Explaining Pythagorean Theory: The Makings of a Collapse

Pythagoras was a Greek mathematician who lived around 500 BC. He was also a huge baseball fan. He dedicated his entire life to devising a way to estimate how many games a team would win just by looking at their runs scored and runs allowed and his dream came to fruition with this equation:

Runs Scored2/(Runs Allowed2+Runs Scored2)

Some of that may not be true, but the Pythagorean winning percentage (named after the actual Pythagorean theory for finding the length of any side of a right triangle: A+ B= C2) has turned out to be an extremely accurate indicator of how a team will perform. In the history of Cleveland baseball, only one season (1988) had a difference of more than .100 points (10%) between their actual winning percentage and their Pythagorean. On an average level it is usually much closer. In the 134 year history of Cleveland baseball (I include the Forest City’s, Blues, Spiders and Infants as Cleveland baseball teams), 127 teams have had their Pythagorean winning percent within .050 (5%) of their actual winning percent. 45 seasons have been within .010 or a 1% margin of error. This is all just to show how accurate of a predictor it is.

Below this is a graph comparing the Indians actual winning percentage (in red) to their pythagorean winning percentage (in blue) for the 2012 season to this point.

The first thing you should notice is something surprising. The Indians have actually won more games than they should have given their run differential. There is a good reason for this that I will go over later. Now, look around game 49. This was a high point in the Indians season as far as record goes, but it was also the highest difference between the two percents. At this point the Indians were winning 9.5% more games than they deserved to according to our friend Pythagoras, a pace that has only been beaten once in Indians history (in 1988 when the Indians won 78 games, but should have won 53) for an entire season and has otherwise not even been approached in over 100 years of baseball. There will always be some random variation from the line (it would be more surprising if there wasn’t any at all), but to have a difference of this magnitude is bordering on a miracle. It should have come as no surprise when the two percentages started creeping towards each other as baseball karma caught up with the Tribe. While two long losing streaks weren’t necessarily expected, they also weren’t unwarranted. 

You can see during the first losing streak (games 100-110) places where the winning percentage dropped (as it does after every loss), but the Pythagorean didn’t. These were close games, the kind that the Pythagorean winning percent can’t decipher. Since it is based completely off run differential, the smaller the differential the less effect it has on the projected winning percentage. This means unlike in actual winning percentage where each win counts the same as every other win, some games are worth more than others. The reason this works out is that over time the averages will always catch up to you. No team can score less runs than they allow and maintain a winning record long term. 

This Indians team does have a couple assets that make it likely to maintain at a level slightly above the projected one. The first is the extreme dichotomy of the starting pitching staff. Pythagoras acts like a pitching staff is one unit, going out night after night, but in reality, some pitchers are much better than others to a point that it really makes a difference. If Justin Masterson wins a close, low scoring game it counts as a win in actual winning percentage and a wash in Pythagorean, but if Ubaldo Jimenez loses a game by a margin of seven it counts as a giant loss for the Pythagorean record, but just a single loss in the real world. Because of this, teams with great offenses will often underperform compared to their Pythagorean (the last Indians championship season in 1948 ended the season 9 games under their projected win total) because they score a lot of runs that don’t really matter. A team with a struggling offense should still win games when their star pitchers are performing, but will likely lose early if the other team scores much. This is exactly what has been happening with the Indians over the past month. In August the Indians have won five games, three of which were won by the staff ace Justin Masterson and a fourth by rookie phenom Zach McAllister, who has been the second best pitcher on the team all season. The Indians simply don’t score enough runs to win when any other pitcher is throwing and both records reflect that.

The second part of staying ahead of Pythagorus is having a good bullpen. It is completely pointless to have great starting pitching (even two out of every five days) if your bullpen is just going to give it away. Again, the entire bullpen doesn’t have to be great, just enough to get through the games the team is going to win anyway. Joe Smith, Vinnie Pestano and Chris Perez offer enough punch to get through at least three innings every time the two above average pitchers throw, so every single one of those games is still winnable despite the poor offense.

Looking at a couple of recent seasons for comparison, 2005 was memorable as one of the worst years for the Indians bullpen in recent years. Cliff Lee, C.C. Sabathia, Kevin Millwood and Jake Westbrook made up a dominant pitching staff, but were hurt by 15 blown saves (not all of which were the fault of Bob Wickman) and won five games less than they were projected to, a big enough difference to mean missing the playoffs. In 2007 the bullpen gelled behind great seasons from Rafael Betancourt and Rafael Perez who were so good it didn’t matter that Joe Borowski was closing. That bullpen still has to be considered one of the best in team history and that team outpaced it’s Pythagorean win total by four games. Mostly the same bullpen, but with a better closer in 2011 finished 5 games ahead.

This year the bullpen is just as good and the offense is even worse, leading to an impressive seven games over where they should be as of now. The Indians do have the talent to keep the difference at where it is now and finish the season with about 70 wins, but they will need to win every time Masterson or McAllister takes the mound. The only other thing they could do at this point to save the season from total embarrassment is to start scoring some runs. It would hurt their differential between Pythagorean and real life, but that is actually a good thing, because it would mean they would be earning their wins, rather than just sneaking a couple a week past the other teams. Management has to see this and understand that if the Indians don’t score more runs, it doesn’t matter how well they pitch. The number one priority in the offseason has to be picking up someone who already knows how to slug, not just another retreaded outfielder who can’t find a home.

Pythagorean winning percentage is a good predictor of success, but a team shouldn’t be trying to beat it, but instead should work with it. Just like in a single game, it really is as simple as the team that scores the most runs wins. 

About Joseph Coblitz

Joseph is the primary writer and editor of and has been since it's inception in 2011. He is a graduate of the University of Akron and currently resides in Goodyear, Arizona.