luckadjusted
NFL Week 9 · 2026

Week 16 2022 · December 24, 2022

Bengals at Patriots, Week 16 2022: who deserved to win?

The Bengals beat the Patriots 22–18, and the replays lean their way: with the same day's form, they win 7 of 10.

Before kickoff the Bengals were 59% favorites. The game turned on a luck play (Q4, 1:05 left): the Patriots fumbled and the Bengals recovered, worth 50 points of win probability to the Bengals.

Final

Cincinnati Bengals 22
New England Patriots 18

December 24, 2022 · Gillette Stadium · Closing line: Bengals −3

Luck index +29 Bengals lucky · −29 Patriots

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 7, Patriots win 3.

  1. 1 CIN 34 NE 7
  2. 2 CIN 37 NE 17
  3. 3 CIN 20 NE 6
  4. 4 CIN 31 NE 20
  5. 5 CIN 21 NE 13
  6. 6 CIN 24 NE 20
  7. 7 CIN 21 NE 19
  8. 8 CIN 10 NE 13
  9. 9 CIN 16 NE 26
  10. 10 CIN 17 NE 36

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 71% of them, Patriots 29%, counting the 4% still level after regulation as half each. The line is what actually happened: Bengals by 4.

Show as a table
Final margin in the replaysShare of replays
Bengals by 17+23.6%
Bengals by 9–1620.2%
Bengals by 1–825.4%
Level after regulation3.5%
Patriots by 1–814.4%
Patriots by 9–168.5%
Patriots by 17+4.5%

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 Patriots: the final margin was Bengals by 4, without the luck Bengals by 5.6. 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, 28 yds made · 98% expected
  • E. McPherson, 43 yds missed · 84% expected
  • Extra point missed · 94% expected
  • Extra point missed · 94% expected
  • Extra point missed · 94% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bengals 8 for 62 yards, Patriots 10 for 82 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 6:30 Delay of Game on the Bengals, 5 yards · pre-snap +2% NE +0.8 pts
Q1 5:16 Unnecessary Roughness on the Patriots, 1 yard +2% NE 0.0 pts
Q1 3:58 Ineligible Downfield Kick on the Patriots (Jahlani Tavai), 5 yards 0% CIN +0.5 pts
Q1 2:33 Roughing the Passer on the Patriots (Matt Judon), 14 yards +3% CIN +1.0 pts
Q1 2:04 Illegal Use of Hands on the Bengals, 10 yards +1% NE +1.1 pts
Q1 0:35 Offensive Holding on the Bengals (Devin Asiasi), 10 yards, wiping out the play +6% NE +2.4 pts
Q2 8:27 Defensive Holding on the Patriots (Carl Davis), 5 yards +1% CIN +0.7 pts
Q2 5:18 Illegal Use of Hands on the Patriots (Joshua Uche), 4 yards +2% CIN +1.2 pts
Q2 1:18 Face Mask on the Patriots (Kyle Dugger), 15 yards +1% CIN +1.8 pts
Q3 14:18 Defensive Pass Interference on the Bengals, 11 yards +1% NE +1.2 pts
Q3 10:02 Delay of Game on the Bengals, 6 yards · pre-snap 0% NE +1.2 pts
Q3 4:29 Offensive Holding on the Bengals, 10 yards 0% NE +2.3 pts
Q4 6:18 Intentional Grounding on the Patriots (Mac Jones), 13 yards +3% CIN +1.0 pts
Q4 6:13 False Start on the Patriots, 5 yards · pre-snap +2% CIN +0.2 pts
Q4 3:12 Defensive Holding on the Bengals (Eli Apple), 5 yards +2% NE +0.3 pts
Q4 1:05 Unnecessary Roughness on the Patriots (Mac Jones), 15 yards +17% CIN +1.1 pts
Q4 0:59 False Start on the Bengals, 5 yards · pre-snap 0% NE +0.2 pts
Q4 0:15 Delay of Game on the Patriots, 5 yards · pre-snap +1% CIN 0.0 pts

Bengals penalties, every game · Patriots penalties, every game · All teams, 2022

When it happened

Patriots’ chance of winning

As low as 0% and as high as 68%. 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 Patriots were ahead in it, below while the Bengals were.
#WhenWhat happenedWin probability forNext drive
1 Q1 0:35 Offensive Holding on the Bengals (Devin Asiasi), 10 yards, wiping out the playJudgment calls · 3 flags in 439 snaps before, position avg 1 per 282 +6% NE NE: Punt
2 Q4 9:10 E. McPherson missed a 43-yard field goalKicks · 84% expected for him +6% NE CIN: Turnover
3 Q4 6:13 The Patriots converted 3rd & 293rd & 4th downs · 12% expectedFalse Start on the Patriots, 5 yardsPre-snap flags +9% NE NE: Touchdown
4 Q4 3:19 The Bengals fumbled and the Patriots recoveredFumble bounces · loose balls are close to 50/50 +10% NE CIN: Punt
5 Q4 1:47 The Patriots converted 3rd & 13rd & 4th downs · 65% expected +7% NE NE: Turnover
6 Q4 1:05 The game turned hereThe Patriots fumbled and the Bengals recoveredFumble bounces · loose balls are close to 50/50Unnecessary Roughness on the Patriots (Mac Jones), 15 yardsJudgment calls · 4 flags in 1774 snaps before, position avg 1 per 697 +50% CIN NE: Turnover on downs
7 Q4 0:19 R. Stevenson dropped a catchable passDrops · 3 drops on 66 catchable balls before this +37% CIN NE: Turnover on downs
8 Q4 0:15 The Patriots were stopped on 4th & 153rd & 4th downs · 20% expectedDelay of Game on the Patriots, 5 yardsPre-snap flags +6% CIN NE: End of game

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.

  • Marcus Cannon (NE T), out (IR) · 0.6 pts
  • DeVante Parker (NE WR), out · 0.5 pts
  • Jalen Mills (NE CB), out · 0.4 pts
  • Jack Jones (NE CB), out · 0.4 pts
  • Jake Bailey (NE P), out (IR) · 0.2 pts
  • Sam Hubbard (CIN DE), out · 0.9 pts
  • Hayden Hurst (CIN TE), out · 0.5 pts
  • Chidobe Awuzie (CIN CB), 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

Bengals 83% · Patriots 17%

Final margin
Bengals by 4
Luck in points
1.6 for the Patriots
Luck-adjusted margin
Bengals by 5.6
Replay with same day's form
Bengals 71% · Patriots 29% 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 16 2022 games · Bengals · Patriots

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