What is post-game win expectancy?

1. Reshuffle the game and replay it. We take every snap each team ran that day and deal them out again at random into new drives, matched by down and distance: on 3rd and 7, a team gets one of its own 3rd-and-long plays from that game. A play can come up twice in one replay, or not at all. Each drive runs until a touchdown, a field goal try, a punt, a turnover or a failed 4th down, over as many possessions as the real game had. Then we see who scored more, and do it all 4,000 times.

   Kept as it happened

   • Every snap’s yards: runs, catches, incompletions, sacks, scrambles, and the flags on them
   • How often each team fumbled, and how many interception-worthy throws its quarterback made
   • The number of possessions

   Drawn again

   • The order the plays come in
   • Whether an interception-worthy throw is caught, at the rate that defense catches them
   • Who recovers a fumble (the fumbling team keeps 52%)
   • Whether a field goal is good, at the league rate for its distance

   No matchup is modeled on its own: there are no player ratings, no pass rush against the quarterback, no receiver against his cornerback. They don’t need to be. Every snap in the deck was played against that opponent that day, so how the pass rush fared against that quarterback, the receivers against those defenders and the line against that front is already in the plays: in the sacks, the scrambles, the completions and the stuffed runs. Where a team ran few plays of a kind that day, some draws come from its earlier games that season. Fourth downs follow one rule for everyone: kick when in range, go for it on short yardage in the other team’s half, and whenever a touchdown is needed late.

2. Compare it with the result. The share of replays a team wins is what its play was worth. Luck is the result (1 for a win, 0 for a loss) minus that share. Times 100 it is a game’s luck index, from −100 to +100; added up over a season it is luck in wins.
3. Find where it came from. This part is not a replay. Every chance play of the real game is scored on its own: what happened, minus how often it happens for that player in that spot, times what was at stake. Here each player’s own record counts: a kicker’s from that distance, in that wind and cold; a receiver’s drop rate; how often that defense catches interception-worthy throws; how often that offense and that defense convert on 3rd and 4th down. Judgment calls count too, at half, each weighted by how often the flagged player draws one. It doesn’t change the replay; it shows where the luck came from.

Each step in full, and how well the numbers hold up: methodology.