How to simulate head to head competition based on winning percentages?

Question

If I have two players that are about to engage in a head to head competition, how do I simulate a winner based only on win percentage?

One idea I had was to create a "weighted winning pool" where I add the two percentages and then randomly pick a number in that pool. If it's in the percentage range of a team then that team wins.

e.g. 100% and 100% =200. If the random number is less than 100 then team A wins, if not then team b wins
e.g. #2 100% and 50% = 150. If the random number is less than 100 then team A wins if not team B wins.

Would this work or is there a more accepted way of doing this?

Thanks in advance.

Answer 1

The standard approach in sports analytics is to use Bill James' "log5" technique. It was originally developed for team winning percentages, but it has successfully been adapted for other things such as batter-pitcher matchups. Dan Fox (who currently works in the front office of the Pittsburgh Pirates) wrote this article describing how it works for individual matchups.

The general technique is a little more complicated, so I'll just include the original winning percentage version here. Let $A$ represent the winning percentage of Team A (ideally the expected winning percentage against an average team) and similarly for $B$. Then the expected winning percentage for Team A is as follows: $$W\% = \frac{A * (1 - B)}{A * (1 - B) + (1 - A)*B}$$