luckadjusted

Week 18 2023 · January 7, 2024

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

The Bills beat the Dolphins 21–14, but it was a coin flip: replayed with the way both teams played, the Bills win 5 of 10. Luck ran their way: injuries alone were worth 3.6 points to the Bills.

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 31 MIA 17
  3. 3 BUF 24 MIA 14
  4. 4 BUF 20 MIA 16
  5. 5 BUF 19 MIA 17
  6. 6 BUF 11 MIA 13
  7. 7 BUF 12 MIA 16
  8. 8 BUF 19 MIA 27
  9. 9 BUF 13 MIA 27
  10. 10 BUF 3 MIA 24

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+10.8%
Bills by 9–1614.5%
Bills by 1–822.7%
Level after regulation6.3%
Dolphins by 1–822.5%
Dolphins by 9–1614.6%
Dolphins by 17+8.6%

Where the luck was

Take the luck out

The final margin was Bills by 7. Remove the luck, one kind at a time, and it becomes Bills by 6.9.

Each row takes one kind of luck out of the margin. Color shows which team it helped. Luck shares are the fitted ones (how much of each component is luck).

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 were stopped on 3rd & 53rd & 4th downs · 38% expectedThe Bills threw an interception-worthy pass, and it was pickedInterceptions · 50% expected to stay out of the defense's hands +20% MIA BUF: Turnover
2 Q1 0:22 The Bills were stopped on 4th & 23rd & 4th downs · 65% expectedThe Bills threw an interception-worthy pass, and it was pickedInterceptions · 50% expected to stay out of the defense's hands +11% MIA BUF: Touchdown
3 Q2 12:21 The Dolphins converted 3rd & 143rd & 4th downs · 22% expected +9% MIA MIA: Touchdown
4 Q3 10:42 The Bills were stopped on 3rd & 53rd & 4th downs · 46% expected +6% MIA BUF: Punt
5 Q3 0:17 The Bills were stopped on 3rd & 133rd & 4th downs · 28% expectedThe Bills fumbled and the Dolphins recoveredFumble bounces · loose balls are close to 50/50 +15% MIA BUF: 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 · 78% expected +7% MIA BUF: End of game
8 Q4 1:17 The Dolphins threw an interception-worthy pass, and it was pickedInterceptions · 49% expected to stay out of the defense's hands +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 99% · Dolphins 1%

Final margin
Bills by 7
Luck in points
0.1 for the Bills
Luck-adjusted margin
Bills by 6.9
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

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 18 2023 games · Bills · Dolphins

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