As we’ve seen, right-handers serve more effectively to the deuce court than to the ad court, and lefties do the opposite. Based on available data, righties win about 64.0% of points to the deuce court against 62.1% to the ad court, while lefties exhibit a bigger difference, winning 59.3% in the deuce court, 62.8% in the ad court.
(These numbers are different than those I originally published last week. There was a bug in my calculations; while it does not change any overall conclusions, it turns out that the lefty gap is considerably wider than the initial numbers showed.)
While the differences are minor, they have some strategic implications. My previously-published win probability tables for a single game assume that players are consistent from point to point, regardless of the direction they serve. It would be foolish to generate new tables for each player’s tendencies, but it is possible to do the math separately for the populations of righties and lefties.
Implications
We start with a paradox. Given a righty server and a lefty server who win equal percentage of service points, the lefty has a better chance of winning a service game. The paradox is compounded by the fact that slightly more points are played in the deuce court, thanks to games ending at 40-15 and (much more rarely) at 15-40.
Two things explain the lefty advantage. First, close games (those that reach 30-30 or deuce) always have equal numbers of deuce and ad points. When the balance between deuce and ad points reaches 50/50, a 63% lefty server is a bit better than 63% (63.07%, to be exact), while a 63% righty server is a bit worse (62.96%.)
Second, the wider difference in deuce/ad outcomes for lefties makes it more likely that a lefty will keep himself in a game, fighting off break points and giving himself another chance to string two points together. As we’ll see in a moment, the difference at break point is the most important aspect of this table.
The table below shows win probabilities for right-handed and left-handed servers who win 63% and 70% of service points. (63% is average for 2011 grand slam matches; 70% is a round number for a dominant serving performance.) Each row shows the likelihood of each type of server winning a game from the given point score.
The most dramatic difference is–as expected–on break point at 30-40 or 40-AD. At both the 63% and 70% levels, left-handedness confers a 2% advantage over right-handedness. There is a noticeable advantage at 40-30 (and AD-40) as well, where the lefty has a better chance of finishing the game immediately, but it is only about one-third the effect of 30-40.
Here is the full table for each type of server at each point. I expect that you’ll keep it handy each time you watch a match.
63% 63% 70% 70% SCORE RH LH RH LH 0-0 79.42% 79.65% 90.02% 90.26% 0-15 64.09% 65.36% 78.51% 79.71% 0-30 43.22% 43.52% 58.69% 58.88% 0-40 18.21% 19.28% 28.46% 29.97% 15-0 88.05% 88.63% 94.75% 95.15% 15-15 76.91% 77.22% 87.49% 87.66% 15-30 57.21% 58.72% 70.95% 72.64% 15-40 29.45% 29.62% 41.28% 41.55% 30-0 94.83% 94.92% 98.02% 98.04% 30-15 88.09% 88.81% 94.17% 94.72% 30-30 74.31% 74.46% 84.53% 84.62% 30-40 46.04% 48.36% 58.22% 61.04% (40-AD) 40-0 98.66% 98.76% 99.56% 99.62% 40-15 96.48% 96.55% 98.61% 98.63% 40-30 90.23% 91.05% 95.17% 95.68% (AD-40) 40-40 74.31% 74.46% 84.53% 84.62%