Math!

For me it remains an open question whether [hockey]
pertains to the realm of mathematics or to that of art.
– M.C. Escher

Well, I have never been so impressed by the work of a fellow blogger as I was last night when I read wildmanmath's article "Why Even A Bad System is Better Than No System At All" over at Copper and Blue. If you have not read this blog post: Stop reading this drivel and go directly to that hyperlink, NOW! Now I am not going to claim that I understand the complexities of mathematics, or even the simple parts. I just have a intuitive feeling about math but no formal education on it (I attempt to read set theory in my free time, but that is about it). So everything I am about to say is wrong and needs to taken as a thinker stepping out of his field and into a pit of quicksand.
Before I reach into the realm of math, I think there needs to be said something about Art. M.C. Escher was the great popularizer of the intersections of mathematics and art, and his works are still some of the most sought after prints that adorn the dorm rooms of college kids. Now most people would recognize (even grudgingly) that all art has some kind of mathematical qualities to it: even if it is only perception, symmetry, and a logic of space. In relation to one of his drawings (but I cannot find which one) he says the quote that begins this humble blog. I think this sentiment can be applied to the game of hockey. Many anti-math (or should we say stats) friends, cough Sachia cough, continually point out that hockey is an art not a science. Wildmanmath gives us a new way to think about the mathematics of hockey: that it is not just the statistics that we use, create, and manipulate which creates a scientific basis for hockey. Instead we can use mathematics to understand the parts of the game which defy statistical analysis: the randomness of the puck, the idea of luck, and maybe even 'clutchness'.


So as I reread this blog post multiple times, I never really quite understood all the details of the project. But one paragraph stood out to me as the important part of the article:
"The corollary of the non-randomness [which is not randomness, but is neither order nor structure] and its effect on puck possession [how strategy plays out in the game] is, and this is what makes hockey so non-transitive [or based on positive feedback loops i.e. game theory], that occasionally, owing to the randomness [again not disorder or contingency] of the puck when in neither team's control, that a bad strategy must sometimes out perform a good strategy. We cannot cover all the possibilities of the puck's behaviour so by definition [how we wish to use language or formulas] what we choose to do, the decisions we make, however, well thought out, must be wrong some of the time [that the words and stats we choose to describe the play of hockey most not only be inadequate in their description but also that if they are adequate then they are still wrong based on the arbitrary nature of their non-randomness]. Conversely, given the randomness of the puck, sometimes the worst decisions must turn out to be right [which is the reason I still have friends and get laid on occasion]." -Wildmanmath (my thoughts in the copper brackets)
Leaving aside the un-witty jokes, my complete misunderstanding of mathematics, and my obtuseness to locate what wildmanmath is actually saying—there is a relevant point in all of this. That while statistics cannot alway account for the beauty of hockey or art, it can still be explained in a scientific manner through the use of mathematics. I will never be able to truly add to this conversation, but I am hoping wildmanmath and others continue to examine how real mathematics can teach us about our beloved game. Might I suggest using this to look at the dirty concept of "clutchness" my friends.

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