How the Models Work

Head-to-head sports: ratings

Every team (or player, or fighter) has a rating. Before a game the model turns the difference between the two ratings, plus home advantage, into a win chance; after it, both ratings move by an amount that depends on how surprising the result was. This is the Elo method, with the refinements that make it forecast well:

Margin of victory. A big win moves ratings more than a narrow one, scaled so that heavy favourites winning big aren't over-rewarded.
Home advantage is fitted per league, and switched off on neutral ground.
Draws, in sports that have them, come from a draw band around an even game (an ordered-logit model), so a close match gets a larger draw chance than a mismatch.
Between seasons every rating is pulled part of the way back toward average, because squads change. New teams start below average.
Playoff games can count for more or less than regular-season ones.

Adjustments, kept only where they help

Some leagues add information the results alone don't have. Each adjustment is tested on the tuning seasons and kept only if it makes the forecasts better on seasons it never saw:

Who is playing. Basketball rates each player by their box-score contribution and compares the side that will play with the side's usual; the NFL uses the starting quarterback; the NHL the starting goalie; MLB the starting pitchers.
Surface in tennis: separate ratings for hard, clay and grass, blended with the overall one.
Weather. Wind, rain, cold and heat at the ground make results less predictable, so rough conditions pull the favourite's chance toward even. A weather weight is only kept where there were enough rough-weather games to learn it from.
Recruiting in college football sets where each team starts a season.

Seasons and titles

Title odds come from playing out the rest of the season thousands of times, game by game, with each game's chance from the ratings. Each simulated season lets every rating drift a little, because ratings are estimates, and uses the league's real points system, tiebreakers and playoff format. Results already in stay in. The share of simulated seasons a team wins is its title chance. In the off-season the same simulation runs on the next season's schedule once it is published.

Races and fields

For motor racing and fleet sailing the model rates each driver (and car or boat) from every finishing order, weighting recent races more. The chance of any finishing order follows the Plackett–Luce model: the winner is drawn in proportion to strength, then second from those left, and so on. Rain and wind make results less predictable where the data shows it. Season odds replay the remaining races with each series' own points system.

Golf

Golf rates players by strokes gained against the field in every round they play, weighted toward recent rounds and shrunk toward average when there are few of them. A tournament is simulated round by round, with the cut, from each player's rating and the course conditions.

Live games

Once a game starts, the win chance updates from the score and the time left: the pre-game rating gap sets the expected margin, and the remaining time sets how much can still change (a random walk for high-scoring sports, a Poisson model for low-scoring ones).

Honest testing

Every model's settings are chosen on older seasons only. The most recent seasons are held back and scored as if forecast on the day, using only what was known before each game. Those held-back scores are what the track record shows. The model is compared with three baselines:

Base rate: the home side's usual win rate (or every entrant equal in a race).
Recent form: ratings from the last few games only.
The market: closing betting odds with the bookmaker's margin removed, where they exist. The market is very hard to beat; being close to it is a good result.

The main score is log loss, which punishes confident misses heavily; lower is better. We also show accuracy and calibration: of all the games given 70%, the favourite should win about 70%.

SailGP has its own model, described on the SailGP track record page.