It turns out that does not skew things.
Think about it like this.
Imagine we start by deleting ALL games played between men and women. And we first do our optimization for just the men. What would we see?
The men would look like they do now. We always can shift the ratings up or down without affecting things. We could make SVB 900 if we want. Then everyone else would just go up 78 points. But let's leave it the way it is--just the men with SVB at 822.
Now, we optimize just the women. They would look about the way they do now. But we'd have to decide how to shift them up or down. Perhaps we decide to make Siming the same as SVB, 822. Then all the other women would be about 40 points above what you see now and there would be no reason to think a man's rating and a woman's rating can be compared. We just wouldn't know.
So we have Siming at 822, Karen Corr at 760 or so, Kristina Tkatch at 740 or so, and so on.
Now we start adding in the coupling games. And this is where people's intuition about what to expect may not be very good. Suppose the first match we add (and the only match) is Wilkie 12 Siming 4. For this match Siming is performing 167 points below Wilkie and there are no other forces between the groups. So Siming goes to 584, Karen to 520, and Kristina to 500. In other words this one match completely decided how the women are shifted compared to the men. It doesn't matter that Kristina has all her games against women or most of her games against much weaker women. Now add in another 141 Siming/men games and the 122 Chezka/men games and 43 Fu/men games i mentioned. Now there are about 300 games rather than 16 determining the big shift. At this point there is about a two thirds chance the shifting is right within 15 points. Siming could be at 770 or at 800. But she's pretty unlikely to be at 745 or 815.
Now we add in Karen Corr's couple thousand games against men. Now there is a pretty good chance the shift is right within maybe 6 points.
Now we add in many more thousands of games from top-100 women played against men. Melissa Herndon alone has played many hundreds of games against men on the Mezz West State tour. Oscar and Vilmos are both rated 773. Just against Oscar and Vilmos Melissa has played 73 games (23 wins 50 losses). that's performing 113 points below them, 660. Her rating is 663. And of course she's also played Rodney and Edgie Geronimo and Ellerman and Ernesto and and Butera and on and on. And Melissa has played a lot of 600 and 550 male players. And if she didn't beat them the way she is supposed to, that would affect the shift.
There are several more Melissa's. And then the bulk of 550 and 600-level women that play top women's events in the USA also go back and play in weekly and regional tournaments and league and so forth against the men.
There is a lot of coupling.
