Edward A . Bender 1 The Better of Two Teams

Let's look at the simplest case first: two competitors, say the Comets and the Meteors. If they play each other enough, the better one will win more games and so we'll know which is better. To illustrate, suppose the Comets would win a game 55% of the time. • If they play once, then there is a 45% chance the Meteors would win, a minor upset since the Comets are slightly better. • If they play twice, then there is about a 50% chance of a tie, which is not good. • If they play three times, then there is about a 42.5% chance that the Meteors have an upset win. At this rate, how many games would be needed until the Comets would had only a 20% chance of scoring an upset? The answer is 71 — a lot of games to play. Here is a table of how many games it takes to reduce the probability of upset below 30% 20% and 10% for various probabilities of the underdog winning a single game. The bottom line will be explained after the table.