luckadjusted

Week 4 2025 · September 29, 2025

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

The Broncos beat the Bengals 28–3, and it was no fluke: replayed with the way both teams actually played, the Broncos win 9 of 10. The Bengals had the bounces: judgment calls alone were worth 2.5 points to the Bengals.

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 +10 Broncos about even · −10 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 1, Broncos win 9.

  1. 1 CIN 17 DEN 13
  2. 2 CIN 21 DEN 23
  3. 3 CIN 23 DEN 28
  4. 4 CIN 14 DEN 23
  5. 5 CIN 16 DEN 27
  6. 6 CIN 13 DEN 27
  7. 7 CIN 10 DEN 26
  8. 8 CIN 6 DEN 25
  9. 9 CIN 13 DEN 37
  10. 10 CIN 3 DEN 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

Bengals win 10% of them, Broncos 90%, counting the 1% 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+0.4%
Bengals by 9–161.7%
Bengals by 1–86.9%
Level after regulation1.4%
Broncos by 1–819.5%
Broncos by 9–1624.0%
Broncos by 17+46.1%

Where the luck was

Take the luck out

The final margin was Broncos by 25. Remove the luck, one kind at a time, and it becomes Broncos by 19.1.

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).

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 · 37% expected +9% CIN CIN: Field goal
2 Q1 9:15 The Bengals were stopped on 3rd & 23rd & 4th downs · 52% 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 3:43 The Broncos converted 3rd & 73rd & 4th downs · 34% expected +6% DEN DEN: Touchdown
5 Q1 0:22 The Broncos converted 3rd & 53rd & 4th downs · 34% expected +8% DEN DEN: Touchdown
6 Q2 14:08 Illegal Formation on the Bengals, 5 yards, wiping out the playPre-snap flags +13% DEN DEN: Touchdown
7 Q2 10:39 The Broncos converted 3rd & 43rd & 4th downs · 46% expected +6% DEN DEN: Touchdown
8 Q2 2:04 The Broncos were stopped on 4th & 13rd & 4th downs · 67% expectedThe Broncos threw an interception-worthy pass, and it was pickedInterceptions · 50% expected to stay out of the defense's hands +7% CIN 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
5.9 for the Broncos
Luck-adjusted margin
Broncos by 19.1
Replay with same day's form
Bengals 10% · Broncos 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 Week 4 2025 games · Bengals · Broncos

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