More stats on women at the WSOP

A few days ago I presented a rudimentary statistical analysis showing, I believe, that women in the WSOP Main Event performed less well on average than the men did, in terms of surviving to the money. I wanted to do another test of how the women cashing did compared to the men cashing, in terms of final standings, but I couldn't do it until now. With the last female in the field eliminated a few hours ago, I can now proceed.

First, though, I have to admit a small problem. I was told that 13 women cashed. This apparently came from Nolan Dalla doing a hand count of the field when the bubble was reached. I have been able to find no list of the names of these women. From news reports of those who went deepest, plus a little detective work, I have been able to identify 12 women in the list of the payouts. But if there were 13, I sure can't figure out who the 13th one is. I've checked a whole bunch of gender-ambiguous names on the list, using several sources (such as Google image search), and can't find whoever the last one is--if Dalla is right about the number.

The 12 I confidently identified (name, finishing spot):

Moutinho, 29

Musumeci, 62

Crawford, 85

Callaway, 203

Koerner, 299

Luu, 310

Naugoks, 391

Renaud, 398

Rousso, 511

Andrews, 521

Kerstetter, 590

Gazes, 609

Fortunately, I can do the math with just 12, though in order to do so, I'm going to have to pretend that there were only 12 women cashing, along with 680 men, for a total of 692--even though there were really 693 in the money. Because I don't know where the missing data point is, it won't systematically skew the results; it will just make them a little less robust. (However, because the number of women became smaller as the event wore on, and those remaining got more media attention, I'm positive that the missing woman--if there indeed is one--did not finish above the 142nd spot, when it was widely reported that only three women were left, and she is much more likely to be among the earlier exits than the later ones.)

I'm going to run what's called the Mann-Whitney U-test, which you can read a little about here. Basically, you put all your data points in order, then perform a statistical test on their rankings to determine if those with characteristic A are, on average, more toward the high end of the list, more toward the low end of the list, or similar in distribution when compared to those with characteristic B.

You enter lists of the rankings into an online calculator such as this one, and it spits some numbers back at you. In this case, I did it two ways. The first time I entered the raw place-finishing numbers in as two datasets and let the software do everything else. The second time I calculated the value of C myself (it's the sum of the number of men each of the 12 women bested, in this case 4230), then directly entered the values for n1, n2, and U. Both methods gave the same results, giving me confidence that I did it all correctly.

The bottom line is this: The p-value of the resulting statistical test is 0.83, which means, roughly, that if we ran the tournament a whole bunch of times from where things stood when the money bubble burst, we would see at least this level of difference between the sexes' average subsequent performance by chance alone 83% of the time.

In other words, the women's performance, once in the money, was not statistically distinguishable from that of the men. Put yet another way, the distribution of the women's final standings is very much what one would expect if one just randomly picked 12 out of the last 692 finishers. Their results do not tend to cluster meaningfully toward either the high or the low end of the list.

So once this group of women hit the money, their results were completely comparable to the men. Of course, this is a very small sample, so the test does not have a lot of resolving power. But to tell you the truth, I was expecting, based on the previous results, that the women in the money would be sufficiently clustered low in the standings that their mean performance would be demonstrably lower than the men's collective average. It was not so.

You can get a sense of this graphically, too. Below is a plot of the women as pink dots against the blue line of the men in the money. (I swear I did not pick those colors; they are what the Excel chart wizard chose by default!) It is, strangely, oriented with the best lower on the left, though that doesn't really matter. (It's late and I'm too tired to figure out how to make this just a horizontal line the way I originally envisioned it.) Click on it for the bigger version.

Even without running any numbers, you can basically eyeball it and see that the women are not noticeably clustered toward the top or bottom of the line.

The only odd thing is how they tend to show up in pairs, one going out soon after another of her kind. It's probably rooted in the same biological phenomenon that causes women always go to the restroom together, but that's one of those mysteries to which we men are doomed to stay eternally ignorant.

Conclusion: As far as can be determined with the very small sample, once female players reached the money, they performed, on average, as well as the men did in terms of finishes--in striking contrast to the most likely conclusion about women's performance from the start of the tourney to the money bubble.