## Thursday, September 13, 2018

### The Pythagorean Expectation 9/13/18

Hey baseball fans!

The title of this post really sounds like the name of a "Big Bang Theory" episode, right? Correct! Today's blog post is very stat-heavy and mathematical. In other words, it should be pretty fun for me to write! Anyway, while perusing through Baseball Reference and looking at team win-loss records throughout the years, I came across the following stat: the Pythagorean expectation. Basically, this stat tells you how many games a team should've won based on how many runs they scored and gave up in a given season. The actual formula is as follows: runs scored raised to the power of 1.83 divided by the sum of runs scored raised to the power of 1.83 and runs allowed raised to the power of 1.83.

Let's look at the 2017 season as an example for understanding how the stat is actually implemented.  The 2017 Red Sox scored 785 runs and allowed 668 of them. Plug those numbers into the Pythagorean expectation formula and you get a winning percentage of .573. Multiply that by 162, the amount of games in an MLB season, and you get that the BoSox should've won 93 games in 2017, which they actually did. The 2017 Yankees, on the other hand, should've won 100 games according to the formula, but instead only won 91. Now, does this mean that the formula is faulty? Maybe, but it could also mean that the Yankees were just unlucky. The same thing goes for the 2017 Indians, who should've won 108 games in '17 but only won 102. Then you have a team like the 2017 Padres, a team that should've won only 59 games according to the Pythagorean expectation formula, but actually won 71 games.

So, why is this formula good to use in order to judge the prowess of MLB teams? Well, I've always been a big fan of run differential and this statistic uses exactly that to determine how good a team is. This same formula using different exponents is also used in the NFL, NBA, and NHL, so you know it's valid. After all, it was created by the great Bill James (pictured below). In conclusion, I may be old school when it comes to stuff like sabermetrics, but this new way of looking at teams is really quite interesting.

Thanks for reading this post and I hope you enjoyed it. Check back soon for more of "all the buzz on what wuzz."