luckadjusted
NFL Week 9 · 2026

Week 4 2024 · September 29, 2024

Bengals at Panthers, Week 4 2024: who deserved to win?

The Bengals beat the Panthers 34–24, and the replays lean their way: with the same day's form, they win 8 of 10. The Panthers had the bounces: judgment calls alone were worth 8 points of win probability to the Panthers.

Before kickoff the Bengals were 63% favorites. The biggest swing (Q2, 5:37 left): Defensive Holding on the Bengals (Cam Taylor-Britt), 5 yards, wiping out the play, worth 16 points of win probability to the Panthers.

Final

Cincinnati Bengals 34
Carolina Panthers 24

September 29, 2024 · Bank of America Stadium · Closing line: Bengals −4.5

Luck index +22 Bengals about even · −22 Panthers

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 8, Panthers win 2.

  1. 1 CIN 38 CAR 12
  2. 2 CIN 27 CAR 8
  3. 3 CIN 20 CAR 6
  4. 4 CIN 28 CAR 16
  5. 5 CIN 34 CAR 24
  6. 6 CIN 26 CAR 19
  7. 7 CIN 30 CAR 26
  8. 8 CIN 8 CAR 6
  9. 9 CIN 17 CAR 20
  10. 10 CIN 7 CAR 20

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 78% of them, Panthers 22%, counting the 2% still level after regulation as half each. The line is what actually happened: Bengals by 10.

Show as a table
Final margin in the replaysShare of replays
Bengals by 17+28.4%
Bengals by 9–1621.3%
Bengals by 1–828.1%
Level after regulation2.0%
Panthers by 1–811.6%
Panthers by 9–166.5%
Panthers by 17+2.1%

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 +1.6 points to the Bengals: the final margin was Bengals by 10, without the luck Bengals by 8.4. 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.

  • E. McPherson, 56 yds made · 67% expected
  • E. Pineiro, 48 yds made · 79% expected
  • E. McPherson, 46 yds made · 83% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bengals 5 for 39 yards, Panthers 6 for 37 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 1:01 Illegal Contact on the Panthers (Michael Jackson), 2 yards +1% CIN +0.3 pts
Q1 0:05 Illegal Use of Hands on the Bengals (Daxton Hill), 5 yards +3% CAR +0.8 pts
Q2 5:58 False Start on the Panthers, 5 yards · pre-snap +3% CIN +0.4 pts
Q2 5:37 Defensive Holding on the Bengals (Cam Taylor-Britt), 5 yards, wiping out the play +16% CAR +4.9 pts
Q2 0:22 Defensive Pass Interference on the Panthers (Michael Jackson), 17 yards +4% CIN +1.8 pts
Q2 0:17 Defensive Pass Interference on the Panthers (Jaycee Horn), 3 yards +2% CIN +0.2 pts
Q3 6:06 False Start on the Panthers, 5 yards · pre-snap +2% CIN +1.0 pts
Q3 4:08 Offensive Holding on the Bengals, 10 yards +1% CAR +0.9 pts
Q4 14:15 Offensive Pass Interference on the Bengals (Tee Higgins), 9 yards +2% CAR +1.2 pts
Q4 3:17 Neutral Zone Infraction on the Panthers, 5 yards · pre-snap +1% CIN +1.1 pts
Q4 2:37 Offensive Holding on the Bengals, 10 yards, wiping out the play +3% CAR +1.2 pts

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

When it happened

Panthers’ chance of winning

As low as 0% and as high as 70%. 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 Panthers were ahead in it, below while the Bengals were.
#WhenWhat happenedWin probability forNext drive
1 Q1 13:48 The Panthers converted 3rd & 43rd & 4th downs · 46% expected +6% CAR CAR: Turnover on downs
2 Q1 9:12 The Panthers were stopped on 4th & 13rd & 4th downs · 67% expected +9% CIN CAR: Turnover
3 Q1 7:40 The Bengals converted 3rd & 43rd & 4th downs · 47% expected +7% CIN CIN: Punt
4 Q1 3:56 The Panthers converted 3rd & 93rd & 4th downs · 29% expected +6% CAR CAR: Turnover
5 Q1 0:08 The Bengals converted 3rd & 33rd & 4th downs · 44% expected +5% CIN CIN: Touchdown
6 Q2 12:16 The Panthers converted 4th & 33rd & 4th downs · 53% expected +8% CAR CAR: Touchdown
7 Q2 5:37 Defensive Holding on the Bengals (Cam Taylor-Britt), 5 yards, wiping out the playJudgment calls · 7 flags in 1655 snaps before, position avg 1 per 215 +16% CAR CAR: Touchdown
8 Q2 0:48 The Bengals converted 3rd & 53rd & 4th downs · 42% expected +7% CIN 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.

  • Adam Thielen (CAR WR), out (IR) · 0.6 pts
  • Derrick Brown (CAR DT), out (IR) · 0.6 pts
  • Damien Lewis (CAR G), out · 0.5 pts
  • Jordan Fuller (CAR FS), out (IR) · 0.4 pts
  • Shy Tuttle (CAR DT), out · 0.2 pts
  • Trent Brown (CIN T), out (IR) · 0.6 pts
  • B.J. Hill (CIN DT), out · 0.4 pts
  • Sheldon Rankins (CIN DT), out · 0.3 pts
  • Brad Robbins (CIN P), out (IR) · 0.1 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 94% · Panthers 6%

Final margin
Bengals by 10
Luck in points
1.6 for the Bengals
Luck-adjusted margin
Bengals by 8.4
Replay with same day's form
Bengals 78% · Panthers 22% 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 2024 games · Bengals · Panthers

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