luckadjusted
NFL Week 9 · 2026

Week 5 2021 · October 10, 2021

No FTN charting for this game (drops and interception-worthy throws are not modelled).

Packers at Bengals, Week 5 2021: who deserved to win?

The Packers beat the Bengals 25–22, and the replays back it up: with the way both teams actually played, the Packers win 9 of 10. The Bengals had the bounces: kicks alone were worth 19 points of win probability to the Bengals.

Before kickoff the Packers were 56% favorites. The game turned on a luck play (Q4, 0:26 left): E. McPherson missed a 57-yard field goal, worth 33 points of win probability to the Packers. The biggest single swing (OT, 8:12 left): M. Crosby missed a 40-yard field goal.

Final (OT)

Green Bay Packers 25
Cincinnati Bengals 22

October 10, 2021 · Paul Brown Stadium · Closing line: Packers −2

Luck index +15 Packers about even · −15 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. Packers win 9, Bengals win 1.

  1. 1 GB 58 CIN 24
  2. 2 GB 41 CIN 17
  3. 3 GB 40 CIN 20
  4. 4 GB 36 CIN 19
  5. 5 GB 34 CIN 20
  6. 6 GB 52 CIN 41
  7. 7 GB 25 CIN 17
  8. 8 GB 34 CIN 29
  9. 9 GB 31 CIN 29
  10. 10 GB 23 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

Packers win 85% of them, Bengals 15%, counting the 2% still level after regulation as half each. The line is what actually happened: Packers by 3.

Show as a table
Final margin in the replaysShare of replays
Packers by 17+42.9%
Packers by 9–1621.9%
Packers by 1–818.9%
Level after regulation1.6%
Bengals by 1–89.5%
Bengals by 9–163.9%
Bengals by 17+1.3%

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 +4.1 points to the Bengals: the final margin was Packers by 3, without the luck Packers by 7.1. 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.

  • M. Crosby, 44 yds made · 81% expected
  • M. Crosby, 44 yds made · 81% expected
  • M. Crosby, 22 yds made · 100% expected
  • M. Crosby, 36 yds missed · 93% expected
  • E. McPherson, 57 yds missed · 60% expected
  • M. Crosby, 51 yds missed · 69% expected
  • M. Crosby, 40 yds missed · 87% expected
  • E. McPherson, 49 yds missed · 69% expected
  • M. Crosby, 49 yds made · 71% expected
  • Extra point missed · 94% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Packers 2 for 10 yards, Bengals 2 for 21 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
Q2 2:34 False Start on the Packers (Robert Tonyan), 5 yards · pre-snap +2% CIN +0.4 pts
Q2 0:01 False Start on the Packers, 5 yards · pre-snap +3% CIN 0.0 pts
Q3 0:58 Offensive Holding on the Bengals, 10 yards +9% GB +2.2 pts
Q4 14:17 Tripping on the Bengals (D.J. Reader), 11 yards +2% GB +1.1 pts

Packers penalties, every game · Bengals penalties, every game · All teams, 2021

When it happened

Bengals’ chance of winning

As low as 0% and as high as 77%. 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 Packers were.
#WhenWhat happenedWin probability forNext drive
1 Q4 3:27 The Bengals’ two-point try was good3rd & 4th downs · 47% expected +14% CIN CIN: Missed field goal
2 Q4 2:16 M. Crosby missed a 36-yard field goalKicks · 93% expected for him +23% CIN GB: Missed field goal
3 Q4 0:26 The game turned hereE. McPherson missed a 57-yard field goalKicks · 60% expected for him, 2 of 2 from 45+ before +33% GB CIN: Turnover
4 Q4 0:03 M. Crosby missed a 51-yard field goalKicks · 69% expected for him, 12 of 14 from 45+ before +29% CIN GB: Missed field goal
5 OT 8:12 M. Crosby missed a 40-yard field goalKicks · 87% expected for him +42% CIN GB: Field goal
6 OT 6:44 The Bengals converted 3rd & 23rd & 4th downs · 61% expected +14% CIN CIN: Missed field goal
7 OT 2:33 The Packers were stopped on 3rd & 163rd & 4th downs · 24% expected +24% GB GB: Field goal
8 OT 2:00 M. Crosby made a 49-yard field goalKicks · 71% expected for him, 12 of 15 from 45+ before +28% GB –

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.

  • Xavier Su'a-Filo (CIN G), out (IR) · 0.3 pts
  • Fred Johnson (CIN OT), out · 0.2 pts
  • Jaire Alexander (GB CB), out (IR) · 0.9 pts
  • Josh Myers (GB C), out · 0.6 pts
  • Elgton Jenkins (GB G), out · 0.5 pts
  • Marquez Valdes-Scantling (GB WR), out (IR) · 0.4 pts
  • Za'Darius Smith (GB LB), out (IR) · 0.4 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

Packers 80% · Bengals 20%

Final margin
Packers by 3
Luck in points
4.1 for the Bengals
Luck-adjusted margin
Packers by 7.1
Replay with same day's form
Packers 85% · Bengals 15% 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 (not available for this game); injuries from snap counts and injury reports. No FTN charting for this game (drops and interception-worthy throws are not modelled).

Methodology and validation · All Week 5 2021 games · Packers · Bengals

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