luckadjusted

Week 15 2025 · December 14, 2025

Bills at Patriots, Week 15 2025: who deserved to win?

The Bills beat the Patriots 35–31, but it was a coin flip: replayed with the way both teams played, the Bills win 5 of 10. Luck ran their way: 3rd & 4th downs alone were worth 13 points of win probability to the Bills.

Before kickoff the Bills were 57% favorites. The biggest swing (Q4, 10:15 left): Offensive Holding on the Bills, 10 yards, wiping out the play, worth 26 points of win probability to the Patriots.

Final

Buffalo Bills 35
New England Patriots 31

December 14, 2025 · Gillette Stadium · Closing line: Bills −2.5

Luck index +49 Bills lucky · −49 Patriots

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. Bills win 5, Patriots win 5.

  1. 1 BUF 45 NE 23
  2. 2 BUF 27 NE 13
  3. 3 BUF 26 NE 17
  4. 4 BUF 27 NE 22
  5. 5 BUF 30 NE 28
  6. 6 BUF 17 NE 19
  7. 7 BUF 19 NE 24
  8. 8 BUF 20 NE 29
  9. 9 BUF 17 NE 32
  10. 10 BUF 38 NE 61

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

Bills win 51% of them, Patriots 49%, counting the 6% still level after regulation as half each. The line is what actually happened: Bills by 4.

Show as a table
Final margin in the replaysShare of replays
Bills by 17+10.6%
Bills by 9–1613.9%
Bills by 1–822.9%
Level after regulation6.3%
Patriots by 1–821.8%
Patriots by 9–1614.3%
Patriots by 17+10.3%

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 +1.5 points to the Patriots: the final margin was Bills by 4, without the luck Bills by 5.5. Luck shares are the fitted ones (how much of each kind is luck).

Penalties: Bills 2 for 15 yards, Patriots 7 for 65 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 4:55 False Start on the Bills (Josh Palmer), 5 yards · pre-snap +1% NE +0.7 pts
Q2 5:53 Face Mask on the Patriots (Brenden Schooler), 15 yards +1% BUF +0.8 pts
Q3 5:04 Defensive Holding on the Patriots (Craig Woodson), 5 yards +3% BUF +1.6 pts
Q3 3:49 Offensive Holding on the Patriots (Marte Mapu), 10 yards +1% BUF +0.8 pts
Q3 1:45 Offensive Holding on the Patriots, 10 yards, wiping out the play +6% BUF +1.5 pts
Q3 1:45 False Start on the Patriots, 5 yards · pre-snap +1% BUF +0.8 pts
Q4 10:15 Offensive Holding on the Bills, 10 yards, wiping out the play +26% NE +3.8 pts
Q4 8:19 Defensive Pass Interference on the Patriots (Carlton Davis), 15 yards +10% BUF +1.2 pts
Q4 5:19 False Start on the Patriots, 5 yards · pre-snap 0% BUF +0.2 pts

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

When it happened

Patriots’ chance of winning

As low as 0% and as high as 94%. 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 Patriots were ahead in it, below while the Bills were.
#WhenWhat happenedWin probability forNext drive
1 Q1 13:00 The Patriots converted 3rd & 73rd & 4th downs · 38% expected +12% NE NE: Touchdown
2 Q3 1:39 The Patriots were stopped on 3rd & 253rd & 4th downs · 18% expectedThe Patriots threw an interception-worthy pass, and it was pickedInterceptions · 52% expected to stay out of the defense's hands +12% BUF NE: Touchdown
3 Q4 12:08 The Bills were stopped on 3rd & 23rd & 4th downs · 62% expected +8% NE BUF: Touchdown
4 Q4 11:22 The Bills converted 4th & 33rd & 4th downs · 53% expected +22% BUF BUF: Touchdown
5 Q4 10:15 Offensive Holding on the Bills, 10 yards, wiping out the playJudgment calls +26% NE NE: Touchdown
6 Q4 10:10 The Bills converted 3rd & 143rd & 4th downs · 24% expected +18% BUF BUF: Touchdown
7 Q4 8:19 Defensive Pass Interference on the Patriots (Carlton Davis), 15 yardsJudgment calls · 48 flags in 6387 snaps before, position avg 1 per 213 +10% BUF BUF: Touchdown
8 Q4 1:54 The Patriots were stopped on 4th & 53rd & 4th downs · 45% expected +13% BUF –

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.

  • Will Campbell (NE T), out (IR) · 0.7 pts
  • Robert Spillane (NE LB), out · 0.3 pts
  • Milton Williams (NE DT), out (IR) · 0.2 pts
  • Christian Benford (BUF CB), out · 0.8 pts
  • Terrel Bernard (BUF LB), out · 0.4 pts
  • Ed Oliver (BUF DT), out (IR) · 0.4 pts
  • Michael Hoecht (BUF DE), out (IR) · 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

Bills 71% · Patriots 29%

Final margin
Bills by 4
Luck in points
1.5 for the Patriots
Luck-adjusted margin
Bills by 5.5
Replay with same day's form
Bills 51% · Patriots 49% 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 15 2025 games · Bills · Patriots

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