Insight: Murray and Raonic had higher win probabilities when hitting run-around forehands. But unlike Raonic, Murray did not benefit from this tactic.
In Part 1, I show that offensive tactics may have deceptively high win probabilities because players often use them when already up in the point. Then in Part 2, I show that the opposite is true for defensive tactics. These results exemplify the process of causal inference, which is used to determine why statistics are the way they are. However, causal inference can also be applied to tactics that are not clearly offensive or defensive. In addition, for any statistical result, the causal mechanism, or set of factors generating that result, does not have to be the same for every player. For example, one player’s cause can be another’s effect.
To demonstrate how causal mechanisms can differ across players, I analyze the run-around forehand in the 2016 Wimbledon Men’s Final. With this tactic, a player runs around a ball that was hit to the backhand side of his court in order to hit his stronger, or at least more versatile, forehand. Unfortunately, doing so leaves the forehand side of his court vulnerable to a potential counterattack. For this analysis, I consider only baseline-to-baseline rally shots for which the contact point was on the backhand side of the player’s court. Per Table 1, Murray hit a run-around forehand (i.e. when FOREHAND = 1) on 20 of his 101 such shots, and Raonic did so on 62 of his 136. As in Parts 1 and 2, I use regressions, but now I evaluate the conditions under which run-around forehands have higher win probabilities.
As shown in Table 2, Murray and Raonic have positive FOREHAND coefficients, and thus higher win probabilities on run-around forehands, though only Raonic’s coefficient is significant (Regressions 1, 5). However, other variables could have also affected these win probabilities. For instance, both players had higher win probabilities on short, centered, and defensive incoming balls (Regressions 2, 6). Not only that, but they were significantly more likely to hit run-around forehands when receiving centered and defensive (but interestingly, not short) incoming balls (Regressions 3, 7). Therefore, it is unclear from this analysis which specific variables are responsible for the higher win probabilities.
To investigate that question, I regress WIN on all four variables for each player (Regressions 4, 8). Murray’s FOREHAND coefficient flips from positive in Regression 1 to negative in Regression 4, but his other coefficients barely change from Regression 2. As a result, the likely cause of his higher win probability was not FOREHAND but rather a combination of CENTEREDt-1 and DEFENSIVEt-1 (though not SHORTt-1 because he was less likely to hit run-around forehands on short balls). In contrast, Raonic’s FOREHAND coefficient in Regression 8 barely changes from Regression 5, but his coefficients for the incoming ball change greatly from Regression 6. Thus, the likely cause of his higher win probability was FOREHAND. This finding makes sense because he has a weak backhand, so he has to run around it whenever possible.
All in all, in this three-part series, I first uncover a tactic with a deceptively high win probability and then uncover one with a deceptively low win probability. Finally, I analyze a group of variables whose causal mechanisms differ across players. In all cases, the deeper meaning behind the numbers is different than it appears on the surface. But an analyst or coach can use causal inference to translate those numbers into more informed tactical advice for tennis players.
Table 1: Summary Statistics
Table 2: Win Probability Regressions
