Do You Have a Better Chance to Upset a Stronger Player with the 11-Point Rule?

By Fangxing Li, fli6@utk.edu

Do we a have better chance to upset a stronger player under the best of five, 11-point rule than under the old best of three, 21-point rule? Most people probably agree that the chance is bigger. But, the real question is, by how much? Is it really considerable? I guess few people have seriously thought about how much the actual benefit is. This article will tell you the actual increased chance for a lower-rated player to make an upset.

To make it easy to understand, let’s assume there are two players, A and B. We also need to assume that the results of their games are only related to their skill levels. Other factors, like home court advantage, mental toughness, familiarity with opponent’s playing style, etc., are all neutral to the results. Also we assume the players always play at their best.

Now, we need to define their skill levels using Probability of Winning a Single Point (PWSP) between two players. PWSP of A against B means the chance for A to win a single point against B. For example, if the PWSP of A against B is 45%, then if A plays with B for 100 points, A will normally win about 45 points. Of course, B will win 55 points, i.e., PWSP of B is 55%.

Then, we need to understand that the chance of winning a single point is totally different from winning a set/game. For an extreme example, assume the PWSP of A is 90% and B is 10%. In other words, B may win 1 point in every 10 points. However, the chance for B to win an 11-point set is much, much less than 10%, even less than 1 out of a million, because it is extremely rare that B can win 11 points before his opponent does that first.

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