Reference

Glossary & Methodology

What the numbers mean and how they are produced.

So what exactly is shown?

Everything is derived from the score difference of each game. The only information going into the model is the final score difference, the ten players on the court, and a few variables for fatigue, rest and first possession. A time decay half-life of 270 days means games gradually lose weight as they age.

Interpretation: a player with a rating of 1.5 makes their team 1.5 points better than an average replacement.

How the ratings are formed

Consider a game with four below-average teammates and five slightly above-average opponents. The expected point differential is determined by those nine players, and performance relative to that expectation is what moves a rating.

For this reason it is neither inherently good nor bad to have better or worse teammates. The only barometer is performance versus expectation given the other nine players.

Player stats

Proj Diff — Sum of team ratings minus opponent ratings.

Tm Quality — Sum of teammate ratings, excluding the player.

Team Quality — Sum of team ratings, including the player.

Opp Quality — Sum of opponent ratings.

Gospel — Result versus expectation. Actual score differential minus what the model projected, averaged over games.

% Pos Teammates / % Pos Opps — Share of games where teammates, or opponents, are net positive.

% as Favorite — Share of games where the team is favored.

% Better Tm — Share of games with better teammates than opponents.

Other 9 Diff — Average difference between teammate and opponent ratings.

1st / Last Game Rate — Share of runs where the player appears in the first or last game.

Games

A Quality / B Quality — Sum of that team's player ratings.

Spread — Team A Quality minus Team B Quality.

vs Spread — Actual score difference minus the spread.

A Win Prob — Win probability from a logistic regression on team qualities.

Moneyline — That win probability expressed as American odds.

Clock — Whether the game ran on a clock rather than to a fixed score.

1st Poss — Which team started with the ball, inferred from who held the court.

Player days

1st Game / Last Game — Game number where the player first and last appeared that day.

Longest Run On / Off — Longest consecutive stretch playing or sitting.

Pairings

Gospel w/ Tm and Gospel vs Opp — Result versus expectation when two players share a team, or face each other. Quality columns exclude both listed players.

Days

MVP – Player with the highest Gospel value that day (min 3 games).

LVP – Player with the lowest Gospel value that day (min 3 games).

MVP Gospel – Gospel value of the MVP that day (min 3 games).

LVP Gospel – Gospel value of the LVP that day (min 3 games).

Avg Rtg (Players) — Mean rating of everyone present, each counted once.

Avg Rtg (Games) — Mean rating across all player-games, so players who played more weigh more.

Unique Winners — Share of attendees who won at least one game.

Parity — Standard deviation of the named metric. Lower means a more even day.

Overview

This is a RAPM-style model, inspired by work such as Jacob Cutter's RAPM writeup.

Basic plus-minus measures point differential while a player is on the floor. Adjusted plus-minus uses regression to control for the other nine players, attributing impact more fairly. Regularized adjusted plus-minus shrinks those coefficients with ridge regression, stabilizing estimates for players with small samples.

Conceptual chain

Game results → score differential → on/off stints → regression with one regressor per player → ridge regularization → per-player ratings representing impact in points per game.

Regularization

The ridge penalty λ is chosen by cross-validation across [0.1, 0.5, 1, 5, 10, 25, 50, 100]. Players with fewer than 20 games are grouped into tiers rather than given their own coefficient, so a two-game sample cannot produce an extreme rating.