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Game Intelligence in Team Sports


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After reading this journal article Co-Authored by Nicklas Lidstrom I can see why more Athletes are choosing the NCAA route to the NHL. Or maybe I should also say why NHL teams are choosing NCAA coaches.   ;)  





In this paper, we make an attempt to develop a mathematical theory on game intelligence in team sports. It is central to this theory to value game situations by their potential. Intuitively, the potential is the probability that the offense scores the next goal minus the probability that the next goal is made by the defense. We give many examples to illustrate the width of the applicability of our results, but the set of chosen situations is by no means exhaustive.
In Section Team handball; shot proportions, we argue that the classical efficiency thresholds—e g that back court and wing players should have 50% and 80% mean shot efficiency, respectively—are likely to be non-optimal. It would be interesting to investigate this issue further.
One of the authors, Nicklas Lidström, relied on a set of first principles which he used to analyze how to play game situations during his career as a professional ice hockey player. His approach constitutes a cornerstone in the present paper.
In Section Ice hockey; chasing the puck, we analyzed whether a defense player should charge or hold back. We note here that it appears that the vast majority of backchecking hockey players judge that it is optimal to charge. Nicklas thought that it was optimal for him to hold back, which consequently was how he played in such situations.
The example in Section Ice hockey; pass or dribble presents Nicklas’ analysis of why it is optimal to pass early in that situation, and in similar ones.
Further, in one against one situations, Nicklas recalls using his reached out stick extensively as a first line of defense against opposing forwards. He believed that this increased the width with which he could operate. The operating width is equivalent to the quantity r in the examples of this paper. Hence he made the action to dribble less attractive in terms of potential for the opposing forwards. This had the effect that he could stear the forward further to the sides—preferably their back hand side—to make that alternative, too, lower in potential than what he thought he could have obtained otherwise.
We note that Nicklas’ S shaped strategy in the two against one examples in ice hockey is different to how most defense players choose to play such situations. It seems that most defenders eventually decide to let go of the non-puck holding forward to focus on the forward with puck possession instead.



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Proof. The first conclusion follows from [17, Theorem 2.1]. For the second part, if y* is the global minimizer and y* ≠ arg miny Є vi(y) for any i = 1, …, n, then for any i such that vi(y*) = v(y*) there is a non-zero gradient qi such that for small λ > 0 we have that y* − λqi Є and vi(y* − λqi) < v(y*). Further, since y* is the global minimizer and the potential functions are continuous and convex then there exist a j ≠ i such that v(y*) ≤ v(y* − λqi) = vj(y* − λqi). Hence, since the potential functions are continuous there exist a j ≠ i such that vj(y*) = v(y*).


That's enough proof for me, I'm convinced.

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As an aside, that website- plosone.org, is one of my favorites. If you have an interest in science they publish a lot of interesting stuff, and much of it is actually understandable to the average human.

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