Mathematicians Explain Sports to Each Other
Ten sports as mathematicians explain them: open and closed sets in basketball, Poisson-distributed soccer goals, golf as a minimization, baseball's 162-game sample, and the marathon as an integral.
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2017-06-28-mathematicians-explain-sports-to-each-other/ (CC BY-NC 4.0)Transcript
[1] Basketball: "So is three-point range a closed set?" "No, a sequence of three-pointers may converge to a two-pointer." "Ah, that must be why they call them 'open threes.'" "Presumably."
[2] Tennis: "Any questions?" "Nah, it's all just projectile motion. This game is easy." … "Well… there is air resistance." "THIS GAME IS IMPOSSIBLE."
[3] Soccer: "Each team generates goals according to a Poisson distribution, typically 0.5 < λ < 1.5." "So where do the humans come in? You could do the whole thing in Excel." "That's what I've been telling them!"
[4] Golf: "Just minimize Σᵢ₌₁¹⁸ (xᵢ − parᵢ)." "Cool. Anything else I should know?" "Nope. The rest follows trivially."
[5] Baseball: "Then you spend a year taking samples until n = 162." "I see. Because the underlying distributions are so similar that you need large n?" "Yeah. Plus you're mostly just standing around anyway."
[6] Hockey: "What's 'offsides'?" "It's this sort of arbitrary condition on how you parametrize your position, based on the puck's position with respect to time. Should I walk you through it?" "Nah, sounds like technical details."
[7] Marathon: "Let ∫₀ᵀ v(t) dt = 26.2 miles. Then minimize T." "Ugh. Sounds exhausting." "Yeah, I hate underconstrained optimization questions."
[8] Tee-ball: "So it's like baseball?" "Yes, but controlling for a lot of variables."
[9] Cricket: "So each transposition is a point… and the time variable is unbounded above?" "Yeah, it's kind of an ill-defined problem."
[10] Skiing: "You're going down an icy mountain. Your goal is to minimize your coefficient of kinetic friction." "Um… why?" "Don't ask. It's axiomatic."