luckadjusted

Week 10 2023 · November 13, 2023

Broncos at Bills, Week 10 2023: who deserved to win?

The Broncos beat the Bills 24–22, but the Bills played well enough to win it: they take 7 of 10 replays with the same day's form. Luck ran their way: kicks alone were worth 42 points of win probability to the Broncos.

Before kickoff the Bills were 71% favorites. The game turned on a luck play (Q4, 0:35 left): Defensive Pass Interference on the Bills (Taron Johnson), 28 yards, worth 29 points of win probability to the Broncos. The biggest single swing (Q4, 0:04 left): W. Lutz made 36-yard field goal.

Final

Denver Broncos 24
Buffalo Bills 22

November 13, 2023 · New Era Field · Closing line: Bills −7.5

Luck index +67 Broncos very lucky · −67 Bills

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 3, Bills win 7.

  1. 1 DEN 26 BUF 7
  2. 2 DEN 24 BUF 15
  3. 3 DEN 31 BUF 28
  4. 4 DEN 20 BUF 22
  5. 5 DEN 19 BUF 23
  6. 6 DEN 16 BUF 24
  7. 7 DEN 17 BUF 29
  8. 8 DEN 12 BUF 27
  9. 9 DEN 20 BUF 40
  10. 10 DEN 17 BUF 45

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 33% of them, Bills 67%, counting the 4% still level after regulation as half each. The line is what actually happened: Broncos by 2.

Show as a table
Final margin in the replaysShare of replays
Broncos by 17+4.8%
Broncos by 9–168.6%
Broncos by 1–815.3%
Level after regulation4.1%
Bills by 1–825.7%
Bills by 9–1618.4%
Bills by 17+23.1%

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 +13.5 points to the Broncos: the final margin was Broncos by 2, without the luck Bills by 11.5. Luck shares are the fitted ones (how much of each kind is luck).

The kicks

How likely each kicker was to make that kick (his own record, the distance and the weather), and what happened.

  • W. Lutz, 40 yds made · 85% expected
  • W. Lutz, 49 yds made · 69% expected
  • W. Lutz, 40 yds made · 85% expected
  • W. Lutz, 36 yds made · 90% expected
  • Extra point missed · 93% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Broncos 10 for 61 yards, Bills 5 for 63 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

WhenFlagWin probability for
Q1 13:42 False Start on the Broncos, 5 yards · pre-snap +3% BUF +0.8 pts
Q1 12:39 Offensive Holding on the Bills, 10 yards +2% DEN +1.1 pts
Q1 9:25 False Start on the Bills, 5 yards · pre-snap +1% DEN +0.8 pts
Q1 5:59 False Start on the Broncos (Michael Burton), 5 yards · pre-snap +3% BUF +0.9 pts
Q2 14:28 Ineligible Downfield Pass on the Broncos, 5 yards +4% BUF +0.6 pts
Q2 10:33 Unnecessary Roughness on the Bills (Dorian Williams), 15 yards +2% DEN +1.7 pts
Q2 3:36 Defensive Offside on the Broncos, 1 yard · pre-snap +2% BUF 0.0 pts
Q2 1:15 Offensive Holding on the Broncos, 10 yards, wiping out the play +5% BUF +1.5 pts
Q3 14:17 Offensive Holding on the Broncos (Javonte Williams), 10 yards +4% BUF +1.1 pts
Q3 13:13 False Start on the Broncos, 5 yards · pre-snap +1% BUF +0.3 pts
Q3 12:20 Offensive Holding on the Broncos (Dwayne Washington), 10 yards +4% BUF +0.6 pts
Q4 11:47 False Start on the Broncos (Courtland Sutton), 5 yards · pre-snap +2% BUF +0.4 pts
Q4 6:41 False Start on the Broncos, 5 yards · pre-snap +3% BUF +0.8 pts
Q4 0:35 Defensive Pass Interference on the Bills (Taron Johnson), 28 yards +29% DEN +3.2 pts
Q4 0:07 Defensive Too Many Men on Field on the Bills, 5 yards · pre-snap +11% DEN +0.5 pts

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

When it happened

Bills’ chance of winning

As low as 0% and as high as 62%. 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 8:30 The Bills were stopped on 3rd & 43rd & 4th downs · 48% expectedThe Bills threw an interception-worthy pass, and it was pickedInterceptions · 49% expected to stay out of the defense's hands +13% DEN BUF: Punt
2 Q3 10:03 The Broncos were stopped on 3rd & 63rd & 4th downs · 34% expectedThe Broncos fumbled and the Bills recoveredFumble bounces · loose balls are close to 50/50 +12% BUF DEN: Punt
3 Q4 11:42 The Broncos converted 3rd & 103rd & 4th downs · 24% expected +15% DEN DEN: Touchdown
4 Q4 4:37 The Bills fumbled and recovered it themselvesFumble bounces · loose balls are close to 50/50 +12% BUF BUF: Touchdown
5 Q4 1:09 The Broncos converted 3rd & 63rd & 4th downs · 34% expected +17% DEN DEN: Field goal
6 Q4 0:35 The game turned hereDefensive Pass Interference on the Bills (Taron Johnson), 28 yardsJudgment calls · 15 flags in 4460 snaps before, position avg 1 per 216 +29% DEN DEN: Field goal
7 Q4 0:07 Defensive Too Many Men on Field on the Bills, 5 yardsPre-snap flags +11% DEN DEN: Field goal
8 Q4 0:04 W. Lutz made 36-yard field goalKicks · 90% expected for him +36% DEN –

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.

  • Tre'Davious White (BUF CB), out (IR) · 1.1 pts
  • Christian Benford (BUF CB), out · 0.8 pts
  • Dawson Knox (BUF TE), out (IR) · 0.7 pts
  • Micah Hyde (BUF FS), out · 0.7 pts
  • Matt Milano (BUF LB), out (IR) · 0.5 pts
  • Kaiir Elam (BUF CB), out (IR) · 0.4 pts
  • Kareem Jackson (DEN SS), out (IR) · 0.4 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 19% · Bills 81%

Final margin
Broncos by 2
Luck in points
13.5 for the Broncos
Luck-adjusted margin
Bills by 11.5
Replay with same day's form
Broncos 33% · Bills 67% 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 10 2023 games · Broncos · Bills

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