Week 4 2023 · October 1, 2023
Dolphins at Bills, Week 4 2023: who deserved to win?
The Bills beat the Dolphins 48–20, and it was no fluke: replayed with the way both teams actually played, the Bills win 10 of 10. The Dolphins had the bounces: fumble bounces alone were worth 10 points of win probability to the Dolphins.
An off day for the Dolphins: their defense played far below its usual level. In a fresh game against the Bills they would win 32% of the time; with this day’s form, 2%. The numbers
Before kickoff the Bills were 57% favorites. The biggest swing (Q2, 12:08 left): Defensive Pass Interference on the Dolphins (Kader Kohou), 43 yards, worth 9 points of win probability to the Bills.
Final
 Miami Dolphins | 20 |
|---|---|
 Buffalo Bills | 48 |
Replay with same day's form
Luck index +2 Bills about even · −2 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. Dolphins win 0, Bills win 10.
- 1 MIA 14 BUF 16
- 2 MIA 23 BUF 30
- 3 MIA 42 BUF 53
- 4 MIA 33 BUF 48
- 5 MIA 38 BUF 57
- 6 MIA 24 BUF 47
- 7 MIA 24 BUF 49
- 8 MIA 20 BUF 48
- 9 MIA 17 BUF 50
- 10 MIA 20 BUF 62
Three other ways to ask
Each answers a different question, so none of them replaces the replay above.
Before kickoff
The closing betting line, turned into a probability. What everyone knew before the game.
Same teams, fresh 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.
Only coin-flips re-rolled
Every kick, fumble bounce, drop, conversion and judgment call redrawn; everything else fixed. The narrowest view of luck.
An off day for the Dolphins
Their defense played far below its usual level. In a fresh game against the Bills they would win 32% of the time; with this day’s form, 2%.
Same teams, fresh game
Replay with same day's form
30 points apart for the Dolphins: the gap is how differently this game went from what the two teams usually are.
| Unit | This game | Usual level | Better or worse than usual |
|---|---|---|---|
| Dolphins offenseEPA per play gained | +0.36 | +0.17 | better by 0.19 |
| Dolphins defenseEPA per play allowed | +0.51 | +0.08 | worse by 0.43 |
| Bills offenseEPA per play gained | +0.51 | +0.19 | better by 0.32 |
| Bills defenseEPA per play allowed | +0.36 | +0.07 | worse by 0.28 |
EPA (expected points added) per play on competitive snaps, turnovers left out because they are valued as luck. Usual level: the team’s earlier games this season plus half of last season, pulled toward the league average. One team’s defense and the other team’s offense are the same snaps, so one game can’t fully say whose day it was; it shows how far this one was from both teams’ norms.
How 4,000 replays ended
Dolphins win 2% of them, Bills 98%. The line is what actually happened: Bills by 28.
Show as a table
| Final margin in the replays | Share of replays |
|---|---|
| Dolphins by 17+ | 0.1% |
| Dolphins by 9–16 | 0.3% |
| Dolphins by 1–8 | 1.3% |
| Level after regulation | 0.2% |
| Bills by 1–8 | 4.0% |
| Bills by 9–16 | 10.3% |
| Bills by 17+ | 83.9% |
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.
The kicks
How likely each kicker was to make that kick (his own record, the distance and the weather), and what happened.
- T. Bass, 53 yds made · 71% expected
- T. Bass, 33 yds made · 95% expected
Penalties: Dolphins 8 for 98 yards, Bills 4 for 20 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
| When | Flag | Win probability for |
|---|---|---|
| Q1 11:10 | Unnecessary Roughness on the Dolphins (Kader Kohou), 15 yards | +5% BUF +1.6 pts |
| Q1 7:20 | Defensive Offside on the Bills (Tre'Davious White), 5 yards · pre-snap | +1% MIA +0.2 pts |
| Q2 12:08 | Defensive Pass Interference on the Dolphins (Kader Kohou), 43 yards | +9% BUF +2.5 pts |
| Q2 10:35 | Illegal Formation on the Bills, 5 yards · pre-snap | +4% MIA +1.3 pts |
| Q2 9:58 | Illegal Formation on the Dolphins, 5 yards · pre-snap | +3% BUF +0.9 pts |
| Q2 8:53 | False Start on the Dolphins (Julian Hill), 5 yards · pre-snap | +1% BUF +0.5 pts |
| Q4 12:51 | Ineligible Downfield Pass on the Dolphins, 5 yards, wiping out the play | +1% BUF +2.5 pts |
| Q4 10:19 | Offensive Holding on the Dolphins, 10 yards | 0% BUF +0.9 pts |
| Q4 8:27 | Delay of Game on the Dolphins, 5 yards · pre-snap | 0% BUF +0.8 pts |
| Q4 7:01 | Defensive Offside on the Bills (Leonard Floyd), 5 yards, wiping out the play · pre-snap | 0% MIA +2.9 pts |
| Q4 6:54 | Offensive Holding on the Dolphins, 10 yards, wiping out the play | +1% BUF +2.0 pts |
| Q4 5:41 | Defensive Offside on the Bills (Shaq Lawson), 5 yards · pre-snap | 0% MIA +0.3 pts |
Dolphins penalties, every game · Bills penalties, every game · All teams, 2023
When it happened
Bills’ chance of winning
Numbers mark the biggest luck moments, listed below.
