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KOE KOE Kicks Over Expected, or more properly and less catchy Field Goals Over Expected, is a metric built to evaluate american football kickers as fairly as possible. If \(X\) is a random variable that represents the points scored in a field goal, we can assume that \(x \sim B(1,p_{fg})\) , where \(p_{FG}\) is the probability of making a field goal. The expected points of any field goal then, is given by: \[E[x]=3\cdot p_{FG}\] If we then want to measure how the observed output measures against its expected value, we define KOE as:
The best model for our purposes has to be as simple and accurate as possible. If the methodology suggested is free of assumptions that become invalid with changes in the distribution, there is no reason why it could not reproduce comparable results in different leagues and countries. A holdout set of all kicks attempted since 2019 was taken to prevent myself from over-fitting the problem. Only plays when a field goal was actually attempted are included, so only three possible outcomes were considered:
At its core, KOE will be as useful as our estimate of converting a field goal \(\hat{p}_{FG}\) resembles \(p_{FG}\). In order to do this as well as possible, the information fed into the model must help it distinguish how hard each attempt actually was. What determines the difficulty of a kick? The answer is surely as complex as our information allows it to be, but we will try to build a model as simple as possible that best answers this question.