Calculating Baseball Statistics - Pythagorean Winning Percentage

As all fans know, the objective of a baseball team is to win games. In order to win games, a team must outscore it's opponent more often than not. With this in mind, noted baseball author and analyst Bill James created a formula for estimating a team's winning percentage based on the number of runs it scores and allows. He named it the Pythagorean Winning Percentage because of its similarity to the famous mathematical theorem of that name.

To calculate Pythagorean Winning Percentage, you need a team's run scored, or "RS" (the number of times they scored) and their runs allowed, or "RA" (the number of times the opponent scored). The formula looks like this:

Pythagorean WP = RS x RA / (RS x RS) + (RA x RA)

The Pythagorean Winning Percentage is the percentage of games a team with that number of Runs Scored and Runs Allowed would be expected to win. It is displayed as a decimal with three numbers after the decimal point, just like Winning Percentage. To calculate the number of wins a team will have, multiply the total number of games times the Pythagorean WP. For example, a team with a .550 Pythagorean WP that plays 162 games can be expected to win about 89 games.

Pythagorean WP is not a perfect system, but it does a pretty good job of predicting the number of wins a team will have when the season is over. It can be useful in several ways, such as predicting how a team will finish the season if they continue to score and allow runs at their current pace. This information could be very helpful to a general manager looking to improve his team. Also, it gives a good indication of whether a team is "really this good" or just playing over its head for a short period of time.

Let's look at a real world example. In 2005, the New York Yankees and Boston Red Sox both finished the season with identical 95-67 records. The Yankees scored 886 runs while allowing 789. The Red Sox scored 910 runs, and allowed 805. Amazingly, their Pythagorean WP would also be the same, at .556, predicting they would finish with the same record, although in the case of the Pythagorean estimate, 90-72.

While the Red Sox and Yankees were shown to be slight overachievers and two equally matched competitors, the Pythagorean WP often shows a team over or underachieving by a decent margin. For example, based on the Pythagorean estimate, the Toronto Blue Jays should have been about 88-74 in 2005, but they finished a disappointing 80-82. Often, though, the Pythagorean estimate is very close. For example, the other two teams in the American League East, the Baltimore Orioles and the Tampa Bay Devil Rays, both finished only 2 wins off the Pythagorean estimate.

While not perfect, the Pythagorean system of estimating winning percentage can be very helpful when evaluating a team's performance, and estimating their future success or failure.