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This post will describe how much chances did you have to win a ladder match, based on the amount of points that you've won / lost in the end of it.
For this we are going to assume a few things about Blizzard ladder system, none of them are far fetched:
First, that Blizzard ladder system rewards and subtracts points based on the players' winning chances. Since Blizzard has access to million of matches, it's reasonable to assume their formulas are fairly accurate.
Second, that if a player's skill is constant, then his points will reach an amount which reflects his skill level and stay near that point (disregarding bonus pool points). Since ladder points shift towards a player's MMR, this assumption assumes that Blizzard's system is a zero-sum system with regard to MMR, or at the very least that the shifts in MMR are slow occurring.
Lastly, this method is only applicable once your points have reached a level that reflects your MMR. You can tell when you've reached this point when the amount of points that you win for matches, and the amount of points that you lose for matches, both become more or less constant. For most players this will be when they start winning / losing around 12 points per match. For very high MMR players, they might reach this point when they are winning much less than 12 points per match, and losing much more. Similarly for very low MMR players, the opposite is true.
Basically you need to have played enough games first before you can use the method described in this post.
The formula:
WinningChances = 100 - PointsWon * 25/6
Some math:
+ Show Spoiler +WinningChances: How much chance in percents did you have to win the match.
WinAmount: How many points you've won (in case of a win)
LoseAmount: How many points you've lost (in case of a loss)
Note that LoseAmount = WinAmount - 24, due to assumption 2.
WinningChances * WinAmount + (100 - WinningChances) * LoseAmount = 0
The above is true because if you play a great enough number of games, your points will not change.
WinningChances * WinAmount + 100 * LoseAmount - WinningChances * LoseAmount = 0
WinningChances * (WinAmount - LoseAmount) = -100 * LoseAmount
WinningChances = -100 * LoseAmount / (WinAmount - LoseAmount)
WinningChances = -100 * (WinAmount - 24) / (WinAmount - (WinAmount - 24))
WinningChances = -100 * (WinAmount - 24) / 24
WinningChances = -25 * (WinAmount - 24) / 6
WinningChances = (WinAmount - 24) * -25/6
WinningChances = WinAmount * -25/6 + 24*25/6
WinningChances = WinAmount * -25/6 + 100
WinningChances = 100 - WinAmount * 25/6
The numbers:
Points won for a match -- your winning chances
0 100.00
1 95.83
2 91.67
3 87.50
4 83.33
5 79.17
6 75.00
7 70.83
8 66.67
9 62.50
10 58.33
11 54.17
12 50.00
13 45.83
14 41.67
15 37.50
16 33.33
17 29.17
18 25.00
19 20.83
20 16.67
21 12.50
22 8.33
23 4.17
24 0.00
* If you lost the match, simply add 24 to the amount of points that you lost and use the formula. For example if you lost 4 points, then you should look at the row corresponding to 20 points won.
**Note that you should disregard any bonus points won, only actual points matter.
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Wow never mind. I think I should just sleep. =_=
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But. If i have a 0% chance of winning, how did i win?
I think you're confusing future odds with informed predictions due to past results.
Also, I doubt the system is that simple. Where did you draw these conclusions from? Is it merely the fact that points go up to +/- 24?
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I just won 20 straight games using 1/1/1 build against protoss and zerg. How do you calculate this?
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On August 18 2011 19:25 Fishgle wrote:
But. If i have a 0% chance of winning, how did i win?
I think you're confusing future odds with informed predictions due to past results.
Also, I doubt the system is that simple. Where did you draw these conclusions from? Is it merely the fact that points go up to +/- 24?
It shows 0% of winning because the amount of points won is an integer. Obviously each amount represents a certain range of odds you had at winning. For example a player you have 98% chance to win against falls somewhere between 0 and 1 points won range. Which one is it we can not know.
If blizzard rewarded point fractions then it's likely you would never win a full 24 points, precisely because that would indicate that this is a player that you can not beat.
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the points won for a match column is for winning streak or every single win?
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On August 18 2011 19:41 theang123 wrote:
the points won for a match column is for winning streak or every single win?
Every single win.
When you are on a long winning streak, the formula becomes less accurate. This is because MMR is very volatile and changes much faster than your points (this is the reason Blizzard added the entire point system, instead of simply telling us our MMR).
