luckadjusted
NFL Week 9 · 2026

Week 18 2023 · January 7, 2024

Bills at Dolphins, Week 18 2023: who deserved to win?

The Bills beat the Dolphins 21–14, but the replays call it close to a coin flip: with the way both teams played, the Bills win 5 of 10.

Before kickoff the Bills were 57% favorites. The biggest swing (Q4, 14:02 left): Return touchdown by the Bills, worth 21 points of win probability to the Bills.

Final

Buffalo Bills 21
Miami Dolphins 14

January 7, 2024 · Hard Rock Stadium · Closing line: Bills −2.5

Luck index +48 Bills lucky · −48 Dolphins

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, Dolphins win 5.

  1. 1 BUF 34 MIA 13
  2. 2 BUF 23 MIA 10
  3. 3 BUF 29 MIA 21
  4. 4 BUF 24 MIA 20
  5. 5 BUF 14 MIA 12
  6. 6 BUF 21 MIA 23
  7. 7 BUF 20 MIA 24
  8. 8 BUF 23 MIA 31
  9. 9 BUF 13 MIA 27
  10. 10 BUF 17 MIA 40

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 52% of them, Dolphins 48%, counting the 6% still level after regulation as half each. The line is what actually happened: Bills by 7.

Show as a table
Final margin in the replaysShare of replays
Bills by 17+11.0%
Bills by 9–1614.6%
Bills by 1–822.2%
Level after regulation6.4%
Dolphins by 1–822.9%
Dolphins by 9–1613.5%
Dolphins by 17+9.3%

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 +0.6 points to the Dolphins: the final margin was Bills by 7, without the luck Bills by 7.6. Luck shares are the fitted ones (how much of each kind is luck).

Penalties: Bills 6 for 41 yards, Dolphins 4 for 29 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 half toward luck; pre-snap fouls, which repeat, don’t count. How calls are valued

WhenFlagWin probability for
Q1 5:58 Defensive Offside on the Bills (Shaq Lawson), 5 yards · pre-snap 0% MIA +0.4 pts
Q1 5:32 Offensive Holding on the Dolphins, 4 yards, wiping out the play +2% BUF +0.7 pts
Q2 8:13 False Start on the Bills (Dawson Knox), 5 yards · pre-snap +2% MIA +0.5 pts
Q2 4:07 Encroachment on the Bills (DaQuan Jones), 6 yards · pre-snap 0% BUF +0.2 pts
Q3 6:27 Offensive Holding on the Bills (Dawson Knox), 10 yards, wiping out the play +6% MIA +1.8 pts
Q4 15:00 False Start on the Dolphins, 5 yards · pre-snap +1% BUF +0.6 pts
Q4 14:58 Illegal Blindside Block on the Dolphins, 15 yards +3% BUF +1.4 pts
Q4 3:12 Defensive Holding on the Dolphins (Jalen Ramsey), 5 yards +2% BUF +0.9 pts
Q4 3:12 Delay of Game on the Bills, 5 yards · pre-snap +1% MIA +0.2 pts
Q4 1:26 Defensive Pass Interference on the Bills (Dane Jackson), 10 yards +5% MIA +0.4 pts

Bills penalties, every game · Dolphins penalties, every game · All teams, 2023

When it happened

Dolphins’ chance of winning

As low as 0% and as high as 86%. 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 Dolphins were ahead in it, below while the Bills were.
#WhenWhat happenedWin probability forNext drive
1 Q1 6:08 The Bills threw an interception-worthy pass, and it was pickedInterceptions · defenses catch 50% of interception-worthy throws +5% MIA BUF: Turnover
2 Q2 12:21 The Dolphins converted 3rd & 143rd & 4th downs · 24% expected +9% MIA MIA: Touchdown
3 Q2 4:36 The Bills got away with an interception-worthy throwInterceptions · defenses catch 50% of interception-worthy throws +5% BUF BUF: Touchdown
4 Q2 0:21 J. Cook dropped a catchable passDrops · 7 drops on 71 catchable balls before this +5% MIA BUF: End of half
5 Q3 6:27 Offensive Holding on the Bills (Dawson Knox), 10 yards, wiping out the playJudgment calls · 11 flags in 3884 snaps before, position avg 1 per 286 +6% MIA MIA: Opp touchdown
6 Q4 14:02 Return touchdown by the BillsSpecial teams +21% BUF BUF: Opp touchdown
7 Q4 2:00 The Bills were stopped on 4th & 13rd & 4th downs · 80% expected +7% MIA BUF: End of game
8 Q4 1:17 The Dolphins threw an interception-worthy pass, and it was pickedInterceptions · defenses catch 50% of interception-worthy throws +11% 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.

  • Xavien Howard (MIA CB), out · 1.2 pts
  • Jaylen Waddle (MIA WR), out · 0.9 pts
  • Connor Williams (MIA C), out (IR) · 0.6 pts
  • Bradley Chubb (MIA LB), out (IR) · 0.4 pts
  • Jaelan Phillips (MIA LB), out (IR) · 0.3 pts
  • Raheem Mostert (MIA RB), out · 0.2 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 100% · Dolphins 0%

Final margin
Bills by 7
Luck in points
0.6 for the Dolphins
Luck-adjusted margin
Bills by 7.6
Replay with same day's form
Bills 52% · Dolphins 48% unchanged: why
How much of each is luck?

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

What counts

None by default: our tests measured no carryover after a lucky break. Slide it up to count a break for more than its own swing. 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 18 2023 games · Bills · Dolphins

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