luckadjusted

Week 4 2025 · September 28, 2025

Saints at Bills, Week 4 2025: who deserved to win?

The Bills beat the Saints 31–19, and it was no fluke: replayed with the way both teams actually played, the Bills win 9 of 10.

Before kickoff the Bills were 87% favorites. The biggest swing (Q4, 9:01 left): B. Cooks dropped a catchable pass, worth 19 points of win probability to the Bills.

Final

New Orleans Saints 19
Buffalo Bills 31

September 28, 2025 · New Era Field · Closing line: Bills −15.5

Luck index +9 Bills about even · −9 Saints

Each team’s own plays from this game, resampled into new drives 4,000 times: with the way both teams actually played, how often does this performance win? How the replay works

Ten replays. Saints win 1, Bills win 9.

  1. 1 NO 27 BUF 22
  2. 2 NO 17 BUF 19
  3. 3 NO 36 BUF 41
  4. 4 NO 20 BUF 28
  5. 5 NO 16 BUF 27
  6. 6 NO 13 BUF 26
  7. 7 NO 21 BUF 37
  8. 8 NO 17 BUF 37
  9. 9 NO 10 BUF 35
  10. 10 NO 9 BUF 42

Three other ways to ask

Each answers a different question, so none of them replaces the replay above.

The closing betting line, turned into a probability. What everyone knew before the game.

The line plus what this game showed, weighted by how much one game can tell. It stays close to the line because one game says little.

Every kick, fumble bounce, drop, conversion and judgment call redrawn; everything else fixed. The narrowest view of luck.

How 4,000 replays ended

Saints win 9% of them, Bills 91%, counting the 2% still level after regulation as half each. The line is what actually happened: Bills by 12.

Show as a table
Final margin in the replaysShare of replays
Saints by 17+0.5%
Saints by 9–162.4%
Saints by 1–85.4%
Level after regulation1.8%
Bills by 1–816.5%
Bills by 9–1620.9%
Bills by 17+52.5%

Where the luck was

What the luck was worth

Every lucky and unlucky play, weighted by the moment it happened: its swing in win probability, added up by kind. A missed kick in a decided game counts for nothing; the same kick at the end of a tie game can be most of a win.

Swings add up across a game, so in one that went back and forth they can pass 100%. On the scoreboard the same luck was worth +0.3 points to the Saints: the final margin was Bills by 12, without the luck Bills by 12.3. Luck shares are the fitted ones (how much of each kind is luck).

The kicks

How likely each kicker was to make that kick (his own record, the distance and the weather), and what happened.

  • B. Grupe, 54 yds made · 63% expected
  • B. Grupe, 35 yds made · 92% expected
  • M. Prater, 35 yds made · 93% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Saints 4 for 41 yards, Bills 11 for 55 yards

Every accepted flag, in order, and what it did to the helped team’s chance of winning at that moment, including any play it wiped out (points on the scoreboard in grey). A flag in a decided game is worth nothing; one at the turn of a close game can be worth most of a win. Judgment calls count toward luck, pre-snap fouls mostly don’t. How calls are valued

WhenFlagWin probability for
Q1 8:00 Defensive Holding on the Bills (Tre'Davious White), 5 yards +2% NO +0.7 pts
Q1 2:29 Offensive Holding on the Saints (Ugo Amadi), 10 yards +2% BUF +1.0 pts
Q2 13:52 Intentional Grounding on the Saints (Spencer Rattler), 16 yards +3% BUF +1.7 pts
Q2 8:51 Offensive Holding on the Bills, 10 yards 0% NO +0.9 pts
Q2 4:01 False Start on the Bills, 5 yards · pre-snap 0% NO +0.2 pts
Q2 1:31 Illegal Blindside Block on the Bills (Dorian Williams), 2 yards 0% NO +0.2 pts
Q2 1:22 Illegal Shift on the Bills (Josh Palmer), 2 yards · pre-snap +3% NO +0.9 pts
Q2 1:18 Offensive Holding on the Bills (Khalil Shakir), 1 yard 0% NO +0.1 pts
Q3 10:43 Offensive Pass Interference on the Bills (Tyrell Shavers), 10 yards +2% NO +1.4 pts
Q3 2:21 Defensive Too Many Men on Field on the Bills, 5 yards · pre-snap +1% BUF +0.3 pts
Q4 8:53 Kickoff Short of Landing Zone on the Saints (Blake Grupe), 0 yards · pre-snap 0% BUF 0.0 pts
Q4 7:07 Illegal Use of Hands on the Bills (Shaq Thompson), 5 yards +1% NO +0.7 pts
Q4 7:07 False Start on the Bills, 5 yards · pre-snap 0% NO 0.0 pts
Q4 5:30 False Start on the Bills, 5 yards · pre-snap +1% NO +0.6 pts
Q4 5:18 Roughing the Kicker on the Saints (Nephi Sewell), 15 yards +3% BUF +3.3 pts

