luckadjusted
NFL Week 9 · 2026

Week 9 2023 · November 5, 2023

Bills at Bengals, Week 9 2023: who deserved to win?

The Bengals beat the Bills 24–18, but the replays lean toward the Bills: they take 7 of 10 with the same day's form.

Before kickoff the Bengals were 54% favorites. The biggest swing (Q1, 3:38 left): the Bengals converted 3rd & 10, worth 12 points of win probability to the Bengals.

Final

Buffalo Bills 18
Cincinnati Bengals 24

November 5, 2023 · Paycor Stadium · Closing line: Bengals −1.5

Luck index +70 Bengals very lucky · −70 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. Bills win 7, Bengals win 3.

  1. 1 BUF 37 CIN 14
  2. 2 BUF 38 CIN 20
  3. 3 BUF 24 CIN 10
  4. 4 BUF 34 CIN 23
  5. 5 BUF 34 CIN 26
  6. 6 BUF 22 CIN 17
  7. 7 BUF 23 CIN 20
  8. 8 BUF 24 CIN 26
  9. 9 BUF 7 CIN 14
  10. 10 BUF 14 CIN 30

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

Bills win 70% of them, Bengals 30%, counting the 5% 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
Bills by 17+21.9%
Bills by 9–1621.1%
Bills by 1–825.3%
Level after regulation4.6%
Bengals by 1–816.1%
Bengals by 9–167.2%
Bengals by 17+3.7%

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 +4.3 points to the Bengals: the final margin was Bengals by 6, without the luck Bengals by 1.7. 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.

  • T. Bass, 34 yds made · 94% expected
  • E. McPherson, 20 yds made · 100% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bills 5 for 49 yards, Bengals 6 for 49 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 6:08 Taunting on the Bills (Josh Allen), 15 yards +4% CIN +1.3 pts
Q1 5:58 Roughing the Passer on the Bills (Tim Settle), 15 yards +3% CIN +1.0 pts
Q2 15:00 Defensive Pass Interference on the Bengals (Cam Taylor-Britt), 17 yards +5% BUF +1.7 pts
Q2 10:18 False Start on the Bengals, 5 yards · pre-snap +2% BUF +0.8 pts
Q2 7:31 Delay of Game on the Bengals, 4 yards · pre-snap +3% BUF +0.8 pts
Q2 7:10 Offensive Holding on the Bengals, 10 yards, wiping out the play +4% BUF +2.2 pts
Q2 6:44 Defensive Offside on the Bills (Leonard Floyd), 5 yards, wiping out the play · pre-snap +1% BUF +0.2 pts
Q2 5:50 False Start on the Bengals, 5 yards · pre-snap +1% BUF +0.3 pts
Q2 0:28 Intentional Grounding on the Bills (Josh Allen), 9 yards +1% CIN +0.8 pts
Q3 14:26 Ineligible Downfield Pass on the Bills, 5 yards 0% CIN +0.6 pts
Q3 10:21 Illegal Block Above the Waist on the Bengals (Stanley Morgan Jr.), 8 yards +1% BUF +0.7 pts

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

When it happened

Bengals’ chance of winning

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 Bills were.
#WhenWhat happenedWin probability forNext drive
1 Q1 12:14 The Bengals converted 3rd & 23rd & 4th downs · 63% expected +4% CIN CIN: Touchdown
2 Q1 6:08 Taunting on the Bills (Josh Allen), 15 yardsJudgment calls · 9 flags in 5280 snaps before, position avg 1 per 643 +4% CIN CIN: Touchdown
3 Q1 3:38 The Bengals converted 3rd & 103rd & 4th downs · 30% expected +12% CIN CIN: Touchdown
4 Q2 15:00 Defensive Pass Interference on the Bengals (Cam Taylor-Britt), 17 yardsJudgment calls · 5 flags in 1238 snaps before, position avg 1 per 216 +5% BUF BUF: Punt
5 Q2 7:10 Offensive Holding on the Bengals, 10 yards, wiping out the playJudgment calls +4% BUF BUF: Punt
6 Q2 4:17 The Bills were stopped on 3rd & 23rd & 4th downs · 65% expected +6% CIN BUF: Punt
7 Q4 13:25 The Bills fumbled and the Bengals recoveredFumble bounces · loose balls are close to 50/50 +6% CIN BUF: Touchdown
8 Q4 3:32 The Bills’ two-point try was good3rd & 4th downs · 47% expected +4% BUF –

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
  • Dawson Knox (BUF TE), out (IR) · 0.7 pts
  • Matt Milano (BUF LB), out (IR) · 0.5 pts
  • Kaiir Elam (BUF CB), out (IR) · 0.4 pts
  • DaQuan Jones (BUF DT), out (IR) · 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

Bills 22% · Bengals 78%

Final margin
Bengals by 6
Luck in points
4.3 for the Bengals
Luck-adjusted margin
Bengals by 1.7
Replay with same day's form
Bills 70% · Bengals 30% 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 9 2023 games · Bills · Bengals

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