Quantum Moneyball
by Ken Arneson
2012-10-22 9:54

Just before the beginning of this sentence, this essay could go in an infinite number of directions. But now that the first sentence has been written, the number the infinite directions it could possibly go has been reduced into a much smaller infinity. Who knows what I’ll write next?

It could be anything! Gratitude to their emotions in the water! Or maybe with Zito is blind to park your dastardly actions.

I recently watched a TED Talk by Emily Levine which is like that. It rambles off in a gazillion directions, with little coherency. You could go off now in the direction of watching it. I’m not sure I’d recommend that for you, but I’m glad I did it myself, because it contained one nugget near the end which sent me off in another, more interesting direction.

She rambles this way and that on purpose, not completely polished and slightly unprepared, because she says she likes her talks to remain in a “probability wave” as long as possible. If you’re polished and prepared, you’ve already collapsed your probability wave into single point, and you’ve closed yourself off to new possibilities. She wants to keep open the possibility of “getting on the same wavelength” as her audience.

It’s that idea of “probability waves” that got me intrigued. She’s using ideas from quantum physics to help her understand her art. Using quantum physics as a metaphor sounded interesting, so it sent me scrambling to update myself on quantum physics and probability waves again. And now there’s a very high probability that this essay will devolve into a physics lesson.

* * *

To understand Levine’s metaphor, you need to know about the double slit experiment. This cartoon is the best introduction to it I’ve seen:

That’s kind of freaky. If you’re like me, you still don’t quite get it. I’ll add Professor Brian Greene’s explanation of the double slit experiment on Nova:

* * *

In short:

  • Before observation, a subatomic particle is anywhere in the whole universe.
  • Upon observation, a subatomic particle can no longer be anywhere. It must “collapse” to somewhere specific.
  • Where an “anywhere” ends up collapsing into a “somewhere” is based on probabilities. Some places it can end up turn out to be more likely than others. And these probabilities can interfere with each other, or amplify each other, in the way that one wave can either interfere with another wave, or amplify it.

Ok, if you’re like me, you’re still having trouble understanding the concept of “probability waves.” And when I’m confused, I turn to baseball metaphors.

* * *

Imagine that a baseball player is a subatomic particle. We’re going to pass the player through two slits, and we’ll call these slits “On-base Plus Slugging” and “Plate Appearances”.

Suppose we have a player/subatomic particle named “Kila Ka’aihue”. Let’s say Ka’aihue is projected to hit something like this in 2012:

4% chance his OPS is around .913
8% chance his OPS is around .869
12% chance his OPS is around .837
16% chance his OPS is around .811.
20% chance his OPS is around .786.
16% chance his OPS is around .762
12% chance his OPS is around .738
8% chance his OPS is around .705
4% chance his OPS is around .663

and let’s say he’s projected to get playing time like this:

4% chance he gets around 500 Plate Appearances
8% chance he gets around 450 PA
12% chance he gets around 400 PA
16% chance he gets around 350 PA
20% chance he gets around 300 PA
16% chance he gets around 250 PA
12% chance he gets around 200 PA
8% chance he gets around 150 PA
4% chance he gets around 100 PA

Before the season starts, any combination of these stats are possible. He could hit a .913 OPS and get around 200 PA. Or he could hit .738 and get around 400 PAs. Or any other combination — some are more likely than others, but they can all happen.

Some of these probabilities, however, interfere with each other. If Ka’aihue hits .663, it reduces his odds getting 500 PA, because the A’s will likely give his PAs to somebody else instead. If he hits .913, it reduces his odds of taking a path with only 100 PA, because if he’s playing that well, the A’s will want to give him a lot more than 100 PAs.

Other probabilities amplify each other. If Ka’aihue ends up with a .663 OPS, it increases his odds of ending up with only around 100 PA. If he ends up with a .913 OPS, it increases his odds of ending up with over 500 PA.

* * *

So now, let’s play the 2012 season a million times.

Each time we play, we shoot the Ka’aihue subatomic particle through these two slits, and some particular combination of OPS and PAs ends up on the back wall.

Now, if we chart the one million Ka’aihue outcomes, all the OPSes and PAs, we’ll see something similar to the double slit experiment. We’ll see some areas of high density, and other areas of low density. We’ll get lots of marks where the OPS and PAs are both high, or both low, because that’s where the odds get amplified. We’ll get gaps where one is high and the other is low, because that’s where the odds cancel each other out.

* * *

Now of course, we didn’t play the 2012 season a million times. We only played it once. And in that one, single time, Ka’aihue ended up with .693 OPS in 139 plate appearances — both low. And because of that low outcome, the A’s tried Brandon Moss and Chris Carter at first base, instead.

* * *

You can think of the whole 2012 Oakland A’s season in this way. If Ka’aihue has a low OPS, it amplifies the odds that he’ll also have fewer PAs. If Ka’aihue has fewer PAs, it amplifies the odds of Chris Carter or Brandon Moss or Daric Barton getting more PAs, until one of them starts hitting well. Which is what happened: Moss and Carter ended up in a platoon and hit well.

But if Ka’aihue has a high OPS instead, it amplifies the odds that he’ll get more PAs, and cancels out the odds of Carter and Moss getting a lot of PAs. The whole season takes a completely different path, and probably ends up “collapsing” into a completely different place.

* * *

Baseball is more complicated than just OPS and plate appearances, of course. And in the end, the stat we baseball fans are really interested in measuring on that back wall is team wins.

As the season starts out, there are an infinite number of possible ways the season can play out. Some things are more likely than others, but once we observe the season, all those possibilities collapse into one, single outcome. The 2012 A’s could have ended up with 0 wins or 162, but those are extremely unlikely paths. That would be like a diamond spontaneously jumping out of a locked safety deposit box and into a thief’s pocket. Most likely, the diamond stays in the box. Most likely, the team stays within a “box” between 40 and 120 wins.

Atomic-era general managers will understand all these possible amplifications and cancellations, and construct their teams to maximize the odds that the path their team takes collapses into a championship. The most likely outcome for the A’s was figured by pundits to be around 75 wins. And maybe if you replayed 2012 a million times, it will average to 75 wins. Or maybe, Billy Beane understood how all those waves of statistics amplified and canceled each other out better than anyone else. Maybe, the A’s season collapsing into a single, specific result of 93 wins and an AL West Division title was not quite the miracle we thought it was.

And with that, this essay shall hereby collapse into itself.

* * *

Disclaimer: this metaphor was presented for informational and entertainment purposes only. Baseball players are not actually subatomic particles. Quantum physics are not the most accurate way to describe the behavior of baseball players. Nor are the behavior of baseball players the most accurate way to describe quantum physics. The reader assumes all risk for all unintended uses of this metaphor, including–but not limited to–using Feynman path integral formulations to project future baseball outcomes.

This is Ken Arneson's blog about baseball, brains, art, science, technology, philosophy, poetry, politics and whatever else Ken Arneson feels like writing about
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