When watching a match, it seems that some points are more difficult for the server or returner. There is an oft-cited sense that “40-0 is the best time to break,” suggesting that servers may let up a bit given a big lead.
Building on the work from my last few posts, we can check some of that conventional wisdom. As we’ll see, servers perform about as well as expected at almost every juncture within a game–with the exception of 0-40, when they are at their weakest.
To determine how servers perform at various scores, we first need an estimate of how they “should” perform. Servers win more points at 30-0 than at 0-15, but not necessarily because reaching 30-0 makes you a better server; rather, better servers reach 30-0 more frequently, skewing the sample of 30-0 points.
Before going any further, we need to control for that bias. To do so, I looked at each 2011 grand slam match tracked by Pointstream and found each player’s percentage of service points won. That number, slightly adjusted for deuce/ad court and their handedness (because righties win more points in the deuce court, etc.), is the percentage of points they “should” win at each score.
For example, if a player won 68% of service points in a given match, I estimate that he should have won 68% of 0-0 points, 68% of 15-0 points, and so on (before adjusting for handedness and deuce/ad). This doesn’t account for ups and downs during a match, but it does take into account that players will have different success rates on serve depending on the surface and their opponent.
Across about 11,000 service games, we’ve got a good sample of how players performed at each point score, and we can compare that to how well they should have performed.
For instance, in close to 11,000 game-starting points, servers won 63.5% of points, while–accounting for the overall performance of those players, as well as the advantage of mostly righties serving in the deuce court–they should have won about 64.1% of those points. That’s a minor difference, and 0-0 is one of the nine scores at which players performed within about one percentage point of how we would expect them to.
Of the remaining seven scores, six of them see servers win only two percent more or less than they should. A few notable scores here are 40-0, 40-30, and AD-40. At 40-0, we might expect servers to let up or returners to loosen up, but instead, servers are more successful than ever. That is particularly impressive because the pool of servers who reach 40-0 is already skewed toward the most successful servers. (Though, oddly enough, not quite as much as 30-0. Both of the surprises here may be due to strong servers on mini-streaks.)
40-30 and AD-40 appear to be part of a larger trend where players player better on game point (or tighten up against game point). The server plays better than expected on 40-0, 40-30, and AD-40, and worse than expected (or the returner plays better than expected) at 0-40, 30-40, and AD-40. The only exception is 15-40.
The only point score at which the observed success rate deviates more than two percent from the predicted success rate is 0-40. Servers who get themselves in a 0-40 hole are expected to win only 58.2% of points, but they don’t come close, winning only 54.8% of 0-40 points. Given the results at 0-40 and 40-0, it seems that winning a point, building momentum, and returning to deuce is less common than we might in the professional men’s game.
(In my amateur game, it’s much more common, implying than my regular partners and I aren’t quite as mentally strong as the top 100 players in the world. No offense, regular partners.)
Finally, note that this is not yet an estimate of how players in general respond to the pressure of various moments. At, say, 30-40, the server may be feeling pressure to save break point, but the returner is under pressure, as well. These numbers reflect the outcome given both players’ response to the moment. The results of specific players, as well as stats like double faults and unforced errors, may give us a better idea of what happens when players feel the pressure.
Below, find the complete results. “Obs” is the rate at which players win points given specific scores. “Exp” is the rate at which they “should” have won those points, given their overall performance in each match.
If you’re curious, the “g” preceding each score means “game,” to differentiate 0-0 in a game and 0-0 in a tiebreak. Finally, eagle-eyed readers may note that the observed rates are a bit different than those I published a few days ago. Since then, I added in games with set scores of 6-6 and later, which changed a few of the numbers a bit.
Score Obs Exp Rate g0-0 63.5% 64.1% 0.99 g0-15 60.7% 61.2% 0.99 g0-30 62.0% 60.8% 1.02 g0-40 54.8% 58.3% 0.94 g15-0 63.8% 63.9% 1.00 g15-15 63.4% 63.3% 1.00 g15-30 60.1% 60.5% 0.99 g15-40 61.1% 59.9% 1.02 g30-0 64.9% 66.0% 0.98 g30-15 62.7% 63.2% 0.99 g30-30 64.0% 62.6% 1.02 g30-40 59.3% 59.7% 0.99 g40-0 67.1% 65.8% 1.02 g40-15 65.7% 65.4% 1.00 g40-30 63.7% 62.5% 1.02 g40-40 61.6% 61.4% 1.00 g40-AD 57.9% 58.8% 0.98 gAD-40 62.3% 61.2% 1.02