If tennis players were machines, each player would have the same probability of winning every point. Winning the point at 40-15 would be equally likely as winning the point at 15-40. It seems a safe bet that this isn’t the case, and today I’m going to start talking about the difference, and why it exists.
To begin with, let’s look at the outcome of every grand slam men’s singles point in 2011, sorted by the score before the point was played. (I’ll explain some of this in a minute.)
SCORE PTS WON WIN% REL g0-0 10757 6820 63.4% 1.00 g0-15 3941 2390 60.6% 0.97 g0-30 1552 963 62.0% 0.98 g0-40 591 324 54.8% 0.88 g15-0 6823 4356 63.8% 1.02 g15-15 4858 3081 63.4% 1.00 g15-30 2741 1648 60.1% 0.97 g15-40 1416 866 61.2% 0.96 SCORE PTS WON WIN% REL g30-0 4355 2826 64.9% 1.02 g30-15 4609 2890 62.7% 1.01 g30-30 3366 2155 64.0% 1.01 g30-40 2080 1234 59.3% 0.95 g40-0 2824 1895 67.1% 1.08 g40-15 3819 2507 65.6% 1.03 g40-30 3466 2209 63.7% 1.02 g40-40 4556 2806 61.6% 0.97 g40-AD 1749 1011 57.8% 0.93 gAD-40 2806 1748 62.3% 1.00 SCORE PTS WON WIN% ALL 66309 41729 62.9% DC CT 34679 22024 63.5% AD CT 31630 19705 62.3%
One thing that sticks out is that as players get closer to winning a game (30-0, 40-0), they are more likely to win the next point. When facing (or approaching) break point, they have less success.
Much of that (and maybe all of it) is simply the bias of the sample. If a player reaches 40-0, he’s more likely to be a player who is dominant on serve, or facing a returner who hasn’t found the range. A disproportionate number of 40-0 points are served by players who are better-than-average servers. Similarly, a disproportionate number of 0-40 points are served by players without dominant service games … or served against Novak Djokovic.
Deuce and ad courts
A more useful finding is that players win more points in the deuce court. In this sample, the server won 63.5% of points in the deuce court and 62.3% of points in the ad court. This may be because right-handers (who make up about 85% of this sample) are more successful when serving across their body, but I haven’t tested that yet.
(If it is true that players are better serving across their body, then the difference is even more stark. Assuming that righties and lefties have the same difference in success rates, the “serve across your body” success rate–deuce for righties, ad for lefties–should be about 63.8%, while the “serve away from your body” rate–ad for righties, deuce for lefties–should be 62.1%.)
Thus, the difference between success rates at 0-0 and 0-15 isn’t as extreme as it looks at first; some of the 0-15 winning percentage is due to the difficulty of serving to the ad court. That’s the purpose of the ‘REL’ column, which shows how the winning percentage on that point relates to the average winning percentage in the relevant court.
If this difference is universally true, it would require a change in win probability tables. For instance, when the returner reaches break point–which is more often in the ad court, at 30-40 or 40-AD–his chance of winning the game is a percentage point or two higher than previously estimated. As long as he’s playing a right-hander, anyway.
There’s plenty more to investigate here. To determine whether players really raise or drop their performance levels (for instance, raising their game against break point, or taking it easy at 40-0), we’ll need to switch to a player-by-player basis, to reduce the skewing effect of dropping every player in the same bucket.