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## Wednesday, March 20, 2013

#### Walk Like a Sabermetrician: Calculus

Pickover Calculus and Pizza? I can’t decide.

What prompted this post was not a calculus barb directed at sabermetrics, but one of the reactions to such a barb in a Baseball Think Factory thread: a flat out statement that “calculus has no place in baseball statistics”. On one hand, I really should just ignore this. The statement itself is so outlandish as to be difficult to respond to. It’s akin to saying that “cymbals have no place in music” or that “rice has no place in one’s diet”. Calculus is obviously not used directly by most sabermetricians, and one can certainly be a practice high-level sabermetrics without using any calculus. But to simply write off the possibility of using an entire branch of mathematics in the discipline is absurd.

...I do not wish to give the impression that I think the application of calculus is central to the current practice of sabermetrics. Clearly it is not, given the paucity of work applying it to sabermetric questions. But it is another tool at our disposal, and one that is perfectly suited to assist in the types of sabermetric questions that have always interested me. Calculus certainly has vast applications in understanding the mathematical relationships between sabermetric formulas. Why can you predict team runs scored fairly accurately (at least in a normal team context) using a dynamic equation like Base Runs or a linear weights equation? Why does any variant of the Pythagorean family of win estimators match up so well in practice with linear equations that follow the rule that ten runs = one win? Calculus is also inherent in any sort of exercise involving hypothesis testing, even if it is only implicit. After all, the normal distribution is defined as an integral of a particular function.

I will close with a list of links to articles on this blog that have used calculus in some manner. As you will see, the scope of topics that I have applied calculus to are fairly limited—mostly to understand how events are valued in various offensive measures and to estimate runs per win from non-linear win estimators. Hopefully those of you with more imagination and a broader range of research interests can come up with other applications. Even if what I’ve written about did represent the full extent of possible applications of calculus in sabermetrics, it should be clear that there is a place for it. And if there wasn’t a place for a branch of mathematics which has countless applications in the sciences, statistics, and probability in sabermetrics, I’d suggest it would be time to re-evaluate how we practice sabermetrics.

Repoz Posted: March 20, 2013 at 05:15 AM | 12 comment(s) Login to Bookmark
Tags: sabermetrics, site news

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1. depletion Posted: March 20, 2013 at 08:18 AM (#4392243)
Hi. It might have been me that posted the item the author was referring to. Unfortunately I can't access the full article from this computer. Perhaps in the evening I can take a look. I have nothing against calculus. Far from it. I love it and it loves me and I wish I could read more about it's applicability to baseball.
2. bobm Posted: March 20, 2013 at 08:58 AM (#4392261)
I found this:

13. Bitter Calculus Instructor Posted: September 28, 2012 at 08:49 PM (#4248544)

Has anyone here ever encountered calculus in a baseball paper?

The physics of baseball uses calculus. I remember in a math modeling competition a few years ago, one of the choices was to find the sweet spot on a bat. I imagine calculus would be involved in that.In terms of baseball statistics, projections, ect., though, which is the topic on hand, no. Calculus is not involved. Statistics are based on discrete events: at bats, pitches, plays in the field. Calculus has no place in baseball statistics
3. bobm Posted: March 20, 2013 at 09:04 AM (#4392262)
4. Juilin Sandar to Conkling Speedwell (Arjun) Posted: March 20, 2013 at 09:10 AM (#4392264)
I like that the username of that poster is "Bitter Calculus Instructor".
5. valuearbitrageur Posted: March 20, 2013 at 01:03 PM (#4392518)
Calculus is just one of those obscure old theories no one uses and no one is even sure works, like Astrology and xFIP.
6. snapper (history's 42nd greatest monster) Posted: March 20, 2013 at 01:12 PM (#4392537)
With the advent of massive, cheap, computing power, calculus has become much less necessary. Many of the problems you used to need calculus to solve, can now be solved with brute computational force.

The easiest example is finding the area under a curve. You could always do it by calculus, or by approximation, drawing a series of thin rectangles under the curve and adding up the area. With a modern computer, that latter is very, very easy.
7. depletion Posted: March 20, 2013 at 02:22 PM (#4392640)
How do you check that the computer program is doing it correctly?
See if it matches the theory.

I think you're missing the point of numerical applications on the computer.
8. Joyful Calculus Instructor Posted: March 20, 2013 at 02:30 PM (#4392652)
Oh wow. I didn't realize that quote would come back to bite me.

It was a good article, though. And shows how the ideas of calculus relate well to looking at functions. Like the derivative of pythagorean record showing why 10 runs is equal to a win. I should probably think about what I say more carefully.
9. depletion Posted: March 20, 2013 at 02:44 PM (#4392673)
I should probably think about what I say more carefully.

Why set yourself apart from the crowd?
10. depletion Posted: March 20, 2013 at 02:46 PM (#4392676)
With the advent of massive, cheap, computing power, calculus has become much less necessary.

Not even wrong. Just missing the whole point of numerical computing.
11. Robert in Manhattan Beach Posted: March 20, 2013 at 05:26 PM (#4392959)
I sure was good at calculus in college, and boy does it never come up.
12. bjhanke Posted: March 20, 2013 at 07:50 PM (#4393097)
snapper (#6) - So what can happen is that the computer allows you to just do Simpson's Rule directly, without allowing it to finish up as calculus. That's actually very funny, using Simpson's Rule directly because the computer can do that. - Brock Hanke

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