Powerful serves, sharply angled shots, soaring lobs, sneaky drop shots, lengthy baseline rallies, unforced errors, and disputed points are all elements of professional tennis matches.
Intriguingly, mathematical models tend to show that the chances of winning a game, set, or match in tennis come down to the probability that a player wins a rally when he or she serves.
In the April Studies in Applied Mathematics, Paul K. Newton of the University of Southern California and Joseph B. Keller of Stanford University provide formulas for computing a tennis player’s chances of winning and, in effect, for predicting the outcome of tennis tournaments. In the context of their model, Newton and Keller also prove that the probability of winning a set or match doesn’t depend on which player serves first.