luckadjusted

Week 17 2024 · December 28, 2024

Broncos at Bengals, Week 17 2024: who deserved to win?

The Bengals beat the Broncos 30–24, and it was no fluke: replayed with the way both teams actually played, the Bengals win 9 of 10. The Broncos had the bounces: kicks alone were worth 36 points of win probability to the Broncos.

Before kickoff the Bengals were 60% favorites. The biggest swing (Q4, 0:14 left): the Broncos converted 4th & 1, worth 33 points of win probability to the Broncos.

Final (OT)

Denver Broncos 24
Cincinnati Bengals 30

December 28, 2024 · Paycor Stadium · Closing line: Bengals −3.5

Luck index +11 Bengals about even · −11 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, Bengals win 9.

  1. 1 DEN 25 CIN 21
  2. 2 DEN 24 CIN 26
  3. 3 DEN 28 CIN 33
  4. 4 DEN 20 CIN 27
  5. 5 DEN 22 CIN 33
  6. 6 DEN 16 CIN 30
  7. 7 DEN 13 CIN 30
  8. 8 DEN 16 CIN 37
  9. 9 DEN 3 CIN 28
  10. 10 DEN 3 CIN 34

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 11% of them, Bengals 89%, counting the 1% still level after regulation as half each. The line is what actually happened: Bengals by 6.

Show as a table
Final margin in the replaysShare of replays
Broncos by 17+0.7%
Broncos by 9–162.5%
Broncos by 1–87.8%
Level after regulation1.2%
Bengals by 1–819.4%
Bengals by 9–1623.0%
Bengals by 17+45.4%

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 +8.3 points to the Broncos: the final margin was Bengals by 6, without the luck Bengals by 14.3. 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, 30 yds made · 95% expected
  • C. York, 22 yds made · 98% expected
  • C. York, 33 yds missed · 93% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Broncos 7 for 35 yards, Bengals 3 for 15 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 2:55 False Start on the Broncos, 5 yards · pre-snap +2% CIN +0.7 pts
Q2 12:23 Illegal Use of Hands on the Broncos, 4 yards, wiping out the play +2% CIN 0.0 pts
Q2 7:22 Defensive Pass Interference on the Broncos (Riley Moss), 7 yards +4% CIN +1.5 pts
Q2 3:37 Illegal Contact on the Broncos (Justin Strnad), 5 yards +4% CIN +0.3 pts
Q3 10:29 False Start on the Bengals, 5 yards · pre-snap +2% DEN +1.0 pts
Q3 10:16 Illegal Contact on the Broncos, 5 yards, wiping out the play +6% CIN +2.4 pts
Q3 9:50 Defensive Offside on the Broncos (Nik Bonitto), 4 yards, wiping out the play · pre-snap +3% CIN +1.1 pts
Q3 0:17 Illegal Shift on the Bengals, 5 yards, wiping out the play · pre-snap +32% DEN +6.0 pts
QOT 9:13 Illegal Contact on the Broncos (Damarri Mathis), 5 yards +4% CIN +0.8 pts
QOT 4:15 False Start on the Bengals (Tee Higgins), 5 yards · pre-snap +8% DEN +0.5 pts

Broncos penalties, every game · Bengals penalties, every game · All teams, 2024

When it happened

Bengals’ chance of winning

As low as 23% 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 Bengals were ahead in it, below while the Broncos were.
#WhenWhat happenedWin probability forNext drive
1 Q1 4:32 The Bengals were stopped on 4th & 13rd & 4th downs · 75% expected +13% DEN CIN: Turnover on downs
2 Q2 6:26 The Bengals were stopped on 4th & 23rd & 4th downs · 54% expected +12% DEN CIN: Touchdown
3 Q3 0:17 Illegal Shift on the Bengals, 5 yards, wiping out the playPre-snap flags +32% DEN DEN: Touchdown
4 Q3 0:07 The Bengals converted 3rd & 133rd & 4th downs · 25% expected +14% CIN CIN: Touchdown
5 Q4 5:13 The Bengals were stopped on 3rd & 43rd & 4th downs · 48% expectedThe Bengals fumbled and the Broncos recoveredFumble bounces · loose balls are close to 50/50 +11% DEN CIN: Touchdown
6 Q4 1:51 The Bengals converted 3rd & 63rd & 4th downs · 40% expected +11% CIN CIN: Touchdown
7 Q4 0:14 The Broncos converted 4th & 13rd & 4th downs · 73% expected +33% DEN DEN: Touchdown
8 QOT 2:49 C. York missed 33-yard field goalKicks · 93% expected for him +25% DEN CIN: 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.

  • Logan Wilson (CIN LB), out (IR) · 0.5 pts
  • Evan McPherson (CIN K), out (IR) · 0.4 pts
  • Sheldon Rankins (CIN DT), 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

Broncos 1% · Bengals 99%

Final margin
Bengals by 6
Luck in points
8.3 for the Broncos
Luck-adjusted margin
Bengals by 14.3
Replay with same day's form
Broncos 11% · Bengals 89% 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 17 2024 games · Broncos · Bengals

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