Baseball Primer Newsblog— The Best News Links from the Baseball Newsstand
Wednesday, March 20, 2013
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 highlevel 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 nonlinear 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 reevaluate how we practice sabermetrics.

Support BBTF
Thanks to Sebastian for his generous support.
Bookmarks
You must be logged in to view your Bookmarks.
Hot Topics
Newsblog: OTP  July 2014: Republicans Lose To Democrats For Sixth Straight Year In Congressional Baseball Game (3993  3:51am, Aug 01)Last: Dr. VauxNewsblog: Athletics, Twins Swap Tommy Milone, Sam Fuld (23  3:45am, Aug 01)Last: Dr. VauxNewsblog: Marlins acquire Jarred Cosart from Astros in sixplayer deal (7  3:16am, Aug 01)Last: KT's Pot ArbNewsblog: OT: The Soccer Thread July, 2014 (557  3:04am, Aug 01)Last: Swedish ChefNewsblog: A's Acquire Lester, Gomes For Cespedes (128  3:00am, Aug 01)Last: PreservedFishNewsblog: JULY 31 2014 OMNICHATTER/TRADE DEADLINE CHATTER (363  2:09am, Aug 01)Last: Crispix reaches boiling point with lackluster playNewsblog: Tigers To Acquire David Price (72  1:58am, Aug 01)Last: if nature called, ladodger34 would listenNewsblog: Cardinals Acquire John Lackey (93  1:57am, Aug 01)Last: bjhankeNewsblog: Minnesota Twins sign Kurt Suzuki to twoyear contract extension (7  1:19am, Aug 01)Last: boteman is not here 'til OctoberNewsblog: Yankees land infielders Stephen Drew, Martin Prado at Deadline (20  1:07am, Aug 01)Last: shoewizardNewsblog: Mariners acquire outfielder Chris Denorfia from Padres (4  1:04am, Aug 01)Last: PreservedFishNewsblog: OT: Monthly NBA Thread July 2014 (1074  1:02am, Aug 01)Last: SquashNewsblog: Cliff Lee ReInjures Elbow (18  12:55am, Aug 01)Last: Joyful Calculus InstructorNewsblog: Cubs deal Emilio Bonifacio, James Russell to Braves (10  12:38am, Aug 01)Last: JacobNewsblog: Brewers acquire outfielder Gerardo Parra from Dbacks (5  12:27am, Aug 01)Last: KT's Pot Arb

Reader Comments and Retorts
Go to end of page
Statements posted here are those of our readers and do not represent the BaseballThinkFactory. Names are provided by the poster and are not verified. We ask that posters follow our submission policy. Please report any inappropriate comments.
1. depletion Posted: March 20, 2013 at 08:18 AM (#4392243)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.
See if it matches the theory.
I think you're missing the point of numerical applications on the computer.
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.
Why set yourself apart from the crowd?
Not even wrong. Just missing the whole point of numerical computing.
You must be Registered and Logged In to post comments.
<< Back to main