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so assuming i have 40wins and 25loses, how would the calculation be?
i think having an example is easier for ppl
______________________________________________________________
edit:
sorry OP i misunderstood the calculation.
we just have to see how many points we earn after winning a game to decide the winning rate.
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pretty cool 
how did you reach those percentages? studied samples of points + winratios?
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You're starting from the assumption that the range of possible point awards is mapped to the 0-bound at the top and bottom of the distribution. What allows you to make that assumption? It's possible that the max and min are set to a point on the bell curve where you've got a 90%/10% or 80%/20% chance of victory, isn't it?
To be fair, I think the assumption is reasonable, because you could otherwise create some oddness in the way points behaved at the extremes, but I'm still curious if you have some reason behind it other than that it makes sense it would be that way.
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On August 18 2011 19:51 MyNameIsAlex wrote:pretty cool how did you reach those percentages? studied samples of points + winratios?
I didn't study any samples of win ratios. I reached these percentages from the two assumptions that I mentioned in the OP. Let me clarify:
I am making a statement that for any given 2 players on battle net, if they were to play each other an infinite amount of ladder games (or a sufficient amount), then by the end of it their points will not change much. This is true for any 2 players, assuming that in the initial state their points closely reflected on their MMR, and that the players skill hasn't changed during their matches.
From this statement, I'm extrapolating that by seeing the amount of points won/lost, it's possible to know what odds the system places on each player winning.
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On August 18 2011 19:56 AmericanUmlaut wrote:
You're starting from the assumption that the range of possible point awards is mapped to the 0-bound at the top and bottom of the distribution. What allows you to make that assumption? It's possible that the max and min are set to a point on the bell curve where you've got a 90%/10% or 80%/20% chance of victory, isn't it?
To be fair, I think the assumption is reasonable, because you could otherwise create some oddness in the way points behaved at the extremes, but I'm still curious if you have some reason behind it other than that it makes sense it would be that way.
Take ELO system for example. It tries to adjust player ratings based off wins / losses in such a way, that no matter the skill difference of 2 opponents, if they kept playing and playing there will be little movement in their points. Otherwise it would be possible for top (or bottom) players to gain an edge and increase their rating by playing with players with a big skill gap from themselves. The same is true for the ladder system. If Blizzard allowed players to get 24 points for a win and lose 0 points for a loss by playing an opponent they have 10% win chance against, then a very effective method of increasing your points would be to play opponents whom you have 10% chance to win against.
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There is one HUGE assumption in all of this: the correlation is linear. For all we know, a 70% chance to win would still net you 11 points. The only certainties we have on this is 12 points is even, 0 is hugely favored, and 24 is hugely unfavored.
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On August 18 2011 20:21 aksfjh wrote:
There is one HUGE assumption in all of this: the correlation is linear. For all we know, a 70% chance to win would still net you 11 points. The only certainties we have on this is 12 points is even, 0 is hugely favored, and 24 is hugely unfavored.
If you got 11 points for beating an opponent you had 70% to win against, then after playing 10 games against that player you would end up with 38 more points than you started with (assuming 7 wins 3 losses). It would be extremely weird if the ladder system worked that way, because player's points would keep inflating massively.
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On August 18 2011 20:25 Not_That wrote:Show nested quote +On August 18 2011 20:21 aksfjh wrote:
There is one HUGE assumption in all of this: the correlation is linear. For all we know, a 70% chance to win would still net you 11 points. The only certainties we have on this is 12 points is even, 0 is hugely favored, and 24 is hugely unfavored. If you got 11 points for beating an opponent you had 70% to win against, then after playing 10 games against that player you would end up win 38 more points than you started with (assuming 7 wins 3 losses). It would be extremely weird if the ladder system worked that way, because player's points would keep inflating massively.
The points are inflating.. Look at Season 1 points.
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On August 18 2011 20:26 Giku wrote:Show nested quote +On August 18 2011 20:25 Not_That wrote:On August 18 2011 20:21 aksfjh wrote:
There is one HUGE assumption in all of this: the correlation is linear. For all we know, a 70% chance to win would still net you 11 points. The only certainties we have on this is 12 points is even, 0 is hugely favored, and 24 is hugely unfavored. If you got 11 points for beating an opponent you had 70% to win against, then after playing 10 games against that player you would end up win 38 more points than you started with (assuming 7 wins 3 losses). It would be extremely weird if the ladder system worked that way, because player's points would keep inflating massively. The points are inflating.. Look at Season 1 points.
