Monday, February 18, 2019

Why did I win so many tennis matches against an opponent with whom I felt so evenly matched point by point?

I played tennis for nearly two decades with a friend who shared the same tennis spirit with me. He was a reliable (on time and eager to meet) partner and we played on public courts nearly all through the year. Only injuries, rain or temperatures below 25 would keep us off the courts. In the early days I was a beginner and he patiently played with me as I developed my skills. But over the final few years, even though we felt evenly matched point by point, I seemed to win a surprising number of matches (best of three). In fact, even the three set match became somewhat of a rarity. So the question became, how evenly matched were we point by point? From a mathematical point of view we could try to answer the question a posteriori. That is, by noting my winning percentage in terms of sets, deduce what my per point advantage might be.

In the paper Tennis Probabilities we calculate the probabilities of winning a game, set, match given the probability of winning any given point. The paper includes a table of results from which one can work in reverse. Thus, if I was winning 81.5% of the sets we played, I could read from the table that my probability of winning any one point must be .55, etc. This 55% chance of winning a point is not much better than 50-50 so it never felt like a big advantage......but the numbers tell a different story!

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