They must … [renounce]
The faith they have in tennis, and tall stockings …
And understand again like honest men …
—William Shakespeare. The History of Henry VIII (1612).
The latest news from the world of tennis is about the recent remarks of one Raymond Moore, the 69-year-old CEO of the Indian Wells Tennis Garden. Indian Wells was the site of last week’s professional tournament, which was won (on the woman’s side) by, as it happens, the chief example of tennis’ commitment to “diversity,” Serena Williams—an irony that merely highlighted Moore’s remark, prior to the final women’s match, that in his next life “I want to be someone in the WTA [Women’s Tennis Association] because they ride on the coattails of men.” Naturally, the national press conducted the usual harumphing about Moore’s obvious affliction with old white guyness—another in the series of episodes by which, as Professor Walter Benn Michaels of the University of Illinois at Chicago might put it, the differences between the pay of men and women is fiddled with and weighed in the balance, but it’s never mentioned that the levels of pay under examination are simply light-years away from that of the average person; as Michaels put the point in The Trouble With Diversity, “making sure the women of the upper class are paid just as well as the men of the upper class” is not really a bold strike for the future of humanity. But that’s why the most interesting account of the episode, I think, can be found at The Atlantic, where—although Adam Chandler in no way refers to the fact that this is a dispute between different varieties of multimillionaires—he does have the presence of mind to refer to a story from last fall by Carl Bialik at FiveThirtyEight. That story is about the differences in structure between the men’s game and the women’s game—a story that at least makes a gesture in the direction Michaels would have us go because, unlike so many current forms of discussion in the academy and elsewhere, Bialik understands the significance of math and probability.
In his piece, “Serena Williams Is Getting A Raw Deal By Only Playing Best Of Three Sets,” Bialik takes off from a paper by “a statistician at the RAND Corp.” named Stephanie Kovalchik, and begins by observing the key structural difference between the men’s game in tennis and the women’s: the fact that, in Grand Slam events (the four biggest tournaments of the year: the Australian Open, the French Open, Wimbledon, and the U.S. Open) the men play five sets per match, instead of the ladies’ three. It’s a difference that might appear trivial—after all, Bialik notes, ladies’ matches routinely take longer than the men’s matches at Grand Slam events despite the fact that men must win three sets to the ladies’ two to complete a match. Yet, in reality, it is a difference that makes all the difference—it goes a long way towards explaining just how the CEO of Indian Wells can view women’s tennis as “riding on the men’s coattails.”
Moore’s comments that is followed statements over the past year by two high-ranking men’s players, Novak Djokovic—ranked first in the world and winner at Indian Wells—and Frenchman Jo-Wilfried Tsonga, statements that implied that, while professional tennis has awarded equal pay to both men and women players for decades, male players ought to be paid more because, as The Atlantic’s Chandler wrote, “they attract high[er] viewership.” In turn, the reason apparently often advanced for that higher viewership on the men’s side is that women’s tournaments have a higher volatility: that is, it is more likely for top-seeded men to reach the final matches of a tournament than it is for top-seeded women, an intuition that has been borne out by research. For example, Bialik notes that in last year’s U.S. Open, “only three of the top 10 women’s seeds reached the third round, while nine of the top 10 men’s seeds did.”
In tennis, it seems, fans would rather root for players they already know than players they don’t—a phenomenon also witnessed in golf, where for many years television networks rooted for Tiger Woods to be in the lead or close to it during the tournament because that would have a positive effect on ratings. Tsonga, like Djokovic, have publicly either outright stated or implied that the higher volatility in the women’s game is due to women’s “hormones”—what the paper by RAND’s Kovalchik suggests on the contrary is that the higher volatility of the women’s game does not have to do with women’s bodies, but does have to do with the women’s game’s three-set structure. In other words, the familiar “nature vs. culture” dichotomy so beloved by many in the American humanist academy has little ability to explain what’s going on here.
What does have explanatory power is, Bialik says, the fact that women play best-of-three sets and men play best-of-five in the Grand Slam tournaments. Because they are the only tournaments that have that difference—in all other tournaments women and men play the same number of sets—these data sets can be compared, which is what Kovalchik has done. What she found, Bialik reports, is that “women are no less consistent than men when competing under the same format.” In other words, while upsets—matches in which the lower-seeded player bests the higher-seeded player—happen at about the same rate in tournaments conducted under a best-of-three format, in Grand Slam tournaments (the ones with the highest interest for tennis fans) “upsets are much more common for women than for men.” Obviously, that suggests that the reason why those upsets are more common is because of the format, not because of “hormones.” “Generally in sports,” as Bialik says, “the longer the contest, the greater the chance the favorite prevails”—which is to say that the relevant distinction here isn’t the one between “nature” and “culture” so precious to academics in the humanities, but also that the relevant “natural law” here isn’t the biological differences between men and women. Instead, what’s important about Kovalchik’s research is what scientists and mathematicians call “the law of large numbers.”
According to Wikipedia—itself perhaps an example of the very phenomena in question—the “law of large numbers” describes how “the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.” As an example, the article observes that “while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins.” In short, favorites tend to prevail in Grand Slam contests—but only male ones—simply because the favorites have more opportunity to overcome chance than they do in other tournaments.
What that would imply, in turn, is that the suggestion that men ought to get more money because their matches receive higher ratings is an argument that may be built on sand: it’s got nothing to do with women as women that their matches receive lower ratings, but simply because the format of their game is different. On the other hand, however, it also suggests that Walter Benn Michaels may be on to something when he criticizes his fellow colleagues in the American humanistic academy: by framing conversations about social justice in terms of the difference between something called “culture” and something called “nature,” American humanist academics may actually be retarding, not forwarding, social justice—because the very distinction is itself not relevant to at least some discussions about justice. What that in turn might mean is that the game of American political discussion is about to change radically—with a suddenness, and severity, that may be of a surprise much greater than the one that greeted Raymond Moore.