# Statistical measures of ideal pro strength [#217]

BobMyers: Statistical measures of ideal pro strength (2005-12-14 09:41) [#740]

AshleyF: A quote from Bruce Wilcox's book EZ-GO: "People have asked how much stronger than a professional player is God? While the match has yet to be played, most estimates place God three ranks above top professionals. One pro is reported to have said he wouldn't bet his life against God without a four-stone handicap."

I understand the AGA rating system assumes that a player one stone stronger will win 83% of the time, and two stones stronger 97%. Seems high to me, but in any case maybe these kinds of numbers can be used to address "how strong God is".

Two pros of roughly the same strength each obviously have a 50% of winning. But in many commentaries on pro games, you see a comment such as "if W had only played this move, he would absolutely have had a winning game." Let's assume such situations arise in 50% of all games. In half of those games, White would have won anyway, but the other half would give her the win instead of Black. In other words, her winning percentage would rise to 75%, not that far away from 83%.

In other words, TYPICAL PRO ANALYSIS is one stone stronger than TYPICAL PRO PLAY.

We can now restate the problem of how strong God is by asking, "How many times stronger is God vis-a-vis to the typical go player, compared to how strong the typical pro analysis is vis-a-vis the typical go player?" If the answer is "4x", then God is indeed four stones stronger than top pros.

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BobMyers: Re: Statistical measures of ideal pro strength (2005-12-15 08:17) [#754]

Going back to the original topic, let's now assume for the sake of argument that a 67% winning ratio indicates a one-stone difference, and an 83% winning ratio a two-stone difference. That means that a 75% winning percentage corresponds to approximately a 1.5 stone difference in strength.

If you accept that the collective wisdom of pros analyzing a game finds clear winning lines in one of two lost games, that corresponds to a 75% winning percentage. In other words, such collective human analysis-based strength is 1.5 stones stronger than normal pros during games.

The reason for this approach is that it gives us a potential foothold to think about the strength of God problem. Instead of merely imagining how much stronger he is than pros, we can ask how much relatively stronger he is to pros than collective pro analysis is to pros.

If we assume that His relative margin of strength over pros is three times that of collective pro wisdom, which would seem relatively uncontroversial, that would put him at 4.5 stones stronger than pros.

DaveSigaty: Re: Statistical measures of ideal pro strength (2005-12-17 02:34) [#767]

Bob, I wonder where you get the figure for analysis finding a clear win in one of two lost games? Improvements, yes, but clear winning lines? Having cable television in Tokyo I have watched a lot of the pro analyses on Igo Shogi channel for the last year and a half. I do not think that the idea that half the time - "If only White had played here, she would have won" - stands up. All we really know is that if White had played better then she would have done better. However, the same goes for Black prior to that point in the game, and White prior to some earlier point, etc., back to the start of the game. Doesn't this just take us back to the original topic? :-)

AlexWeldon: ((no subject)) (2005-12-14 14:18) [#742]

Alex: 83% for one rank difference? That sounds really, really high to me. By that logic, I should be able to win something like 5 out of 6 games against someone my level, if only they give me Black with no komi. I wouldn't place money at 5:1 odds in such a game, and I'm pretty sure you don't see that kind of Black/White win ratio in classical games from the pre-komi days.

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malweth: Re: ((no subject)) (2005-12-14 15:21) [#743]

you assume a handicap (black, no komi).

If you are one stone weaker than your opponent, then taking black without komi should give a 50% chance to win (since you are, in effect, playing equally after handicap). This is not necessarily true for the weaker player where 6 stones often doesn't make much of a difference.

Playing equally, the player who is one stone stronger in rank should win approximately 4/5 of the matches. Weaker ranks usually have higher standard deviation but aside from that the approximation should still hold.

Using komi also assumes that games go into the endgame. This is not the common case however - it is much easier to use a handicap stone than the extra komi.

AlexWeldon: Black, no komi. (2005-12-15 14:28) [#758]

Sorry, I should have explained myself more clearly, since it looks like people didn't get what I was saying. I'll try again.

If playing black with no komi is the correct handicap to equalise a game between players one rank apart in playing strength, then playing with such a handicap against an equally ranked opponent should be equal in difficulty to playing someone one stone stronger in an even game with komi. If a 3-dan could beat a 2-dan 87% of the time in an even game, but only 50% of the time if he gave Black, no komi, then he should be able to beat another 3-dan 87% of the time if he was given Black with no komi. I don't think I could beat another 3-dan 5 games out of 6 if my only advantage was taking Black without komi. So the estimate of 87% for one rank difference seems very high to me. If you look at the percentage of wins between unevenly matched opponents in even games given here, it's around 65% for one stone difference for most of the low kyus and dans.

malweth: Re: Black, no komi. (2005-12-15 15:09) [#759]

Could you beat a 4d 87% of the time after taking 2 stones? I'm fairly positive I could beat an AGA 2k given that advantage.

A handicap is only useful if you know how to use it. I'm not sure about a 3d but I'd imagine it's about the same for a 3k -- playing B with no komi would only be useful in about 10% of my games.

66.38.216.89: Re: Black, no komi. (2005-12-16 17:40) [#764]

Alex: No, I don't think I could beat a 4-dan 87% of the time with two stones. Two stone handicap is never quite as big as it seems. I do think I could win two-thirds of the games, though, which is about right.

tderz: Re: winning percentages if taking Black without komi (2005-12-15 14:55) [#744]

1 rank difference is usually set to 1 stone difference if playing handicap.

If not using handicap, there is (seems to be) a a correlation of winning p=67% (don't nail me on that value, it can be different) of games against a player one stone weaker (if not equalized by handicap and/or komi).

When using the ELO ranking system (please check out the original article at gobase or at the EGF site), this winning expectancy is compared with the actual results and players get awarded points added/deducted according to the probability of their results. (Each) delta = 100 points difference should then relate to a winning probability of p (resp. 1-p) and in an ideal world - (each one) grade difference in rank.

The ideal world is somewhat distorted (50 ELO points?) by Black starting even games and GIVING komi, while White starting handicap games and NOT GIVING komi (advantageous).

Hence, one will get skewing, kurtosis at bigger delta and some swivelling distortion at delta = +/-0.

Because this affects all players, which is a big number, tournaments are usually played on even, few tournaments are ONLY played with handicap, the whole system functions (seems to be stable, no known de-/in-flation know to me). Furthermore at delta >= 900, everything can happen.

83% seems to be more the equivalent of a 2-stone handicap.

"5 out of 6 games against someone my level, if only they give me Black with no komi." This sounds like 1/2 (one half or 0.5) handicap, if the other one has the same strength.

If the relation was linear (I guess it's not), if a 1-stone handicap gives a winning percentage of 67%, then 0.5 stone handicap => 58.5% which means I would bet more (and safer) on (100%/8.5% = 1/12) on 7 games out of 12,
resp. 7:5 (esp. if we are not pros).

Greetings, Tommie

NB: (several days later) I am not sure anymore wether "Black with no komi" is 0.5 handicap, if the other one has the same strength, it might be in fact 1.0 handicap.
That'd change the calculation to 67%/100% =ca. 4 out of 6.