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 proper, an ability regression suite with smart regularization.
  • MARKOV, a less-linear method for deriving WAR from ability estimates.


SALO is the “SALO Alternative-wise Log Odds” model.

SALO comprises joint estimation of:

  1. player-parameterized ordered logit likelihoods for shots and penalties;
  2. a Gaussian prior to shrink player ability parameters toward average;
  3. 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 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.
Gordon Arsenoff
Senior Research Specialist