Insight: A higher win probability at net does not necessarily mean you should play the net more often.
Quite often, players have a higher probability of winning a point when they approach the net than when they stay back. However, that information does not account for the strength of the incoming ball. For instance, players often approach the net after receiving short (inside the service line), centered (middle third of the court), and/or defensive (lobbed or floated) balls, which themselves increase the recipient’s win probability. Therefore, a higher win probability at net may overstate the benefit of approaching.
To provide an example, I chart the 2016 Wimbledon Men’s Final between Andy Murray and Milos Raonic. Per Table 1, this match had 391 rally shots, 185 by Murray and 206 by Raonic, for which both players were not at net during contact. Murray approached on 17 of those shots and Raonic on 51 of them. In this table, the “t-1” variables describe the incoming ball; for example, if SHORTt-1 = 1, the incoming ball was short. These variables are controls, whereas WIN is the outcome variable, and APPROACH is the decision variable. Using regressions, I investigate the importance of including the controls.*
First, I regress WIN on APPROACH without controls, which is the same as calculating the raw win probabilities. As shown in Table 2, Murray’s win probability when he approached (CONSTANT + APPROACH) was 35.3% greater than when he did not (CONSTANT), and Raonic’s was 22.8% greater. However, when I add the controls, APPROACH’s coefficient decreases to 22.2% for Murray and 16.4% for Raonic. Unlike before, neither coefficient is statistically significant. Furthermore, when I combine both samples, the coefficient decreases from 26.4% without controls to 17.2% with them.
While I would still advise Murray and Raonic to approach more often, at least when they play each other on grass, the benefit of approaching is not as large as it seems. Thus, when analyzing approach shots, it is essential to control for the incoming ball’s attributes. In theory, there may even be matches in which the raw statistics indicate the players should approach more often when they should actually approach less often. With more data, it would be possible to find out exactly how common those matches are.
Table 1: Summary Statistics
Table 2: Win Probability Regressions
*Logistic regressions are typically used to analyze binary dependent variables, such as WIN. However, I present results from linear regressions instead of logistic ones because linear coefficients can be interpreted as differences in win probability. Having said that, my conclusions are the same with logistic regressions.
