Models, Prediction and Throwing a Baseball: Why Black Box Approximation Is Not Casuality

Last week, I linked to a video of economist Gerd Gigerenzer in which he argued that heuristics and simple rules are not cognitive flaws but actually perform better in the face of the unknowable and uncertain. That’s an important point not only for economists, but also biologists.

But I want to focus on something else: the difference between a model that predicts and one that addresses mechanism. So let’s talk about baseball. In the talk, Gigerenzer argues that most economists*, trying to understand how a baseball outfielder would catch a fly ball, would draw up a set of differential equations to predict where the ball would land, like so:

baseballequation

ZOMG! MATHICISMZ!!

However, an empiricist would approach the problem differently. She might watch video of players catching fly balls. She might ask players what they do to catch a fly ball. When you do this, what emerges are three simple heuristic rules that players use:

1) Fix your gaze on the ball.
2) Start running (this is important!).
3) Adjust your running speed so your angle of gaze remains constant.

So what are baseball players? Masters of differential calculus on the fly (so to speak), or followers of simple rules? Well, each of these models makes predictions.

The human calculator model predicts the following:
1) Players want to know the landing point.
2) Players run to the landing point.
3) Players run in a straight line to that point (minimum distance).
4) Knows where the ball will land.

The heuristic model predicts the following:
1) Players want to catch the ball, not stand at the landing point.
2) Intercepts ball while running, if possible.
3) Runs in a slight arc.
4) Doesn’t know where the ball will land.

When you actually test these two models, the heuristic model is right on every count and the differential calculus model is wrong. But much of the time, the differential calculus model will be a decent approximation of where the player needs to be, although sometimes it will be dreadful (consider a low fly ball: the landing point isn’t anywhere near where a player would ideally catch the ball).

This is relevant to some recent arguments in economics (along with phylogenetic reconstruction in biology**). There has been a very technical argument over various models, such as IS-LM and DSGE (if you have no idea what these are, don’t worry). But what’s interesting is that defenders of these approaches always argue that they have fairly good predictive value, although, in some circumstances they fail, and they often don’t completely describe what happens (mind you, the two schools won’t say anything nice about the other…).

So, let’s return to the differential calculus model of catching a fly ball. It’s a fairly good prediction (except when it isn’t). Sure, there are some minor problems–players run in slight arcs, not straight lines, but it helps us think about things, right?

And the differential calculus model has nothing to with how players actually catch a baseball.

If you need to understand how something actually works, approximate prediction is not good enough. You need a model that incorporates how things actually work (aka those stupid fucking natural history facts).

People always chant “correlation is not causation.” Well, neither is approximation.

Related: Bob O’Hara has some related thoughts about model simplicity.

*And Richard Dawkins. Then again, I’ve never been impressed with Dawkins as a philosopher of biology going back to the ridiculous genetic bookkeeping espoused in The Selfish Gene.

**Anyone who has looked at sequence variation knows DNA does weird things, but GTK models seem to work well. That doesn’t mean they are actually reflecting the mutational process in all situations.

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2 Responses to Models, Prediction and Throwing a Baseball: Why Black Box Approximation Is Not Casuality

  1. hipparchia says:

    well… i would argue that black box approximation IS casuality. ;)

  2. Ryan says:

    With respect to the two models for catching a baseball, the old Metrodome, was infamous with players from visiting teams for a variety of reasons, catching fly balls was one of them. Apparently, players are trained to read the ball off of the bat, estimate where the ball will land, run to that location, look up, and find the ball again. The problem with the Metrodome was that the grayish baseball did not offer much contrast with the gray roof, especially during games played during the day, and finding the ball again while it was in the air was not necessarily a given. In fact, it was quite difficult for visiting players. Instead, in the Metrodome players could never take their eyes off the ball so that they didn’t have to find the ball again while it was in the air. This led to collisions between players or collisions with the backfield wall while attempting to follow the ball in flight that looked painful. It also led to missed fly balls that would have been caught at nearly any other stadium.

    http://www.cbssports.com/mlb/story/12148420

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