In defense of baseball's pythagorean theorem

by Fred Hofstetter on November 8, 2017

Don La Greca undressed Pythagorean Theorem supporters in a florid rant on ESPN radio - a theorem with modest potential for widespread application.

Don La Greca ESPN Radio Rant about Pythagorean Theorem

ESPN’s Don La Greca methodically deconstructing baseball’s Pythagorean Theorem.

Math is hard. Sabermetrics is really hard. I am not very good at them. I find anecdotal evidence and confirmation bias simpler. Nothing in sports feels better than expecting something to happen and watching it come to fruition. The opposite feels foreign, unfamiliar, and unacceptable. So I can understand a resistance to embracing glasses-laden nerds who condescendingly inject fancy stats into every single conversation about sports.

ESPN Radio host Don La Greca was once again forced into the discomfort of having to comment on one of these newfangled stats no one really understands. He explains his inhibition about a “Pythagorean Theorem” as an analytical tool in sports talk:

La Greca is triggered regarding the New York Giants’ offensive line – but he throws baseball accountants into the mix as well. Moneyball and the infestation of math into sports rhetoric is largely thanks to a revolution within MLB front offices. Thanks to the nerd herd, spearheaded by sabermetric mavens Brad Pitt and Jonah Hill, the daily sports narrative has been besieged and forever blemished. Instead of speaking only through aphorisms and clumsy metaphors, sports fans everywhere have been thrust into a life of confronting inconvenient probabilities.

Pity the poor fool damned to such a fate.

Yes, the conversation has been ruined. But maybe the nerds are on to something.

I did a little digging on this so-called “Pythagorean Theorem.” As apoplectic as I am about the dramatic over-complication of modern sports rhetoric, I must admit that upon further research, the Pythagorean Theorem has fringe potential to impact many corners of the sports world – and MAYBE even beyond.

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What is the Pythagorean Theorem of Baseball?

The Pythagorean Theorem is a fundamental relation in Euclidian concerning the three sides of a right triangle. The Theorem states the square of the hypotenuse (the longest side, across from the right angle) equals the sum of the squares of the other two sides. The formula for the Pythagorean Theorem is:

a2 + b2 = c2

The Pythagorean Theorem can be visualized as such:

Pythagorean Theorem Equation Visualization

Named after the ancient Greek mathematician Pythagoras, who is credited with its first recorded proof, the Theorem has been scrupulously tested and proven over thousands of years of vigorous study and deep, deep thought from some of the world’s biggest brained baseball fans. The Theorem has been proven by dissection and rearrangement, by not dissection and rearrangement, algebraically, using differentials, and by converse. Babylonian, Mesopotamian, Indian and Chinese baseball statisticians have all discovered the Pythagorean Theorem independently and in some cases provided their own proofs for special cases. The Theorem may have more mathematical proofs than any other. Literature, musicals, plays, songs, and cartoons have all referenced baseball’s Pythagorean Theorem as a symbol of mathematical mystique or power. It’s really catching on. One century at a time. To the rest of us, it’s some baseball-nerdy balderdash.

Wait. What does this have to do with baseball.

This the kind of thing baseball advanced statistic evangelists salivate over:

It’s a lot of mumbo jumbo, I know. It’s not easy to follow, but you can’t deny the baseball diamond CAN be rotated in the abstract to form a square and you may manipulate the formation of bases to form a right triangle and find distances using the Pythagorean Theorem. The nerds aren’t wrong, they’re simply introducing concepts normal baseball fans want nothing to do with – lengths, distances and other similar advanced intellectual maneuvers.

So, what else could this theorem be used for?

  1. Calculating the distance from third to first base
    The distance from home to first base and home to third base is 90 feet each. 90 squared = a big number. The square root of that number probably equals something.
  2. Figuring out how big of a TV will fit through your front door
    Let’s say your front doorway is 30 inches wide and you want to by a 60 inch TV. You could use the Pythagorean Theorem to figure out how tall of a TV you need to buy in order to fit it vertically through the front door. Or you could just tip the box sideways.
  3. Construction
    If you’re standing on a bridge and need to calculate how far you’d have to throw a rock to hit an occupied port-o-potty on the ground below, you could use the height of the bridge and the horizontal distance between yourself and the port-o-potty to represent the descending diagonal distance the rock must travel.
  4. Navigation and travel
    If you need to travel 400 miles north and 100 miles west to reach your grandmother’s house for a Thanksgiving get-together, you can calculate the shortest distance on a straight line. Roads often criss-cross the hypotenuse rather than ride it directly. Save gas and time by traveling no more than 412.3 miles and bypassing the roads.
  5. Math problems in school
    Teachers and educational administrators love torturing children with repetitive mathematical exercises with marginal utility in the real world.

The potential applications are many. Maybe the baseball nerds stumbled on to something. Who can really know? I’m willing to keep an open mind and give the Pythagorean Theorem a chance to prove itself. But until then, let’s try to keep baseball talk to something we can all understand.


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