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Analysis on pro game winning probabilities.
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Author:  Ootakamoku [ Sat Mar 30, 2013 6:36 am ]
Post subject:  Analysis on pro game winning probabilities.
I have been writing a ranking algorithm for go for a while now. So I made some research into how likely is a win when player x stones weaker. Ofcourse EGD provides some solid stats that can be used as a starting point, clearly demonstrating the stronger the players are, the more unlikely it becomes for the weaker player to win.

Since x to power of strength difference multiplied by 0.5 seems to nicely predict the chance of winning, given the correct x. I figured I can use KGS high dan games as a way of calculating the x, by using games where same players have played against each other multiple games, with different handicaps. The magic number I got was 0.3847. Which produces probabilities of 1 stone 80.7%, 2 stones 92.5%, 3 stones 97.1%. Now if we look up the corresponding values for EGF 7dan games over the last 8 years, from EGD we have 82.0%, 92.5%, 97.1%. Pretty accurate match.

Now for the kicker.. when I ran the same algorithm for GoGoD, which contains 60.000 pro games, the numbers I get are...

1 stone 95.6%, 2 stones 99.6%, 3 stones 99.9% !!!

Looking at EGD statistics when playing against someone 2 stones weaker, the probability of winning is 60% for 9kyu, 61.8% for 5kyu, 66.7% for 1dan, 77.4.6% for 4dan, 92.5% for 7dan. In that light, the 99.6% for pro players might just be believable but still quite surprising for me.

Ohwell, have to keep looking trough the GoGoD to try to find the reason for this weird result, still kinda refuse to belive it would be correct.
Author:  Bill Spight [ Sat Mar 30, 2013 7:38 am ]
Post subject:  Re: Analysis on pro game winning probabilities.
What do you consider to be a one stone difference in pro games?
Author:  Ootakamoku [ Sat Mar 30, 2013 8:35 am ]
Post subject:  Re: Analysis on pro game winning probabilities.
Bill Spight wrote:
What do you consider to be a one stone difference in pro games?


I convert whatever handicap stones and komi there is into an amount of handicap (in stones). So a normal 2 handicap stone game, would be 1.5 handicap stones by that scale. Maybe I didnt understand your question tho.
Author:  Ootakamoku [ Sat Mar 30, 2013 8:36 am ]
Post subject:  Re: Analysis on pro game winning probabilities.
Just realized my mistake, some older games contain no handicap, but black moves first. I naivly assumed that no handicap stones meant w moves first. Duh.
Author:  Ootakamoku [ Sat Mar 30, 2013 9:32 am ]
Post subject:  Re: Analysis on pro game winning probabilities.
Phew! It handles correctly no handicap black moves first games now. And the results look alot more reasonable too.

1 : 85.8%, 2 : 95.9%, 3 : 98.8%,

They are slightly harsher than comparable numbers for EGF 7dan, which makes sense as there are more strong players in GoGoD than your average EGF 7dan.

1 : 82.0%, 2 : 92.5%, 3 : 97.1%.
Author:  HermanHiddema [ Sat Mar 30, 2013 10:46 am ]
Post subject:  Re: Analysis on pro game winning probabilities.
typohh wrote:
I have been writing a ranking algorithm for go for a while now. So I made some research into how likely is a win when player x stones weaker. Ofcourse EGD provides some solid stats that can be used as a starting point, clearly demonstrating the stronger the players are, the more unlikely it becomes for the weaker player to win.


Note that the EGD data is inherently biased, because almost all tournaments use the McMahon system. When, for example, a 2k plays a 1d, that usually happens when the 2k has won twice more than the 1d (e.g. the 2k has 3/4 while the 1d has 1/4). In those situations, there is already a strong pre-selection present. The 2k with 3/4 is probably a stronger 2k than one that has 2/4, while the 1d with 1/4 is probably a weaker 1d than one that has 2/4. So this game is probably between an above average 2k and a below average 1d. This pre-selection effect gets stronger as the rank difference gets larger.

The problem is mostly absent for games between players stronger than 3d, because they usually play above the McMahon bar and therefore start on even terms regardless of their rank.
Author:  Bill Spight [ Sat Mar 30, 2013 11:02 am ]
Post subject:  Re: Analysis on pro game winning probabilities.
typohh wrote:
Bill Spight wrote:
What do you consider to be a one stone difference in pro games?


I convert whatever handicap stones and komi there is into an amount of handicap (in stones). So a normal 2 handicap stone game, would be 1.5 handicap stones by that scale. Maybe I didnt understand your question tho.


What I mean is that among amateurs a 1 rank difference approximately equates to a 1 stone difference in handicap. That is decidedly not true for pro games, and has been different at different points in time.

Also, a one rank difference between amateurs should mean that the weaker player wins about 50% of the time if he takes 2 stones half the time and plays Black half the time. However, traditional custom was for him to simply play Black. That means that White should win more often. Maybe 70.7% of the time. :)
Author:  Ootakamoku [ Sat Mar 30, 2013 1:03 pm ]
Post subject:  Re: Analysis on pro game winning probabilities.
Bill Spight wrote:
What I mean is that among amateurs a 1 rank difference approximately equates to a 1 stone difference in handicap. That is decidedly not true for pro games, and has been different at different points in time.

Also, a one rank difference between amateurs should mean that the weaker player wins about 50% of the time if he takes 2 stones half the time and plays Black half the time. However, traditional custom was for him to simply play Black. That means that White should win more often. Maybe 70.7% of the time. :)


Urm, I dont use the players actual ranks for anything. I simply pick games, where the same two players have played multiple games with varying handicap. For example tagai-sen. We have the same two players playing multiple games, giving each other effectively 0.5 stone handicap. Provides perfect setting for calculating the winrate gain from 1 stone advantage.
Author:  hyperpape [ Sat Mar 30, 2013 1:32 pm ]
Post subject:  Re: Analysis on pro game winning probabilities.
HermanHiddema wrote:
Note that the EGD data is inherently biased, because almost all tournaments use the McMahon system. When, for example, a 2k plays a 1d, that usually happens when the 2k has won twice more than the 1d (e.g. the 2k has 3/4 while the 1d has 1/4). In those situations, there is already a strong pre-selection present. The 2k with 3/4 is probably a stronger 2k than one that has 2/4, while the 1d with 1/4 is probably a weaker 1d than one that has 2/4. So this game is probably between an above average 2k and a below average 1d. This pre-selection effect gets stronger as the rank difference gets larger.
I wonder if one could correct for this by using post-tournament ratings?
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