Definitions

Every number on the site, in plain words and then precisely. All values are for the team with the ball unless noted.

Play value

CASE

How much a play changed the expected final margin for the team with the ball, in points. Zero is exactly what the situation called for.

CASE_i = points_i + f · V(s_i+1) − V(s_i), where V(s) is the expected net points from state s to the end of the game and f is +1 if the same team has the ball next, −1 if possession changes. Summed over a game, CASE equals the final margin minus V at kickoff, exactly.

Points now

The part of a play's value that comes from the race to the next score.

points_i + f · A(s_i+1) − A(s_i), where A(s) is the expected points of the next score. The analogue of EPA, derived from the same value function.

The game after

The part that comes from everything past the next score: mostly the clock and the possessions left.

f · B(s_i+1) − B(s_i), where B(s) is the expected net points after the next score. V = A + B, so points now + the game after = CASE, exactly.

CASE Margin

The expected final margin: the current score plus what the situation is still worth.

margin + V(s), from the offense's side. The line on each game's chart.

EPA

Expected points added, from nflfastR. Shown for comparison; it values the race to the next score only.

nflfastR's epa column, unchanged.

Win probability

CASE Win Probability

The chance the team with the ball wins, from CASE's own projected margin. In the final minutes it also uses timeouts and whether the leader can run out the clock.

z = (margin + V) / max(σ(s), 1), where σ(s) is a fitted model of how much the final margin can still move. In regulation, WP = Φ(z + a(t) + b(t)·z + timeout and kneel-out terms), a probit mapping on t = log(1 + seconds left), fitted on completed seasons with shrinkage so each term is zero wherever the data do not support it. In overtime, WP = Φ(z).

Leverage

How much a play could have changed who won. Near zero in a decided game.

w = dWP/dz, the slope of the win-probability curve at the play: φ(z_mapped) · dz_mapped/dz.

Contested CASE

CASE weighted by leverage, so plays in the balance count for more than plays in a decided game.

Per play: Σ w·CASE / Σ w. Total: Σ w·CASE — a weighted sum, not plays × per play, so snaps in a decided game total little.

Teams and players

Produced, allowed and net

What a team produced with the ball, what it allowed without it, and the difference.

Produced sums CASE over the team's offensive plays; allowed sums the same plays grouped by the defense, so lower is better; net = produced − allowed. Available as CASE and as Contested CASE.

Units

Passing, rushing, special teams, penalties and clock management.

An exclusive partition of every play, so the units add up to the team total.

Player views

What each player was part of: passing, rushing and receiving.

Tabulations, not allocations: a completion counts in full for both the passer and the receiver, so players do not add up to the team.

Win expectancy

The chance of winning implied by how each side played, rather than by the score.

A logistic model of the result on each side's Contested CASE per play in the game, fitted on completed seasons.

Wins against production

How far a record is ahead of, or behind, how the team has played.

Actual wins minus the sum of win expectancy across the team's games. Descriptive, not a forecast.

When the wins were won

A team's wins accumulating across game time, summed over its games.

Win probability summed across a team's regular-season games at each second of game time; it ends at the team's record.

Games

Excitement

How surprising the game was, play by play. A swing from 1% to 10% counts for far more than one from 41% to 50%.

Σ KL(WP_i+1 ‖ WP_i) in bits: the information divergence from the win probability before each play to the one after it, summed over the game.

Tension

How long the game stayed in doubt. 1 is a coin flip held all game; near 0 was never in doubt.

The mean binary entropy of the win probability, in bits.

Plays in doubt

The share of plays with the result genuinely in the balance.

The share of plays with the home team's win probability between 25% and 75%.

Lowest win probability

How close the winner came to losing.

The minimum of the eventual winner's win probability across the game.

Lead changes

How often the lead changed hands on the scoreboard.

Changes in the sign of the scoreboard margin across the game's plays.

Every number carries

As of

When a figure was produced. A week-8 number can differ from the same number in week 9, because more of the season exists.

Every table is stamped with as_of (season and week) and the model version that scored it. Models are fitted on completed seasons and applied forward.