What you're seeing are the bonus pool points causing fixed inflation. I am specifically discussing points not including bonus pool points.
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On August 18 2011 20:11 Not_That wrote:Show nested quote +On August 18 2011 19:56 AmericanUmlaut wrote:
You're starting from the assumption that the range of possible point awards is mapped to the 0-bound at the top and bottom of the distribution. What allows you to make that assumption? It's possible that the max and min are set to a point on the bell curve where you've got a 90%/10% or 80%/20% chance of victory, isn't it?
To be fair, I think the assumption is reasonable, because you could otherwise create some oddness in the way points behaved at the extremes, but I'm still curious if you have some reason behind it other than that it makes sense it would be that way. Take ELO system for example. It tries to adjust player ratings based off wins / losses in such a way, that no matter the skill difference of 2 opponents, if they kept playing and playing there will be little movement in their points. Otherwise it would be possible for top (or bottom) players to gain an edge and increase their rating by playing with players with a big skill gap from themselves. The same is true for the ladder system. If Blizzard allowed players to get 24 points for a win and lose 0 points for a loss by playing an opponent they have 10% win chance against, then a very effective method of increasing your points would be to play opponents whom you have 10% chance to win against.
This isn't a problem for Blizzard because you don't decide who you get to play against.
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On August 18 2011 20:39 Navillus wrote:Show nested quote +On August 18 2011 20:11 Not_That wrote:On August 18 2011 19:56 AmericanUmlaut wrote:
You're starting from the assumption that the range of possible point awards is mapped to the 0-bound at the top and bottom of the distribution. What allows you to make that assumption? It's possible that the max and min are set to a point on the bell curve where you've got a 90%/10% or 80%/20% chance of victory, isn't it?
To be fair, I think the assumption is reasonable, because you could otherwise create some oddness in the way points behaved at the extremes, but I'm still curious if you have some reason behind it other than that it makes sense it would be that way. Take ELO system for example. It tries to adjust player ratings based off wins / losses in such a way, that no matter the skill difference of 2 opponents, if they kept playing and playing there will be little movement in their points. Otherwise it would be possible for top (or bottom) players to gain an edge and increase their rating by playing with players with a big skill gap from themselves. The same is true for the ladder system. If Blizzard allowed players to get 24 points for a win and lose 0 points for a loss by playing an opponent they have 10% win chance against, then a very effective method of increasing your points would be to play opponents whom you have 10% chance to win against. This isn't a problem for Blizzard because you don't decide who you get to play against.
Even so, it makes sense for the system to be this way. Having a system designed in a way that encourages players to seek out opponents that are higher / similar / lower than themselves is inviting trouble. Players can choose the time of day they play for instance. By playing at hours when ladder is mostly empty they can sometimes find different skilled opponents. Stream sniping proves that players have some control over who their opponent is.
Even if players have no say about what opponent they get, there will be players who play opponents further in skill than themselves more than others simply by pure chance alone. Also consider the top / bottom players. They play players higher / lower rated than themselves regularly.
I think a good ladder system should be built according to the assumption that I made. I can't think of a reason why Blizzard's ladder system would behave differently.
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On August 18 2011 20:50 Not_That wrote:Show nested quote +On August 18 2011 20:39 Navillus wrote:On August 18 2011 20:11 Not_That wrote:On August 18 2011 19:56 AmericanUmlaut wrote:
You're starting from the assumption that the range of possible point awards is mapped to the 0-bound at the top and bottom of the distribution. What allows you to make that assumption? It's possible that the max and min are set to a point on the bell curve where you've got a 90%/10% or 80%/20% chance of victory, isn't it?
To be fair, I think the assumption is reasonable, because you could otherwise create some oddness in the way points behaved at the extremes, but I'm still curious if you have some reason behind it other than that it makes sense it would be that way. Take ELO system for example. It tries to adjust player ratings based off wins / losses in such a way, that no matter the skill difference of 2 opponents, if they kept playing and playing there will be little movement in their points. Otherwise it would be possible for top (or bottom) players to gain an edge and increase their rating by playing with players with a big skill gap from themselves. The same is true for the ladder system. If Blizzard allowed players to get 24 points for a win and lose 0 points for a loss by playing an opponent they have 10% win chance against, then a very effective method of increasing your points would be to play opponents whom you have 10% chance to win against. This isn't a problem for Blizzard because you don't decide who you get to play against. Even so, it makes sense for the system to be this way. Having a system designed in a way that encourages players to seek out opponents that are higher / similar / lower than themselves is inviting trouble. Players can choose the time of day they play for instance. By playing at hours when ladder is mostly empty they can sometimes find different skilled opponents. Stream sniping proves that players have some control over who their opponent is. Even if players have no say about what opponent they get, there will be players who play opponents further in skill than themselves more than others simply by pure chance alone. Also consider the top / bottom players. They play players higher / lower rated than themselves regularly. I think a good ladder system should be built according to the assumption that I made. I can't think of a reason why Blizzard's ladder system would behave differently.