| # | When | What happened | Win probability for | Next drive |
|---|---|---|---|---|
| 1 | Q1 11:10 | Unnecessary Roughness on the Dolphins (Kader Kohou), 15 yardsJudgment calls · 7 flags in 1173 snaps before, position avg 1 per 216 | +5% BUF | BUF: Touchdown |
| 2 | Q2 14:11 | The Dolphins fumbled and recovered it themselvesFumble bounces · loose balls are close to 50/50 | +7% MIA | MIA: Touchdown |
| 3 | Q2 13:30 | The Dolphins converted 3rd & 83rd & 4th downs · 32% expected | +5% MIA | MIA: Touchdown |
| 4 | Q2 12:08 | Defensive Pass Interference on the Dolphins (Kader Kohou), 43 yardsJudgment calls · 7 flags in 1173 snaps before, position avg 1 per 216 | +9% BUF | BUF: Touchdown |
| 5 | Q2 10:35 | Illegal Formation on the Bills, 5 yardsPre-snap flags | +4% MIA | MIA: Punt |
| 6 | Q2 8:34 | The Dolphins were stopped on 3rd & 173rd & 4th downs · 20% expectedThe Dolphins fumbled and recovered it themselvesFumble bounces · loose balls are close to 50/50 | +7% MIA | MIA: Punt |
| 7 | Q2 4:02 | The Dolphins were stopped on 3rd & 23rd & 4th downs · 61% expected | +5% BUF | MIA: Punt |
| 8 | Q2 2:20 | The Dolphins were stopped on 3rd & 13rd & 4th downs · 74% expectedThe Dolphins fumbled and the Bills recoveredFumble bounces · loose balls are close to 50/50 | +8% BUF | MIA: Punt |
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.
- Jordan Poyer (BUF SS), out · 0.6 pts
- Connor Williams (MIA C), out · 0.6 pts
- Eli Apple (MIA CB), out · 0.5 pts
- Connor Williams (MIA G), out · 0.4 pts
- DeShon Elliott (MIA FS), out · 0.4 pts
- Robert Jones (MIA G), out (IR) · 0.3 pts
- Jaelan Phillips (MIA LB), 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
Dolphins 0% · Bills 100%
- Final margin
- Bills by 28
- Luck in points
- 12.5 for the Bills
- Luck-adjusted margin
- Bills by 15.5
- Replay with same day's form
- Dolphins 2% · Bills 98% unchanged: why
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 2023 games · 
Dolphins · 
Bills
More from Week 4 2023
- Lions at Packers DET 34–20 · replay 94% for the winner
- Falcons vs Jaguars JAX 23–7 · replay 80% for the winner
- Ravens at Browns BAL 28–3 · replay 94% for the winner
- Bengals at Titans TEN 27–3 · replay 43% for the winner
- Broncos at Bears DEN 31–28 · replay 34% for the winner
- Rams at Colts LA 29–23 · replay 77% for the winner
- Vikings at Panthers MIN 21–13 · replay 93% for the winner
- Steelers at Texans HOU 30–6 · replay 87% for the winner
- Buccaneers at Saints TB 26–9 · replay 87% for the winner
- Commanders at Eagles PHI 34–31 · replay 89% for the winner
- Raiders at Chargers LAC 24–17 · replay 89% for the winner
- Cardinals at 49ers SF 35–16 · replay 93% for the winner
- Patriots at Cowboys DAL 38–3 · replay 98% for the winner
- Chiefs at Jets KC 23–20 · replay 82% for the winner
- Seahawks at Giants SEA 24–3 · replay 89% for the winner