Saints penalties, every game · Bills penalties, every game · All teams, 2025

When it happened

Bills’ chance of winning

As low as 49% and as high as 100%. Numbers mark the biggest luck moments, listed below.

nflfastR’s in-game win probability. It ignores the betting line, so it starts near even. Shaded above the middle while the Bills were ahead in it, below while the Saints were.
#WhenWhat happenedWin probability forNext drive
1 Q2 13:52 The Saints were stopped on 3rd & 53rd & 4th downs · 41% expectedIntentional Grounding on the Saints (Spencer Rattler), 16 yardsJudgment calls · 0 flags in 612 snaps before, position avg 1 per 625 +7% BUF NO: Punt
2 Q2 3:42 The Bills were stopped on 3rd & 223rd & 4th downs · 19% expected +9% NO BUF: Punt
3 Q2 1:31 The Saints were stopped on 3rd & 53rd & 4th downs · 33% expectedThe Saints threw an interception-worthy pass, and it was pickedInterceptions · 50% expected to stay out of the defense's handsIllegal Blindside Block on the Bills (Dorian Williams), 2 yardsJudgment calls · 4 flags in 1597 snaps before, position avg 1 per 445 +13% BUF NO: Punt
4 Q3 9:33 The Bills converted 3rd & 83rd & 4th downs · 35% expected +8% BUF BUF: Touchdown
5 Q3 0:17 The Saints converted 3rd & 33rd & 4th downs · 43% expected +5% NO NO: Touchdown
6 Q4 12:56 The Bills were stopped on 4th & 13rd & 4th downs · 77% expected +10% NO BUF: Touchdown
7 Q4 9:01 The Saints were stopped on 3rd & 133rd & 4th downs · 23% expectedB. Cooks dropped a catchable passDrops · 4 drops on 168 catchable balls before this +19% BUF NO: Field goal
8 Q4 8:01 The Bills converted 3rd & 53rd & 4th downs · 45% expected +7% BUF BUF: Touchdown

Missing players

Key players (usually on the field for half the snaps or more) who missed this game or part of it, valued by position and quality. The same players are missing in every replay, so this counts as luck in points only.

  • Spencer Brown (BUF T), out · 1.2 pts
  • Matt Milano (BUF LB), out · 0.5 pts
  • Ed Oliver (BUF DT), out · 0.4 pts
  • Tyler Bass (BUF K), out (IR) · 0.3 pts
  • Tylan Grable (BUF T), out (IR) · 0.2 pts
  • DeWayne Carter (BUF DT), out (IR) · 0.2 pts
  • Chase Young (NO DE), out · 0.5 pts
  • Foster Moreau (NO TE), out (IR) · 0.4 pts
  • Dillon Radunz (NO OL), out · 0.3 pts

Adjust the assumptions

Disagree with how much of a fumble bounce or a pass interference call is luck? Change it and the coin-flip replay reruns in your browser.

Only coin-flips re-rolled

Saints 3% · Bills 97%

Final margin
Bills by 12
Luck in points
0.3 for the Saints
Luck-adjusted margin
Bills by 12.3
Replay with same day's form
Saints 9% · Bills 91% unchanged: why
How much of each is luck?

0% treats it as skill, 100% as pure luck. The tick is our fit.

What counts

We tested momentum on 19,000 lucky breaks and found none, so it's off by default. Why

Flip a play

Force the other outcome, in this game and in every replay: a made kick becomes a miss, a stop becomes a conversion, a flag goes the other way.

About these numbers

Play-by-play and win probability from nflfastR via nflverse; kicks valued against each kicker’s own record; drops and interception-worthy throws from FTN charting; injuries from snap counts and injury reports.

Methodology and validation · All Week 4 2025 games · Saints · Bills

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