Chess psychometrics – Female privilege II

In the last post we have seen that women on average bring fewer Elo points to the table if they draw tournament chess games against men. Fewer than if they would play other women and fewer than men would require to draw against men.

One explanation for this would be that men are more inclined to make disfavorable draws against women. In this scenario men would willingly donate Elo points to women instead of pushing for a win. Maybe because they try to specifically show goodwill to female opponents, maybe because they just can’t muster the same aggression as against male players.

However, this statistically robust phenomenon could also be due to confounding. The most realistic confounder is age or speed of improvement. Young players improve quickly. Therefore they will generally be stronger than their rating implies. This of course results in the effect that they will on average be lower rated than their opponent in drawn games.

To make sure that we are not chasing a chimera we bin our Elo differences by age for both male and female players against male opposition. Then we can look for each age group separately whether women have „drawing privilege“ compared to males of the same age. This takes care of the improvement issue, in fact it probably overcorrects, because boys probably improve a little faster.

The following plot shows the number of games for each 5 year age span.

Here we have to confront an ugly truth: Our unique identification of players is not very unique. There aren’t actually any player of the age 0-5 and not many more at the age of 90+. These are noise, due to misidentification. However, the age groups 15-35 rise far above the noise, indicated in the figure by the black line, so this is the area where our results may be reasonably accurate. Additionally, we have to take the possibility into account, that the Elo difference in drawn games is an underestimate diluted by misidentified and possibly misgendered players.

Here are the corresponding Elo difference between male and female drawing players. Inside the black box are the observations where the sample number rose above the noise line in the earlier plot. The age groups 10-15 and 45-50 should maybe also be removed, but they fit the overall trend even if 10-15 is a major outlier.

So what do we observe? The female drawing privilege drops steadily with age. At age forty it is only half of what it used to be at age twenty. The effect size is slightly smaller, so maybe having many young players did make a difference. Overall we see that our results are not confounded by age. In fact they fit the theory very well that men are unwilling to try hard to beat young women.

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