Pythagoras & Orioles & the Winning Mysteries

We all know the pre-Socratic philosopher Pythagoras by his theorem involving the area of right triangles. Beyond that, however, this figure who was of such importance in the ancient world—who was considered to be one of the many “god-men” of the Classical period—has now become otherwise obscure. In fact Pythagoras was the founder of a popular religious cult which, in good Hellenic style, practiced various mysteries, & also led ascetic lives, professing a belief in the transmigration of souls, practicing vegetarianism & famously abstaining from beans.

Oddly, one place where Pythagoras’ name is currently invoked is in the world of baseball, in the form of “Pythagorean expectations” (the original term as coined by Bill James) or, more commonly, “Pythagorean wins.” If you remember your high school geometry class, you’ll recall that the Pythagorean theorem runs as follows: a2+b2=c2, where a is the right angle side of the triangle, b is the base & c is the hypotenuse (the other side!) Bill James created a similar formula to determine how many wins a team would be expected to achieve based on the number of runs they scored & allowed. In James’ original formula, Pythagorean expectation is described as follows:

This formula, like others that James created, has received some tweaking over the years, but the idea behind it remains the same: whatever a team’s actual won-loss record states at a given point of time, there is an ideal won-loss record that exists that more clearly captures the team’s true essence.

Now we turn our gaze to this very baseball season, & to the city of Baltimore, Maryland, home of the Orioles baseball team. As of this writing, the Orioles are tied for first place with the New York Yankees for first-place in the American League East Division; worth noting here that 1. the American League East is typically considered baseball’s strongest division, & 2. the Yankees are considered one of the top two or three teams in the Majors this year, & were a favorite to win the division from the onset. If the Yankees were to have been challenged for the division, conventional wisdom this spring ran, it would be by their long-time rivals, the Boston Red Sox & perhaps the always tough Tampa Bay Rays. The Orioles were seen as a cellar team, lagging behind the Toronto Blue Jays.

Adam Jones looks to the heavens

But the Red Sox, as they have a wont to do at regular intervals throughout their existence, found all sorts of intriguing—if hideous—ways to implode & jettison their season, & Toronto suffered a staggering number of injuries both to their starting pitching staff & to key players. Tampa has performed well thru the season overall, tho they are held back by a somewhat weak offense, & also lost their slugging third baseman Evan Longoria for a good portion of the year. Now Longoria is back in the line-up, & that seems to have given them a bit of a boost, tho it’s clear that he’s still suffering effects from the injury.

CC Sabathia, who has been injured off & on in 2012

The Yankees, meanwhile, dominated as expected for the first half of the season, & they were seen as an easy division winner. Boston was done, & while the Rays might challenge them (& have been favored to take one of the two “wild card” playoff spots), they were seen as sufficiently flawed to have little chance of taking the division title.

& then there were the Orioles. They’ve spent the season occupying one of the top three spots in the division standings—they even led at one point in the spring before the Yankees caught them; after all, there’s often a surprise team in the first month or two that is ultimately humbled by the real powers. But Baltimore, as they say in baseball, “refused to go away.” Despite being scoffed at by most baseball pundits, who opined bluntly that the Orioles are not “for real,” they stayed within striking distance of the division lead, & also maintained their position as one of the top candidates for the wild card spots. & as of yesterday, 9/4/12, when the Yankees lost to Tampa & the Orioles defeated Toronto, Baltimore & New York found themselves in a tie for first.

The Yankees are a team filled with stars, but stars who are old in baseball years—as a result, they’ve suffered a number of key injuries down the stretch. Some commentators recently have said, well yes, the Orioles took 2 out of 3 from the Yankees this past weekend, & yes, they’re in a dead heat, but this is not the “real” Yankees, & the Orioles will soon see their magic coach become a pumpkin again.

Pythagoras: detail from Raphael's "School of Athens": on paper

The reasoning, beyond simple line-up comparisons (& yes, the Yankees do look like the far better team “on paper”), has to do with run differential, which if you followed the Pythagorean expectation formula above, is obviously key to that method of calculating “expected” or it might be said “ideal” (in the philosophical sense) wins. The Yankees have outscored their opponents by 83 runs, the second best total in the American League (trailing only Texas at 118); Tampa is close, with an +81 differential, & they do only trail the Yankees & Orioles by 1-1/2 games. The Orioles, meanwhile, have surrendered 19 more runs than they have scored, & still are tying the Yankees with a record of 76-59. By point of comparison, the Red Sox have been outscored on the season by 8 runs, & their won-lost record stands at 63-74, a full 14 games out of first; the team with the closest run differential to the Orioles (admittedly, in the National League) is the Philadelphia Phillies, who have been outscored by 21 runs, have a 65-71 record & are 18-1/2 games out of first place in the National League East!

