Point Outcomes by Game Score

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

SCORE     PTS    WON   WIN%
ALL     66309  41729  62.9%
DC CT   34679  22024  63.5%

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.

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.