Pythagorean Theorem Applied

Each team in my 1947 APBA baseball replay has reached 40, or nearly 40 games, played this season. With 25 percent of the games completed, teams are beginning to show what they are capable of doing and how the season could turn out.

Of course, there’s still a lot of games to be played and, as APBA players know, anything can happen. Trends can change, players can get hot, teams can go on streaks. So, it’s somewhat premature to try and predict how the American League and National League will turn out.

But, that said, one of the characteristics of a true APBA fan is the obsession for statistics and math. I’ve noted before that I don’t keep many detailed stats for a replay. Every time I tried before, I ran into computer issues. I had two die on me and once, in a moment of confidence, I put my stats on a laptop I used at work. I was suddenly laid off and the computer was no longer accessible.  But, grabbing a calculator and a pen and figuring out batting average and earned run averages is still a vital part of why I do this game.

This year, I’m tracking home runs and RBIs, won-lost records and saves for all. And I’m keeping game-by-game batting averages for Ted Williams and Joe DiMaggio. All are jotted down on paper so I won’t lose it by being either computer inept or a victim of journalism layoff economics.

So, with a quarter of the season completed, it looks like the Yankees and Red Sox are in a dead heat. Detroit is a good team as well, following closely behind. The Washington Senators are proving to be a really poor team in the American League. In the National League, fueled by Whitey Kurowski’s 11 home runs so far, the Cardinals are by far the best.

I decided to do some more math and applied Bill James’ Pythagorean Theorem for baseball to this season. The formula, for those who are not into Bill James, is based upon runs scored and runs given up. Take the number of runs a team scores and multiply it by itself, squaring the figure. Then, divide that by the number of runs scored squared added to the number of runs given up squared.

What?

Here’s the formula: (Runs scored)2 /  [(runs scored)2 + (runs allowed)2]

Then, take that figure and divide it by the number of games played in a season. In my case of 1947, 154 games, to determine the expected won-loss record.

By doing this, I noticed a few things. Both the Boston Red Sox and the New York Yankees are expected to go 106-48 for the season. The Chicago White Sox, which are playing at about a .500 pace, have a collapse in their future, according to the theorem. Because the team hasn’t scored many runs so far and given up 50 more than scored, the Sox are predicted to win only 52 games. The hapless Senators will win only 47 game and finish last in the American League, based on James’ math.

In the National League, the Cardinals dominate. The theorem shows a stunning final record of 122-32. Brooklyn is second with a forecasted record of 95-59 – one game better than their actual record of 94-60, which was good enough to win the real 1947 National League pennant. Pittsburgh is predicted to win only 44 games, which doesn’t seem too far-fetched of a record when considering the Pirates are 10-28 now in my replay.

Obviously, it’s still early in the season to really extrapolate firm predictions from the math. The Cardinals could face Braves’ pitchers Warren Spahn and Jonny Sain in a low-scoring weekend series ahead and the numbers could be skewed some.

Still, it’s fun to apply the theorem and get one idea of what could happen. The Red Sox-Yankees season race looks good no matter how you add it up.