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I think not quite but almost. Suppose Fedor and Kristina are 100 points apart. That means Fedor has a 2/3 chance of winning each game and Kristina a 1/3 chance. If they play 81 games, Fedor is expected to won 54 and Kristina 27. Now suppose we look at those 81 games as 27 groups of 3 We...

Think of the 2-to-1 race. For the stronger player to win he must win the first 2 games. The chance of doing that is 2/3 X 2/3 which is 4/9, a little shy of half. As the race gets longer, as you show, the difference gets smaller.

Here are the current top 100 players in Asia by Fargo Ratings

Two things. First those lists require 300 and not 200 games. The second one is the bigger one. To avoid having long retired players on the “top player” lists, we exclude players with fewer than 150 games last 2 years. This is normally not a stringent requirement. But if Asian players are not...

I don't know what you mean by stopping the analysis at 730. I'm presenting all the data as clearly as I can. The top 8,000 players, roughly the top 10% of established players, are 3% women. That's down from the roughly 10% women in the entire population, consistent with much observed fact that...

These are the direct matchups we have between Siming Chen and Han Yu during that decade

No. I think FargoRate approach would faithfully reproduce an actual non-normal distribution of skill. What will still be normally distributed, though, is the error/statistical fluctuation of each rating. This may cause some smoothing. As one example, imagine first the distribution of all APA...

Amongst established players, the top 100 go down to 789 and includes 3 women. This below is from a list of Chinese players in the APP and includes all 3 women. The world top player lists have restrictions that exclude some of the players.

This is all 121,400 players with 100 or more games in the system. The average is 465 and standard deviation 108. As we get more players into the system, the left side will build up more than the right and the whole curve will seem like it is just sliding to the left and keeping the same shape.

Siming Chen, han yu, and sha sha Liu are all 793 or higher and amongst the top 100 established ratings.

Ratings of any large group of players seems to be normally (bell curve) distributed. Standard deviation usually around 100 to 110. This photo is from my Facebook profile. I think it was all established players at some point.

Here is the idea. Let's make the hypothesis that the unknown distributions of talent (potential) for men and women look like this. That is, in a universe where equal numbers of men and women play and train and there are no social factors, the distribution of skill for men and women are shifted...

Some may be interested in this discussion on the issue

Another factor besides simple numbers (fewer women playing) is the nature of the culling of the populations of players--how meritocratic is it? We might find 10,000 males and 1,000 females play and compete with a certain level of commitment. At first glance if there are no inherent differences...

Nice job.

Thanks for the clarification.

Clearly Brett plays APA league and that is off our radar He also plays in a Thursday in-house 9-Ball league that uses LMS and a Tuesday traveling league that uses LMS. In the last 3 months, he has 160 league games going into FargoRate. In that same 3 months, Brett has 10 tournaments totaling...

Even though games from APA leagues and tournaments have not been going into FargoRate, many of the high finishers in this tournament have well established ratings. Number of games in FargoRate in parentheses. https://compusport.ca/CS/GeneralSearch/Index/11130?callFromHomePage=True Final 8...

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