luckadjusted

Wild Card 2024 · January 12, 2025

Broncos at Bills, Wild Card 2024: who deserved to win?

The Bills beat the Broncos 31–7, and it was no fluke: replayed with the way both teams actually played, the Bills win 9 of 10.

Before kickoff the Bills were 71% favorites. The biggest swing (Q2, 10:49 left): the Broncos converted 4th & 8, worth 14 points of win probability to the Broncos.

Final

Denver Broncos 7
Buffalo Bills 31

January 12, 2025 · New Era Field · Closing line: Bills −7.5

Luck index +10 Bills about even · −10 Broncos

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. Broncos win 1, Bills win 9.

  1. 1 DEN 20 BUF 14
  2. 2 DEN 19 BUF 22
  3. 3 DEN 13 BUF 17
  4. 4 DEN 17 BUF 24
  5. 5 DEN 14 BUF 23
  6. 6 DEN 20 BUF 31
  7. 7 DEN 17 BUF 31
  8. 8 DEN 10 BUF 27
  9. 9 DEN 10 BUF 31
  10. 10 DEN 13 BUF 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

Broncos win 10% of them, Bills 90%, counting the 1% still level after regulation as half each. The line is what actually happened: Bills by 24.

Show as a table
Final margin in the replaysShare of replays
Broncos by 17+0.4%
Broncos by 9–161.6%
Broncos by 1–87.0%
Level after regulation1.5%
Bills by 1–820.7%
Bills by 9–1627.4%
Bills by 17+41.5%

Where the luck was

Take the luck out

The final margin was Bills by 24. Remove the luck, one kind at a time, and it becomes Bills by 12.6.

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, 26 yds made · 97% expected
  • W. Lutz, 50 yds missed · 64% expected
  • T. Bass, 27 yds made · 96% expected
  • T. Bass, 34 yds made · 91% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

When it happened

Bills’ chance of winning

As low as 39% and as high as 100%. 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 Broncos were.
#WhenWhat happenedWin probability forNext drive
1 Q1 13:37 The Broncos converted 3rd & 83rd & 4th downs · 32% expected +8% DEN DEN: Touchdown
2 Q1 8:28 The Bills converted 4th & 13rd & 4th downs · 76% expected +6% BUF BUF: Field goal
3 Q1 3:06 False Start on the Bills (James Cook), 5 yardsPre-snap flags · 2 flags in 1513 snaps before, position avg 1 per 860 +6% DEN DEN: Punt
4 Q2 10:49 The Broncos converted 4th & 83rd & 4th downs · 32% expected +14% DEN DEN: Punt
5 Q2 0:05 W. Lutz missed 50-yard field goalKicks · 64% expected for him, 37 of 53 from 45+ before +9% BUF DEN: Punt
6 Q3 8:53 The Broncos were stopped on 3rd & 53rd & 4th downs · 42% expectedT. Franklin dropped a catchable passDrops · 2 drops on 34 catchable balls before this +8% BUF DEN: Punt
7 Q3 7:21 Offensive Holding on the Bills (Dalton Kincaid), 10 yards, wiping out the playJudgment calls · 6 flags in 1259 snaps before, position avg 1 per 280 +6% DEN DEN: Punt
8 Q3 3:15 The Bills converted 4th & 13rd & 4th downs · 76% expected +7% BUF BUF: Touchdown

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.

  • Kaiir Elam (BUF CB), out · 0.5 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

Broncos 1% · Bills 99%

Final margin
Bills by 24
Luck in points
11.4 for the Bills
Luck-adjusted margin
Bills by 12.6
Replay with same day's form
Broncos 10% · Bills 90% 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 Wild Card 2024 games · Broncos · Bills

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