Zach Britton

How have the Orioles accomplished this? They’ve won a lot of close games—a fact that most of the sabermetrically-inclined will put down to luck, & as we know luck only holds so long. They have a bona fide young star in centerfielder Adam Jones, & a good player in right fielder Nick Markakis (tho he was injured for a significant amount of time); they have a dominant bullpen with closer Jim Johnson & set-up Pedro Strop, & such a bullpen will enable a team to have a good record in close games; they also have a talented catcher in Matt Wieters, & they have the very streaky Mark Reynolds & Chris Davis: destroyers of baseballs when they’re on a roll & almost sure outs—with oodles of strikeouts—when they’re not. Lately, both have been hot, especially Reynolds; & young starting pitcher Zach Britton, who was out with a shoulder injury until July, has been dominating like a true ace.

There are essentially four weeks remaining in the season, & there’s a good chance that at least a couple of teams who are currently in the playoff picture will fade by the beginning of October. Certainly the Orioles could be one of those teams, & if one were a gambler (which I’m not), that would probably be the smart bet.

Epicurus

But as they say, the “games aren’t played on paper, they’re played on the field.” I love this: being strongly of the Epicurean bent, I strive to believe in “what is” rather than “what is actually true" sub specie aeternitatis. It’s intriguing to me how Pythagoras has been attached to this very idealistic pursuit of calculating team’s “ideal” (in the Platonic sense) records; of course, Pythagoras was also an idealist philosopher & an influence on Plato. He would indeed believe in the form of the New York Yankees & the form of the Baltimore Orioles, & would certainly understand the concept that the Orioles’ record is a shadow cast on the wall of the cave—an imperfect & distorted likeness.

For myself, I’ll follow the story with interest—it’s these very narratives that make the epic baseball season so compelling. Of course, tho I’ve long given my allegiance to the San Francisco Giants & the National League, I still have enough vestigial Red Sox fan in me from my youth to get delight on those rare occasions when the Yankees fall—tho interestingly, when I was in grade school & high school, the Orioles were the dominant team always ahead of the Sox—I was too young to really be cognizant of the early 1960s Yankees powerhouses featuring Mantle, Maris, Ford et al. I remember the Orioles of Frank & Brooks Robinson, Jim Palmer, Mike Cuellar, Boog Powell, Paul Blair & more—incredibly strong teams.

Soon enough, October 3rd will be upon us, & if we don’t know how the regular season portion of the 2012 baseball epic ends that morning, we certainly should by that night. Until then—probability & the ideal aside—days will pass, plays will be made, pitches thrown, balls hit, & games will be won & lost.

Orioles Park at Camden Yards: Cave of Shadows or Seat of Being?

All images link to their source

1. Bust of Pythagoras of Samos in the Capitoline Museums, Rome: Wiki Commons: by Galilea, who publishes it  under the Creative Commons Attribution-Share Alike 3.0 Unported license.
2. Pythagorean expectation formula: Wikipedia page on the subject. 
3. Adam Jones popping one up: Wiki Commons, by user Keith Allison, who publishes it under the Creative Commons Attribution-Share Alike 2.0 Generic license.
4. C.C. Sabathia [Yankees star pitcher]: Wiki Commons by chris.ptacek, who publishes it under the Creative Commons Attribution 2.0 Generic license.
5. Detail from Raphael's "The School of Athens": Wiki Commons, public domain
6. Zach Britton Wiki Commons, by user Keith Allison, who publishes it under the Creative Commons Attribution-Share Alike 2.0 Generic license.
7. Epicurus, ancient Greek philosopher. From Thomas Stanley, (1655), The history of philosophy: Wiki Commons, public domain
8. Oriole Park at Camden Yards: Wiki Commons by Kevin Farner, who publishes it under the Creative Commons Attribution 2.0 Generic license