luckadjusted

Week 9 2023 · November 5, 2023

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

The Bengals stole one. They beat the Bills 24–18, but replayed with the way both teams actually played, the Bills win 8 of 10. Luck ran their way: injuries alone were worth 9 points of win probability to the Bengals.

The Bengals won on an off day: their defense played far below its usual level. In a fresh game against the Bills they would win 59% of the time; with this day’s form, 16%. The numbers

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 +84 Bengals very lucky · −84 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 8, Bengals win 2.

  1. 1 BUF 42 CIN 12
  2. 2 BUF 30 CIN 10
  3. 3 BUF 27 CIN 10
  4. 4 BUF 26 CIN 13
  5. 5 BUF 21 CIN 10
  6. 6 BUF 24 CIN 16
  7. 7 BUF 10 CIN 6
  8. 8 BUF 16 CIN 14
  9. 9 BUF 23 CIN 26
  10. 10 BUF 13 CIN 26

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.

The Bengals won on an off day

Their defense played far below its usual level. In a fresh game against the Bills they would win 59% of the time; with this day’s form, 16%.

43 points apart for the Bengals: the gap is how differently this game went from what the two teams usually are.

UnitThis gameUsual levelBetter or worse than usual
Bills offenseEPA per play gained +0.18 +0.20 worse by 0.02
Bills defenseEPA per play allowed +0.21 +0.08 worse by 0.13
Bengals offenseEPA per play gained +0.21 +0.12 better by 0.09
Bengals defenseEPA per play allowed +0.18 +0.08 worse by 0.10

EPA (expected points added) per play on competitive snaps, turnovers left out because they are valued as luck. Usual level: the team’s earlier games this season plus half of last season, pulled toward the league average. One team’s defense and the other team’s offense are the same snaps, so one game can’t fully say whose day it was; it shows how far this one was from both teams’ norms.

How 4,000 replays ended

Bills win 84% of them, Bengals 16%, 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
Bills by 17+33.7%
Bills by 9–1624.1%
Bills by 1–825.8%
Level after regulation1.0%
Bengals by 1–810.3%
Bengals by 9–163.9%
Bengals by 17+1.1%

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 +3.3 points to the Bengals: the final margin was Bengals by 6, without the luck Bengals by 2.7. 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 toward luck, pre-snap fouls mostly don’t. 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 +1.2 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 3:38 The Bengals converted 3rd & 103rd & 4th downs · 28% expected +12% CIN CIN: Touchdown
2 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
3 Q2 7:10 Offensive Holding on the Bengals, 10 yards, wiping out the playJudgment calls +4% BUF BUF: Punt
4 Q2 6:14 The Bengals were stopped on 3rd & 103rd & 4th downs · 28% expected +5% BUF CIN: Punt
5 Q2 4:17 The Bills were stopped on 3rd & 23rd & 4th downs · 63% expected +6% CIN BUF: Punt
6 Q2 2:39 The Bengals converted 4th & 13rd & 4th downs · 74% expected +5% CIN CIN: Touchdown
7 Q2 1:46 The Bengals converted 3rd & 73rd & 4th downs · 35% expected +5% CIN CIN: Touchdown
8 Q4 13:25 The Bills fumbled and the Bengals recoveredFumble bounces · loose balls are close to 50/50 +5% CIN BUF: 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.

  • 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 16% · Bengals 84%

Final margin
Bengals by 6
Luck in points
3.3 for the Bengals
Luck-adjusted margin
Bengals by 2.7
Replay with same day's form
Bills 84% · Bengals 16% 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 9 2023 games · Bills · Bengals

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