How it works

Three numbers for every team

For every Division I team the model keeps an offence (points it scores per 100 possessions above the league average), a defence (points it allows per 100 possessions above average; lower is better) and a tempo (possessions it adds to a 40-minute game). Possessions in a game are counted from the box score: field-goal attempts, minus offensive rebounds, plus turnovers, plus 0.475 of free-throw attempts (0.44 for women's games), averaged over the two teams.

Each morning every team's three numbers are solved together from all of the season's games between Division I teams, so a 50-point win over a weak team counts for less than a 5-point win at a strong one. Three refinements, each kept because it made the predictions better on seasons the model had not seen:

• Recent games count more. A game's weight halves every 90 days.
• Three-point luck is discounted. Half of the gap between the threes a team made and the threes it would have made at its own season rate (pulled toward the league rate until it has taken about 150) is removed before rating. Three-point shooting swings a lot from night to night and repeats less than anything else in the box score.
• Blowouts are capped. A margin beyond 60 points per 100 possessions counts as 60.

Before the first game: the roster

Each rating starts the season at a preseason value and is pulled toward it with the weight of about 4 games (3 for women's teams), a pull that fades as games accumulate. The preseason value is a regression fitted on every past team-season, on the team's offence and defence last season and the season before, the share of last season's minutes that returns (from every player's minutes in last season's box scores), the transfers arriving from other Division I teams (their minutes share at their old team times that team's rating, and their own box-score production), and the strength of the conference. Rosters come from ESPN's team pages. Built this way, the preseason rating explains 70% of the spread in men's end-of-season ratings, against 62% for last season's rating alone (women's: 73% against 69%).

From ratings to a prediction

Φ is the normal curve. Early in the season, ratings are pulled hard toward the preseason value, so raw margins come out too small; they are stretched by a factor that falls from 1.12 before a team's first game to 1.06 for teams with many games behind them (men's; women's 1.18 to 1.07). σ is 10.0 points for men's games and 10.8 for women's, and is a little wider while teams have played few games. Both were fitted on past seasons. Home court is currently worth 3.9 points in men's games and 4.2 in women's.

The Four Factors and luck

A possession ends in one of four ways that matter: a shot, a turnover, an offensive rebound or free throws. Each team's rate on each (effective field-goal percentage, turnovers per possession, share of its misses it rebounds, free throws per shot) is adjusted for opponents the same way as the ratings. On past seasons, shooting decides about 44% of the margin per possession, turnovers 25%, offensive rebounding 21% and free throws 10% (men's games; women's are within two points of each). Some of it is luck: across a season, how well opponents shoot threes against a team repeats little from one half of its games to the other (a correlation of 0.21 for men's teams), and their free throws even less (0.18). The ratings already discount half of three-point luck; the Style and luck pages show how much each team has had.

Player ratings

A player's rating is the points per 100 possessions a team gains with him or her on the floor instead of an average Division I player. Production comes from the box score with Game Score's weights, split into an offensive part (points, shooting, offensive rebounds, assists, turnovers) and a defensive part (defensive rebounds, steals, blocks, fouls), per 100 possessions on the floor. Its scale is fitted to team results, and every team's players are then adjusted by the same amount so that, weighted by minutes, they add up to the team's rating; that step carries defence and everything else a box score misses. The scale was chosen by how well last season's player ratings, weighted by this season's minutes, predict this season's team ratings, transfers included: they explain 72% of the spread for men's teams and 80% for women's, against 66% and 73% for last season's team rating alone. This season each player starts from last season's rating, regressed the way past players' ratings carried over, and moves toward this season's as minutes come in.

Missing players

The ratings learn about an injury only as the games without the player come in. So before each game the model checks the box scores for regulars (players who have appeared in at least half the team's games, averaging 15 minutes or more) who did not play in the team's last game; four times in five, a team missing a regular is missing one again next time. Each missing player is valued from minutes and a box-score game score per 40 minutes, against a replacement level, and the margin moves by 0.14 points per unit of value for men's games and 0.26 for women's (a 30-minute starter is typically worth 2 to 4 points). Fitted on past seasons with each season held out, this lowers log loss from 0.5234 to 0.5225 (men) and 0.4656 to 0.4638 (women); the scorecard's past-season figures do not include it. A player who returns is counted as soon as he or she appears in a box score again.

The rooting guide

For every game in the coming week, the season simulation records each team's chance of a bid, a 1 seed and its conference title with each result. Comparing simulated seasons by result alone would mislead: a team that loses to a weak opponent in a simulation was usually drawn weak for the whole season, so the loss would look far more costly than it is. Instead each effect is measured from the game-day luck of that one result (whether it went the way its chance said, given the strengths drawn), which separates what the result does from what it reveals. Estimates from games that rarely flip are shrunk toward zero, and another team's game is shown only when its effect is clear of the simulation's noise.

The season, simulated

Each morning the rest of the season is played out 20,000 times. In each run every team's true strength is drawn around its rating, with a spread that shrinks as it plays: about 5 points per 100 possessions before a men's team's first game, 3 after ten games and under 1 by the end of the season (measured on past seasons as how far ratings moved from that point to the end). Every remaining game is then played with the same formula as the game predictions, followed by the conference tournaments (up to 12 teams by conference record, single elimination on a neutral floor; real formats vary) and the NCAA tournament.

The field is picked by a model of the committee: automatic bids for the conference tournament winners, and at-large places by a logistic regression on the resume the committee sees, using our rating and its rank in place of the NET, wins and losses, wins against the top two quadrants, losses to the bottom two, and schedule strength. It was fitted on every tournament since 2012 and, with each season held out in turn, picks 92% of the men's at-large teams and 90% of the women's. Seeds come from a second regression on the same resume, which lands within one line of the real seed 80% of the time for men's teams and 84% for women's. Teams are placed on the S-curve without the committee's conference and geography rules. In the women's tournament the top 16 seeds host the first two rounds, and the simulation gives seeds 1 to 4 home court.

How it is tested

Every past season was replayed day by day: each morning the model was rated on that season's earlier games only and predicted the day's games, and every setting above was chosen on seasons other than the one being scored. The scorecard shows the results. This season every prediction is saved before the game starts, with the betting line shown at the time, and is never changed afterwards.

What it does not know

Injuries, suspensions, a star sitting out, travel and motivation. It sees only results and box scores, so a team that has just lost its best player stays overrated until the games show it. Games against teams outside Division I are left out of the ratings and are not predicted.

Data

Scores, box scores, schedules, rosters and betting lines from ESPN's public scoreboard; past seasons (men's from 2011-12, women's from 2011-12 with full box scores from 2016-17) from the sportsdataverse archive of the same feed. Nothing here is betting advice.