How Best-of-Five-Set Matches Benefit Dominant Male Tennis Players

This post was inspired by an article on The Economist, which went through some possible explanations for why, in recent years, the best male tennis players have dominated Grand Slams more than the best female tennis players. An addendum at the end of the article noted that part of the reason for this is that women’s matches in Grand Slams are three sets, while men’s matches are five sets, therefore making upsets more likely in the women’s game.

Not being able to calculate probabilities in my head, I was curious to see how the different match lengths affects the chances of the “better” player winning the match. Assume that a given male player and a given female player have the same probability of winning a particular set. The tables below show, for selected probabilities of winning a set that are greater than 0.5, the probability of those players winning a particular match, if their probabilities of winning a particular set remains constant. They also show the probability of those players winning a Grand slam tournament (although more caution should be taken with these probabilities, given that a player’s probability of winning a particular set is likely reduced as they progress through the tournament).

	Probability of winning match
Probability of winning set	Female	Male
0.5	0.500	0.500
0.6	0.648	0.683
0.7	0.784	0.837
0.8	0.896	0.942
0.9	0.972	0.991

	Probability of winning Grand Slam
Probability of winning set	Female	Male
0.5	0.004	0.004
0.6	0.031	0.047
0.7	0.143	0.241
0.8	0.415	0.620
0.9	0.797	0.933

So the fact that men play five sets does make a bit of difference to a dominant male player’s chances of winning a Grand Slam match (and the tournament) compared to a dominant female player’s. But it doesn’t look like it’s enough to primarily explain the greater recent dominance of Federer, Nadal and Djokovic compared to the top female players. Also, as noted in the article, there have been long periods when the top female players have been more dominant (Graf, Seles, Navratilova, Evert, etc), so the set structure just favours the top male players being more dominant, it by no means guarantees it.