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:
\[KOE= X - E[X]\]
In a given field goal attempt \(x_i\) if \(x_i=3\) and the Field Goal is made KOE will be ge given by
\[KOE= 3- 3 \cdot p_{FG}^i \]
And if \(x_i=0\) and the Field Goal is missed
\[KOE= -3 \cdot p_{FG}^i \]
KOE will penalize misses more severly as the estimated probability goes higher, and offer higher rewards for converting difficult kicks.
