luckadjusted

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 3.1 points 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

October 1, 2023 · New Era Field · Closing line: Bills −2.5

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. 1 MIA 29 BUF 31
  2. 2 MIA 23 BUF 30
  3. 3 MIA 30 BUF 41
  4. 4 MIA 16 BUF 31
  5. 5 MIA 38 BUF 57
  6. 6 MIA 17 BUF 40
  7. 7 MIA 26 BUF 51
  8. 8 MIA 13 BUF 41
  9. 9 MIA 17 BUF 50
  10. 10 MIA 20 BUF 62

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.

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%.

30 points apart for the Dolphins: the gap is how differently this game went from what the two teams usually are.

UnitThis gameUsual levelBetter 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 replaysShare of replays
Dolphins by 17+0.1%
Dolphins by 9–160.3%
Dolphins by 1–81.3%
Level after regulation0.2%
Bills by 1–84.0%
Bills by 9–1610.3%
Bills by 17+83.9%

Where the luck was

Take the luck out

The final margin was Bills by 28. Remove the luck, one kind at a time, and it becomes Bills by 15.5.

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).

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
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

When it happened

Bills’ chance of winning

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 Dolphins were.
#WhenWhat happenedWin probability forNext 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
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 2023 games · Dolphins · Bills

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