Now this is silly, stream sniping affects literally about .0001 percent of the players on the ladder and no one is going to alter the time of day they're playing because it may or may not change the average skill of who they're playing, and honestly even if they did I have no idea how anyone would find out at all how average skill alters over time of day. Frankly I think most of this is useless anyway, the Blizzard matchmaking system is very good at placing people against others who have similar odds at winning, having a 10% chance to win or lose is going to be so rare as to not matter to the overall ladder.
Considering top/bottom I point out that this only affects the extreme top and bottom also something like .0001 percent, and they are going to continue in the direction they're going anyway because they're the very top or bottom.
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On August 18 2011 20:50 Not_That wrote:Show nested quote +On August 18 2011 20:39 Navillus wrote:On August 18 2011 20:11 Not_That wrote:On August 18 2011 19:56 AmericanUmlaut wrote:
You're starting from the assumption that the range of possible point awards is mapped to the 0-bound at the top and bottom of the distribution. What allows you to make that assumption? It's possible that the max and min are set to a point on the bell curve where you've got a 90%/10% or 80%/20% chance of victory, isn't it?
To be fair, I think the assumption is reasonable, because you could otherwise create some oddness in the way points behaved at the extremes, but I'm still curious if you have some reason behind it other than that it makes sense it would be that way. Take ELO system for example. It tries to adjust player ratings based off wins / losses in such a way, that no matter the skill difference of 2 opponents, if they kept playing and playing there will be little movement in their points. Otherwise it would be possible for top (or bottom) players to gain an edge and increase their rating by playing with players with a big skill gap from themselves. The same is true for the ladder system. If Blizzard allowed players to get 24 points for a win and lose 0 points for a loss by playing an opponent they have 10% win chance against, then a very effective method of increasing your points would be to play opponents whom you have 10% chance to win against. This isn't a problem for Blizzard because you don't decide who you get to play against. Even so, it makes sense for the system to be this way. Having a system designed in a way that encourages players to seek out opponents that are higher / similar / lower than themselves is inviting trouble. Players can choose the time of day they play for instance. By playing at hours when ladder is mostly empty they can sometimes find different skilled opponents. Stream sniping proves that players have some control over who their opponent is. Even if players have no say about what opponent they get, there will be players who play opponents further in skill than themselves more than others simply by pure chance alone. Also consider the top / bottom players. They play players higher / lower rated than themselves regularly. I think a good ladder system should be built according to the assumption that I made. I can't think of a reason why Blizzard's ladder system would behave differently.
Like I said above, I think your assumptions are reasonable from the standpoint of what makes sense for a ladder system, but based on what you're saying, they are just assumptions and not observations or logical deductions based on observations. There are no natural or mathematical laws forcing Blizzard to design its ladder system well, and based on the parts of b.net that we can observe well, it seems reasonable to suppose they might not have.
Since you'll never (or rarely) face the same opponent many times, the ladder could be built with the goal that your points will stay the same over a very large number of games against the opponents the ladder picks for you, rather than the ELO concept that they'd stay constant against a given opponent. Which means that the earlier poster's idea that the point distribution could be nonlinear would still work, and so would mine that the cutoff points aren't at the 0 bound, since the resulting point drift would be cancelled out by the fact that you're playing opponents both stronger and weaker than yourself.
What you might be able to do to get a better foundation for your assumptions is to go find the b.net game histories of high-level professional players, who in fact are generally matched up against people only on one side of the spectrum from themselves. If you can demonstrate that there is neither upward nor downward drift, that would bolster your argument somewhat, though you'd still have the issue that skill changes over time.
Again, I don't actually think you're wrong, but if we're going to do this kind of thought experiment without evidence, we should really consider the possibilities and not just assume that the most intellectualy pleasing solution is the right one.
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EPT
