Column: Tennis broken down by the numbers

Thinking about the NBA in this way led me to think about other sports in which this might be the case. To fit the idea, we need something in which perfection in some area is expected and demanded and the level of skill is so high that single mistakes can doom you instantly.

So what jumps immediately to mind for these criteria, besides the NBA? Well, obviously, Sauron (I’d say that one single mistake doomed him pretty significantly — how do you leave Mount Doom undefended like that?) and COS 226: Algorithms and Data Structures (A 90 percent average grade on the midterm? Really?), but since we’re talking about sports here, let’s go in a different direction: men’s tennis.

These days, it seems like if you convert a break point in a men’s tennis match, the match is yours. It also seems like the player on serve win almost every point when they hit a first serve that stays inside the lines. To test these beliefs, I ran a quick study on 31 games from the third round and beyond of the 2009 US Open. I know that’s not a huge sample size, but a fellow can’t just spend all day researching tennis, can he? I mean, dang.

The data tells us, right off the bat, that break points are a pretty major factor. While this argument might be slightly tautological, the fact that 71.2 percent of the break points won were by the eventual match-winner, as opposed to just 54.4 percent of total points, at least suggests that they are of paramount importance. Looking at the serving data, we find that in the last five rounds of the 2009 US Open, 61.2 percent of first serves were put in play, and 72.5 percent of those put in play were won. Counting double faults, servers won 51.9 percent of second serves, for an overall winning percentage of 64.5 percent of points for the server. That might not sound too ridiculously high, but when you consider that there are not many possible states in a tennis game, it actually becomes quite major.

It is not difficult to run through the possible scoring states of a tennis game and their likelihoods given the probabilities that the server will win as given above. Having done so, you know what’s crazy? The server winning 64.5 percent of the points gives him a whopping 82.1 percent chance of winning the game! This, of course, assumes things that cannot be proven but are used for convenience, like constant probability for each point regardless of the past. No wonder break points are so important. On the contrary, if the server wins 51.9 percent of the points (the second-serve statistics), he has about a 54.7 percent chance of winning the game.

So what if we eliminated faults in men’s tennis? This would turn every serve into a second serve and could lead to more interesting game theoretic strategy. With a fault available, most men’s tennis players go all out on the first serve, which yields a fault around 40 percent of the time (according to my data), and when they do fault, they scale their speed back on the second serve in favor of accuracy. With that safety net eliminated, I think you would see some interesting results. Theoretically, most players would play more conservatively (if you counted faults as lost points, only 44.4 percent of first serves produce a won point), but the element of surprise when your opponent expects a conservative serve and you launch an aggressive serve at him might make up for that sometimes.

To those who would say that this would create too much parity, I say that I’m not entirely convinced that’s true. In my data set, the players who won the match won 69.1 percent of points on their serves, while those who lost the match won 60.0 percent (a 15.1 percent advantage for the winners). Counting only points decided on the second serve (including double faults), players who eventually won the match won 55.2 percent, as opposed to 48.7 percent — admittedly larger in raw terms but percentage-wise a comparable 13.4 percent increase. The winning players have a similar advantage, and every game becomes more hotly contested. You might even see an advantage for better players because worse players might not even have an advantage on serve anymore.

Faults will never be eliminated in men’s tennis, and I’m fine with that. I’m sure plenty of people who know a lot more about tennis than I do think this is a terrible idea and could back that up. But it’s interesting to think about. And what if, to split the difference, we said that each player was allowed 6 faults per set, to be used at his discretion until they were used up? Now that’s some game theory.