# April Check-In: Pythagorean Wins

You don’t need the mind of Pythagoras to understand scoring runs is good and allowing runs is bad. This extremely basic concept also provides an estimation of what a team’s true performance should be, using similar math to your middle school geometry teacher’s favorite formula. Different variations of the principle exist, and this article will use Baseball Prospectus’ Pythagenpat method.

At 20 wins, the Boston Red Sox have the most wins through one month of baseball. But your boisterous buddy from the Boston burbs and your old math teacher may not agree on who the best team in baseball has actually been so far. Based on their output of 149 runs for and 90 against, Boston ranks second in Pythagorean win expectancy. They are sandwiched between the two 19-win teams, just behind Houston and ahead of Arizona.

The Pythagorean formula actually quite likes Boston’s record and considers them a team worth 19.4 wins. It also says Houston has grossly underachieved and estimates they should have won 21.6 games instead. In 4th place lie the Yankees in both actual and expected wins. At 18-9, they are thus far the team closest to their Pythagorean estimation which expected 17.8 wins.

At the bottom of the league sit the lowly Royals. Their 7 wins are just slightly worse than their expected record, having scored 89 runs to their opponents 150, or just a little bit more bad than Boston has been good. Even the Marlins, fresh off a fire sale and losers of a 20-1 drubbing, have done better runs-wise than Kansas City. Miami has the second lowest Pythagorean win percentage.

But what about the Reds, a team that started out so poorly they fired their manager after a dismal 3-15 start? They are actually Pythagoras’ biggest underachievers. Their -42 run differential would suggest the performance of a 10-18 team rather than a 7-21 one.

Before the “stats are for nerds who don’t watch games,” crowd press enter on their angry comments (if they have managed to find this piece), take a deep breath and relax. Baseball like all sports is full of random variation, and we know results in April are to be taken with a grain of salt. As for this formula? Well, it has actually predicted every team’s record within three wins. Even with blowouts and cancellations, the graph below depicts the correlation between expected wins (x-axis) and actual wins (y-axis).

The relationship is near linear, with a correlation of more than 90%. No outliers exist. The biggest overachievers have been Seattle and the New York Mets, sitting above the trendline at 16 and 17 real wins, respectively.

Can we explain why some teams’ records deviate from their run-based expectancies? Perhaps. Taking a look at one-run games, or the most random games, is a good place to start. Boston is 8-2 in such games, tops in baseball despite ranking

On the other hand, the Nationals rank 15th in the same metric, yet sport just a 1-8 mark in one-run games. This partially explains their 12-win start despite a 14-win run differential. Furthermore, the expected run output of the Nationals equates to that of a 16-win team, as they are the biggest underachievers by what Baseball Prospectus calls its second-order win expectancy. Behind them are last year’s pennant winners followed by cellar-dwelling Cincinnati and Kansas City, who rank fourth and fifth in second-order underachievement. Funny how that works. The Reds have won just one of seven single-run affairs, while the Royals have won four of nine.

So what does this all mean? Boston is not a 120-win team as their record suggests. They’re also not a 117 win team, even though their first-month run spread estimates they would win 97 more games at this pace. We know the Astros are good and the Royals are bad. But neither of them are as polarizing as their prorated win-expectancies say they would be at this pace of 118 and 44 wins, respectively (which just so happen to add up to 162).

The takeaway here is that a team’s first-month record or its first-month run differential can’t predict how they’ll perform going forward with certainty. Washington can’t possibly lose nearly every one-run contest. The Dodgers are closer to a .540 ballclub than a .440 ballclub. And the Reds won’t have to keep firing their manager every month. Probably.

But it’s baseball, and the stat geeks or back-in-my-day crowd don’t know what will happen. What good is a baseball column without some bold (or not-so-bold) predictions? I’ll pick three teams to overachieve and underachieve their expected wins for the entire season.

My overachievers: the Phillies, the Rays and the Yankees. I select the first two for their progressive bullpen usage which has been mocked by old-school strategists. Thus far those strategies have found the Philadelphia overachieving by 0.7 wins and Tampa Bay winning 0.4 games fewer than expected. I choose New York because of their elite bullpen which has been seventh in ERA but first in K%.

As for my underachievers? I’ll take the Astros, Nationals and Twins. I select Houston because their team is so talented and unlikely to reach its ability-based potential in a random sport. I’ll take Washington because I think their manager has no idea how to manage or use one of the greatest hitters ever in his lineup. Lastly, I pick Minnesota because I live in Minneapolis and work with Twins homers whose overestimation of their favorite team’s talent brings me glee. They also have the second-lowest bullpen strikeout rate in the majors. That helps.