Define terms

[wmbelk]

Original:

So we model the probability p_k that a referee calls a foul in play k as a function of the players involved. Hence we define two latent variables for each player, namely:

theta: which estimates the player’s ability to have a foul called when disadvantaged, and
b: which estimates the player’s ability to have a foul not called when committing.
Note that the higher these player’s parameters, the better the outcome for the player’s team. These two parameters are then estimated using a standard Rasch model, by assuming the log-odds-ratio of p_k equals theta-b for the corresponding players involved in play k. Also, we place hierarchical hyperpriors on all theta’s and all b’s to account for shared abilities between players and largely different numbers of observations for different players.

Modified for smear:

So we model the probability p_k that a smear happens in play k as a function of the players involved. Hence we define two latent variables for each player, namely:

Juke: which estimates the player’s ability to avoid a smear when disadvantaged, and
Focus: which estimates the player’s ability to smear when committing.
Note that the higher these player’s parameters, the better the outcome for the player’s team. These two parameters are then estimated using a standard Rasch model, by assuming the log-odds-ratio of p_k equals juke-focus for the corresponding players involved in play k. Also, we place hierarchical hyperpriors on all theta’s and all b’s to account for shared abilities between players and largely different numbers of observations for different players.