Should tennis players strive to serve fewer points?

Last month Craig O’Shannessy published an article about how the top players on the ATP Tour play more points served by their opponents than on their own serve. The article claims that the best and most experienced players are more efficient with their serve and developing players should strive to emulate that.

A conversation with Damien Saunder around how a coach should react to this article, and this sort of advice in general, got me thinking.

I have a lot of respect for O’Shannessy (no relation) in general, and he is regarded as the ATP’s stats guru with a terrific track record of popularising the available data. But this article displays the very common fallacy of mistaking effect for cause, something that leads many coaches to chase wild geese.

Let’s establish the facts first, from some basic mathematics. A top player generally wins tennis matches because he wins more points than his opponent (modulo nesting). As players alternate serve, this is equivalent* to saying that he wins a higher percentage of points on his serve than his opponent does in the opponent’s service games.

The other thing that elite men’s tennis has is a serve advantage. Players tend to win about 64% of their points on serve against opponents of similar strength, which leads to about 81% of service games won, broadly compatible with an independent and identically distributed IID† points assumption. This varies by surface and individual style.

This means that inferior players have winning point percentages on serve closer to 50% than their opponents. This naturally leads to more close games. And closer games under the rules of tennis have more points as they go to deuce and a situation where either player needs to win by two points. Thus, the inferior player has to serve more points. No magic mental games required.

Have a look at the outliers in the article. Wawrinka is low because his ranking is inflated from the U.S. Open win and his overall point winning ratio is not as good as the others in the Top 10. The young players mentioned in the article like Kyrgios and Pouille are also low, because the 20-month sample period includes a time when they were even younger and not top 20 quality. Federer is high because his injury has prevented him earning points; when he was on the court he was elite. In other words, there is a tight correlation between the basic percentage of points won and this new statistic.

Imagine a different sport — like volleyball — where the team on serve has a distinct disadvantage at elite level. If the scoring system was like tennis, you would see the best teams play more points on their serve just because they are the more competitive situations. It’s nothing to do with trying to keep the pressure on their opponents, it’s just a result of the scoring system.

The lesson I would take from this case study is to consciously distance yourself from analysing minute variations in outcomes. It can get to be like reading tea leaves. You cannot coach an outcome, only adaptive processes that produce the ones you want more often than not. Don’t try to coach the KPI as making your opponent’s service games longer, glance at it as an imperfect indicator of a better player.

* It’s arguable that I’m defining the statistic out of existence here, so let’s look at an extreme example. Imagine a typical close match of 150 points, where Player A wins 63% of points on serve compared to Player B’s 60% on his serve. If they had served 75 points each (50%/50%), A would have won 47 points on serve and 30 on return. That’s 77 points to 73. If B had played longer service games, let’s say 84 points to 66 on A’s serve, that’s a massive 56%/44% split of service activity which is well beyond the bounds of the data O’Shannessy showed. It’s like one player averaging 7 points per service game (plenty of deuces) compared to 5½ per service game (win to 15 or 30). It’s almost physically impossible to get that discrepancy with this mix of service point win percentages. Yet Player A would still have won 75 points, a reduction of only two. The point is: a basic stochastic process with service win% as the only input (pair) explains all the variation in outcomes.

† While the IID assumption makes for an easy modelling process, with enough data we see that players don’t follow it exactly throughout matches and there is more autocorrelation than a truly random process. That effect of a combination of mental & physical performance is for another post.

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