Tennis doesn’t feel random, because, as we swing, we feel like we’re in full control of the racket, and thus the result of the shot. This control is an illusion.
Each stroke generates a distribution of outcomes at decision time, from which a sample is drawn at execution time.
Don’t believe me? Let’s assume that tennis shots are not random; they are completely controllable by the person hitting them. The pros would never miss. They wouldn’t rarely miss, they would never miss, because missing loses the point, and, clearly, that’s bad. The only reason professional players miss is that even they do not have full control over the results of their shots.
This concept is crucial to tennis strategy. The result of any particular tennis shot is unpredictable, aka random. The appropriate model for a tennis shot is not anything along the lines of “that shot was in, therefore it was good” or “that was an error, therefore it was bad.” Each stroke generates a distribution of outcomes at decision time, from which a sample is drawn at execution time. Even after we observe that sample, the result of that particular shot, we don’t necessarily know from what distribution it was drawn, and therefore we need more information in order to classify it as a “good” or “bad” shot, strategically.
Judge Decisions, Not Results
Good shots raise our equity in the point at decision time, while bad shots lower it. When I say “equity,” I’m referring to a player’s win probability at a given time. For example, say player A wins 3 out of every 4 of his service points. Player A starts his service points with 75% equity, and his opponent with 25% equity. Each player’s equity varies as the point unfolds, and various shots are hit.
Our strategic analysis is far more accurate when we analyze a player’s decisions, rather than when we analyze the specific results of individual shots. For each shot, we focus on the entire distribution of outcomes that particular shot selection generated, rather than a random sample drawn from that distribution in some particular instance.
Good strategists routinely choose shots that produce distributions which raise their equity, while poor strategists rarely do.
Random, But Improvable
Both skill and shot selection effect the span and density of a shot’s distribution of outcomes. An elite player hitting an easy shot may hit 90% of his balls within 1 foot of where he’s aiming, whereas a recreational player hitting a difficult shot may frequently produce results varying by 15 feet or more. A shot’s distribution will be wider when the player is weak, and/or when the attempted shot is difficult, and likewise will become narrower as the player improves, and when the shot is easy.
Strategy – Navigating The Uncertainty
As we make decisions on court, we determine from which random distributions our results will be drawn. Smart shots produce favorable distributions, which raise our equity in the point, while stupid shots produce unfavorable distributions, which lower our equity. Skilled players produce tighter distributions, while weaker players produce looser ones. Difficult shots have a wider range of outcomes than easy shots. Good strategists routinely choose shots that produce distributions which raise their equity, while poor strategists rarely do. This is why a good strategic player will routinely beat an inferior strategic player of the same technical skill.
Tennis strategy is about navigating this probabilistic decision landscape better than your opponent. The first step in navigating any territory is to effectively map it. Understanding that a tennis shot is best understood as probability distribution over a range of outcomes, rather than an individual, distinct, informative event, is the first step to creating that effective map.
