Pythagorean Formula and Baseball Betting

Chris Archer of the Tampa Bay Rays. Jim McIssac/Getty Images Sport

Many baseball bettors are likely to be familiar with the Pythagorean Formula and how it is used for determining how many games a team should have won based on the number of runs it scored and the number of runs it allowed. The formula created by Bill James was "Expected wins = runs scored(2)/runs scored(2)+ runs allowed(2)."

The exponent used was later changed from 2.0 to 1.83 and because the formula invented by James closely resembles the Pythagorean Theorem we were taught in school, it is frequently referred to as the Pythagorean Expectation.

The problem with the Pythagorean Expectation was the method stated how many games a team should have won up to that point. It said nothing about a team's chances of winning a particular game, so I decided to look for a way of using something similar to create odds on any baseball game. The first step was to look for the simplest variables that would have to be included.


When it comes to a baseball team there are a multitude of baseball statistics that you can look at. You can use hundreds of different batting of pitching statistics, but as bettors, the only thing we are concerned with is if we win or lose our bet. Therefore, a team's wins and losses are really the primary stat we're interested in as far as teams go.

The starting pitchers also have to be taken into consideration and we run into the same problem in that we can look at a pitcher's ERA, his walks/hits to innings pitched, etc., but the only thing we're interested in is how his team does when he's on the mound.

Since we win or lose our wagers whether or not the starting pitcher gets a decision or not, we can't go by a pitcher's win-loss record, but instead have to go with the team record in games started, or TRGS.

The Method

Since a team will have many more games than an individual pitcher will have starts, we need to factor the pitcher's TRGS, which will be squared.

Therefore, the numbers we need are simply a team's record and the starting pitcher's TRGS.

For an example, let's use a game between Team A and Team B. Team A is 69-52 on the year and their starter has a TRGS of 17-8. Team B has a record of 60-60 and their pitcher has a TRGS of 13-13. We can tell that Team A is going to be favored, but by how much?

First we square Pitcher A's numbers and 17*17=289 and 8*8=64. Next we add the team's win-loss record of 69-52 so we have:

Team A Pitcher: 289-64
Team A Record: 69-52
Team A Total: 358-116

We do the same thing for Team B's pitcher and 13*13=169, so we have:
Team B Pitcher: 169-169
Team B Record: 60-60
Team B Total: 229-229

The next step is to add Team A's wins to Team B's losses and we get 358+229=587. Next add Team B's wins to Team A's losses and we get 229+116=345. Next, take the team with the most wins and divide that number by the sum of both team's wins, so that you get 587/(587+345) or 587/932=.630 or 63%. Therefore, Team A has a 63% chance of winning the game. To convert a percentage into a money line number, subtract your winning percentage from a 100, so that 100-63=37. Divide 63 by 37 to get 1.703 or -170. So we now have Team A -170 over Team B.

One more example, with Team C having a record of 53-77 and a pitcher with a TRGS of 9-16. Team D has a record of 75-55 and a pitcher with a TRGS of 18-8.

We square Team C's pitchers numbers to get 9*9=81 and 16*16=256. When we add Team C's record of 53-77 we get:
Team C Pitcher: 81-256
Team C Record: 53-77
Team C Total: 134-333

For Team D, squaring the pitcher's numbers will give us 18*18=324 and 8*8=64. When we add in Team D's record we get:
Team D Pitcher: 324-64
Team C Record: 75-55
Team C Total: 399-119

Adding Team C's wins to Team D's losses gives us 134+119=253. Adding Team D's wins to Team C's losses gives us 399+333=732. Since Team D has the larger number of wins, we will divide Team D's wins by the sum of Team C's wins and Team D's wins, so we have 732/(253+732) or 732/985=.743 or 74.3%. Therefore we have Team D with a 74.3% chance of winning the game.

To convert to a money line, subtract 74.3 from a 100, so that you have 100-74.3=25.7. Next divide 74.3 by 25.7 and 74.3/25.7=2.89 or -289. So we have Team D as lofty -289 favorites.

The final step will be to factor in home field, which is typically 10 cents or .10, making Team D -299 at home and -279 on the road. 

The method works for sides only and does not calculate over/unders.