Intro to SALO
Overview of SALO
SALO is a fully Bayesian skater ability and value model for the NHL.
SALO’s version history is tied to RIT’s annual analytics conferences:
- Version 1 was released at RITHAC 2017.
- Version 2 was released at RITSAC 2018.
- Version 3, in development, was previewed at RITSAC 2019.
SALO consists of two main components:
SALO
SALO is the “SALO Alternative-wise Log Odds” model.
SALO comprises joint estimation of:
- player-parameterized ordered logit likelihoods for shots and penalties;
- a Gaussian prior to shrink player ability parameters toward average;
- a beta-binomial regression for games played in terms of player ability.
The last part means estimates are shrunk to a smarter target than average:
- Players who rarely appear on ice are subject to the most shrinkage.
- Typically, players who are better are trusted wtih more appearances.
- So low-info players should be shrunk toward below average!
MARKOV
MARKOV stands for:
“MARKOV Approximation for Reasonable Konstruction of Overall Value”
MARKOV assumes a Markov chain to map SALO estimates to a WAR scale:
- Work out all states (scores, periods, strengths) the game could be in.
- Derive parameterized short-term transition chances between states.
- Plug in ability estimates for any given player (and neutral assumptions).
- Multiply out out end-game state probabilities from short-term ones.
Why Bayesian?
Bayesian methods allow for advanced, custom model definition.
- Non-Bayesian techniques shrink parameters only toward average.
- Shrinking estimates toward an informed target is a Bayesian move.
Bayesian methods also allow quantifying the uncertainty in estimates.
- Non-Bayesian penalized estimates don’t have proper error bars.
- But describing confidence levels in each estimate is important!
In development
Version 3, in development, is intended to add:
- A further prior for year-to-year smoothing and projection of estimates;
- Basic models for on-ice contributions to shot quality and shooting.
- More years of data.
