Learn · momentum
Does a lucky break create momentum?
No. Across 18,562 pure-luck plays since 2019, the team that got the break did no better on its next drive than the team that got the bad one: −0.07 expected points against average for the lucky side, −0.05 for the unlucky side.
How luck is calculated, in short
Every game replayed 4,000 times from its own plays. Luck is the result minus the share of replays a team wins. Show the 3 steps and an example Hide
- 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.
- 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.
- 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.
An example: Bears 24, Packers 22 Week 18 2024
Who wins the 4,000 replays
- The game
- The Packers lost 24–22, but with both teams’ plays dealt out again, they won 99% of the replays. Packers: 100 × (0 − 0.99) = −99 Bears: 100 × (1 − 0.01) = +99
- One play, scored on its own
- C. Santos made a 51-yard field goal. Going by his record, the distance and the conditions, he makes that kick 62% of the time. From that distance a make is worth 4.5 points more than a miss, on average: the 3 points, plus the field position, since after a miss the other team takes over at the spot of the kick. Luck is what happened (1 for a make, 0 for a miss) minus the 62%, times those 4.5 points: Bears: (1 − 0.62) × 4.5 = +1.7 points Counted at the moment it came, with 0:02 left in the 4th quarter, that was worth 38% of a win to the Bears.
- The season
- The Packers finished 2024 at 11–6. The replays of those 17 games add up to 12.5 wins. Luck in wins: 11 − 12.5 = −1.5
Each step in full, and how well the numbers hold up: methodology.
The test
We took every play since 2019 where chance decided something worth at least a point: a fumble recovery, a field goal a kicker should have made (or missed), a judgment call, an interception-worthy throw that was or wasn’t caught. Then we looked at each team’s next drive, in expected points added, against the average drive.
If momentum were real, the lucky team would play better right after the break and the unlucky team worse. Neither happened. Both drives came in slightly below the average drive, and the difference between them, −0.03 points, is well inside the noise. Per point of luck, the carryover is -0.007 ± 0.016: zero.
| Kind of break | Lucky minus unlucky next drive |
|---|---|
| Fumble bounces | −0.05 pts |
| Interceptions | +0.01 pts |
| Kicks | +0.03 pts |
| Judgment calls | −0.05 pts |
Why it feels real
Runs happen. A team can string together stops and scores, and win probability can swing hard in one direction for a stretch; researchers at the University of Wisconsin–Milwaukee found such runs more often than chance would produce (UWM). That is a different question from ours. Runs can come from one team simply playing better for a while. What we tested is whether a lucky break itself changes what happens next, and it doesn’t.
What we do with it
When a break comes matters, and that we do count. Every lucky or unlucky play is weighted by what it did to the chance of winning at that moment: a break at the turn of a close game counts for many times more than the same break early, and a break in a decided game counts for nothing. On every game page the play the game turned on is marked, when it was luck. Weighted this way, a team’s luck over a season tracks its record luck at a correlation of 0.54, against 0.42 for the same plays in points (how).
Momentum itself is a setting. By default a lucky or unlucky play is worth its own swing and nothing more, which is what the tests above measured. Every “adjust the assumptions” panel has the momentum slider, from none to +100%. Counting momentum doesn’t make the luck-adjusted record a better forecast either: after nine weeks, coin-flip wins forecast the rest of a season at a correlation of 0.425 at the default and 0.427 with +50% (how the luck-adjusted record predicts).