whether or not you play perfectly and what deck you chose. There isn't really a way to calculate X/Y/Z, but I like to think that Z is in the neighborhood of about 20%.
That's really all skill accounts for. The rest is hot streaks and cold streaks and lopsided metagames (i.e. a meta deck sweeping a field that's 70% one of two decks).
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EPT
