Wednesday, April 2, 2014

Doing Math: Pythagorean Theorem for Winning Percentage

Baseball season is officially upon us. At the start of every season, baseball fans everywhere talk about how it's their team's year to win it all. But how do we really know who's year it will be with 161 games left to play in the regular season? There are many ways to try and determine who the next world champ would be. Here is just one of those options.

The Pythagorean Theorem for Winning Percentage

Everybody knows the famous Pythagorean Theorem: a^2+b^2=c^2. So how does this help us to determine a winner? Well with slight modifications, Bill James created the Pythagorean Theorem for Winning Percentage based off of the well known formula so that it states,

W%=[(Runs Scored)^2]/(Runs Scored)^2 + (Runs Allowed)^2].

This formula does not base the winning percentage of a team based on just their Win-Loss record. It gives us a better understanding of how well a team is actually doing based on the runs that they score and the runs that they allow the other team to score.

Many expert analyst are currently saying that the L.A. Dodgers are going to be the 2014 World Series champions. Let's looking into this a little further. According to, the Dodgers had a spring training record of 98 runs scored and 118 runs allowed. Using the formula, we can say

W%=[(98)^2]/(98)^2 + (118)^2]
This would mean that we can expect the dodger to win 40.82% of there games. According to, the actual win percent of the dodgers was .368 or 36.8%. Now let's take a look into the Red Sox spring training results. They had a record of 117 runs scored and 149 runs allowed. When plugging these values into our equation we obtain

W%=[(117)^2]/(117)^2 + (149)^2]
This would mean that we can expect a winning percentage of 38.14% from the Red Sox. According to, the Red Sox had a winning percentage of .393 or 39.3%.

As we can see, this formula is pretty accurate at calculating expected winning percentages for baseball. The math that is done here is working with spring training statistics which don't necessarily show us an accurate representation of how the season will actually unfold. Once the regular season really gets underway, we will more accurately be able to pick who will win the 2014 World Series. In my opinion, the Red Sox will make it back to back champions.

1 comment:

  1. Those are awfully low winning percentages for elite teams. What does that lead you to think? How do they compare to the real season, 10 games in?
    Why are these formulas what they are? Is it pythagorean in nature, or is it just the sum of squares that makes it called that for appearance.

    Also, please cite your ref.s

    Definitely interesting math!