luckadjusted
NFL Week 9 · 2026

Week 4 2025 · September 29, 2025

Bengals at Broncos, Week 4 2025: who deserved to win?

The Broncos beat the Bengals 28–3, and the replays back it up: with the way both teams actually played, the Broncos win 8 of 10.

Before kickoff the Broncos were 71% favorites. The biggest swing (Q2, 14:08 left): Illegal Formation on the Bengals, 5 yards, wiping out the play, worth 13 points of win probability to the Broncos.

Final

Cincinnati Bengals 3
Denver Broncos 28

September 29, 2025 · Empower Field at Mile High · Closing line: Broncos −7.5

Luck index +18 Broncos about even · −18 Bengals

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. Bengals win 2, Broncos win 8.

  1. 1 CIN 33 DEN 23
  2. 2 CIN 20 DEN 17
  3. 3 CIN 21 DEN 23
  4. 4 CIN 14 DEN 19
  5. 5 CIN 14 DEN 22
  6. 6 CIN 16 DEN 27
  7. 7 CIN 9 DEN 22
  8. 8 CIN 19 DEN 36
  9. 9 CIN 14 DEN 35
  10. 10 CIN 13 DEN 41

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

Bengals win 18% of them, Broncos 82%, counting the 3% still level after regulation as half each. The line is what actually happened: Broncos by 25.

Show as a table
Final margin in the replaysShare of replays
Bengals by 17+1.2%
Bengals by 9–164.8%
Bengals by 1–811.1%
Level after regulation2.5%
Broncos by 1–827.9%
Broncos by 9–1620.9%
Broncos by 17+31.6%

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 +7.1 points to the Broncos: the final margin was Broncos by 25, without the luck Broncos by 17.9. Luck shares are the fitted ones (how much of each kind is luck).

Penalties: Bengals 11 for 65 yards, Broncos 7 for 72 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 half toward luck; pre-snap fouls, which repeat, don’t count. How calls are valued

WhenFlagWin probability for
Q1 14:56 Defensive Holding on the Broncos (Patrick Surtain II), 5 yards +2% CIN +0.3 pts
Q1 6:55 Offensive Holding on the Bengals (Tahj Brooks), 10 yards +3% DEN +0.9 pts
Q1 6:05 Defensive Pass Interference on the Broncos (Riley Moss), 22 yards +5% CIN +1.9 pts
Q1 4:30 False Start on the Bengals, 5 yards · pre-snap +1% DEN +0.6 pts
Q2 14:24 Defensive Offside on the Broncos (John Franklin-Myers), 5 yards · pre-snap +1% CIN +0.5 pts
Q2 14:08 Illegal Formation on the Bengals, 5 yards, wiping out the play · pre-snap +13% DEN +4.0 pts
Q2 13:44 False Start on the Bengals, 5 yards · pre-snap +1% DEN +0.3 pts
Q2 12:49 Delay of Game on the Bengals, 5 yards · pre-snap +1% DEN +0.3 pts
Q2 12:07 Delay of Game on the Bengals, 5 yards · pre-snap +2% DEN +0.3 pts
Q2 8:48 Offensive Holding on the Bengals (Tycen Anderson), 10 yards +1% DEN +0.7 pts
Q2 7:58 Illegal Use of Hands on the Bengals (Trey Hendrickson), 5 yards +1% DEN +0.7 pts
Q2 6:10 Offensive Holding on the Broncos, 10 yards +1% CIN +0.9 pts
Q3 11:08 Fair Catch Interference on the Bengals (PJ Jules), 0 yards 0% DEN 0.0 pts
Q3 8:47 Illegal Blindside Block on the Broncos, 15 yards +1% CIN +1.6 pts
Q3 4:39 Offensive Holding on the Bengals, 10 yards 0% DEN +0.8 pts
Q4 15:00 Offensive Holding on the Broncos, 10 yards 0% CIN +0.9 pts
Q4 14:27 False Start on the Broncos, 5 yards · pre-snap 0% CIN +0.3 pts
Q4 4:58 False Start on the Bengals, 5 yards · pre-snap 0% DEN +0.5 pts

Bengals penalties, every game · Broncos penalties, every game · All teams, 2025

When it happened

Broncos’ chance of winning

As low as 42% 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 Broncos were ahead in it, below while the Bengals were.
#WhenWhat happenedWin probability forNext drive
1 Q1 12:33 The Bengals converted 3rd & 63rd & 4th downs · 39% expected +7% CIN CIN: Field goal
2 Q1 9:15 The Bengals were stopped on 3rd & 23rd & 4th downs · 54% expected +4% DEN CIN: Field goal
3 Q1 6:05 Defensive Pass Interference on the Broncos (Riley Moss), 22 yardsJudgment calls · 7 flags in 1511 snaps before, position avg 1 per 213 +5% CIN CIN: Punt
4 Q1 4:34 The Bengals were stopped on 3rd & 23rd & 4th downs · 63% expected +4% DEN CIN: Punt
5 Q1 3:43 The Broncos converted 3rd & 73rd & 4th downs · 36% expected +6% DEN DEN: Touchdown
6 Q1 0:22 The Broncos converted 3rd & 53rd & 4th downs · 35% expected +7% DEN DEN: Touchdown
7 Q2 14:08 Illegal Formation on the Bengals, 5 yards, wiping out the playPre-snap flags +13% DEN DEN: Touchdown
8 Q2 10:39 The Broncos converted 3rd & 43rd & 4th downs · 48% expected +5% DEN DEN: 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.

  • Joe Burrow (CIN QB), out (IR), replaced by j.browning · 4.5 pts
  • Cordell Volson (CIN G), out (IR) · 0.7 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

Bengals 0% · Broncos 100%

Final margin
Broncos by 25
Luck in points
7.1 for the Broncos
Luck-adjusted margin
Broncos by 17.9
Replay with same day's form
Bengals 18% · Broncos 82% unchanged: why
How much of each is luck?

0% treats it as skill, 100% as pure luck. The tick is our fit.

What counts

None by default: our tests measured no carryover after a lucky break. Slide it up to count a break for more than its own swing. 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 2025 games · Bengals · Broncos

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