luckadjusted
NFL Week 9 · 2026

Week 17 2021 · January 2, 2022

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

Chiefs at Bengals, Week 17 2021: who deserved to win?

The Bengals beat the Chiefs 34–31, a result the replays rarely give: with the way both teams actually played, the Chiefs win 8 of 10. Luck ran their way: judgment calls alone were worth 12 points of win probability to the Bengals.

Before kickoff the Chiefs were 60% favorites. The biggest swing (Q4, 3:19 left): the Bengals converted 3rd & 27, worth 17 points of win probability to the Bengals.

Final

Kansas City Chiefs 31
Cincinnati Bengals 34

January 2, 2022 · Paul Brown Stadium · Closing line: Chiefs −3.5

Luck index +83 Bengals very lucky · −83 Chiefs

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. Chiefs win 8, Bengals win 2.

  1. 1 KC 42 CIN 14
  2. 2 KC 34 CIN 13
  3. 3 KC 44 CIN 27
  4. 4 KC 28 CIN 14
  5. 5 KC 28 CIN 17
  6. 6 KC 41 CIN 34
  7. 7 KC 27 CIN 23
  8. 8 KC 47 CIN 45
  9. 9 KC 19 CIN 23
  10. 10 KC 20 CIN 33

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

Chiefs win 83% of them, Bengals 17%, counting the 1% still level after regulation as half each. The line is what actually happened: Bengals by 3.

Show as a table
Final margin in the replaysShare of replays
Chiefs by 17+35.0%
Chiefs by 9–1622.6%
Chiefs by 1–825.4%
Level after regulation1.1%
Bengals by 1–810.8%
Bengals by 9–164.2%
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 +4.4 points to the Bengals: the final margin was Bengals by 3, without the luck Chiefs by 1.4. 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, 46 yds made · 73% expected
  • H. Butker, 34 yds made · 93% expected
  • E. McPherson, 20 yds made · 99% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Chiefs 10 for 83 yards, Bengals 5 for 62 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 11:59 Defensive Pass Interference on the Bengals (Jessie Bates III), 32 yards +8% KC +2.3 pts
Q1 5:31 Offensive Holding on the Chiefs (Blake Bell), 10 yards, wiping out the play +8% CIN +2.8 pts
Q2 9:45 Illegal Formation on the Bengals, 5 yards · pre-snap +2% KC +1.2 pts
Q2 8:38 Defensive Pass Interference on the Chiefs (Rashad Fenton), 5 yards +2% CIN +1.1 pts
Q2 1:46 Defensive Pass Interference on the Chiefs (Rashad Fenton), 14 yards +2% CIN +1.5 pts
Q2 0:41 Offensive Holding on the Chiefs, 10 yards +3% CIN +0.9 pts
Q3 13:30 Offensive Holding on the Chiefs (Dorian O'Daniel), 10 yards +2% CIN +0.7 pts
Q3 10:30 Offensive Holding on the Bengals, 10 yards +1% KC +0.9 pts
Q3 2:21 Offensive Holding on the Chiefs, 10 yards, wiping out the play +9% CIN +2.6 pts
Q4 15:00 Defensive Pass Interference on the Chiefs (L'Jarius Sneed), 11 yards +4% CIN +1.5 pts
Q4 13:28 False Start on the Bengals, 5 yards · pre-snap +3% KC +0.6 pts
Q4 12:42 Horse Collar Tackle on the Chiefs (L'Jarius Sneed), 8 yards +6% CIN +0.9 pts
Q4 5:17 Encroachment on the Chiefs (Chris Jones), 5 yards · pre-snap +1% KC +0.1 pts
Q4 4:13 Offensive Holding on the Bengals (Drew Sample), 10 yards +5% KC +1.2 pts
Q4 0:50 Illegal Use of Hands on the Chiefs (L'Jarius Sneed), 0 yards +6% CIN +1.7 pts

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

When it happened

Bengals’ chance of winning

As low as 15% and as high as 100%. 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 Chiefs were.
#WhenWhat happenedWin probability forNext drive
1 Q1 11:59 Defensive Pass Interference on the Bengals (Jessie Bates III), 32 yardsJudgment calls · 1 flag in 3141 snaps before, position avg 1 per 530 +8% KC KC: Touchdown
2 Q1 5:31 Offensive Holding on the Chiefs (Blake Bell), 10 yards, wiping out the playJudgment calls · 2 flags in 1667 snaps before, position avg 1 per 269 +8% CIN CIN: Touchdown
3 Q3 7:08 The Bengals converted 4th & 13rd & 4th downs · 76% expected +5% CIN CIN: Punt
4 Q3 2:21 Offensive Holding on the Chiefs, 10 yards, wiping out the playJudgment calls +9% CIN CIN: Touchdown
5 Q4 12:42 Horse Collar Tackle on the Chiefs (L'Jarius Sneed), 8 yardsJudgment calls · 11 flags in 1425 snaps before, position avg 1 per 213 +6% CIN CIN: Touchdown
6 Q4 6:09 The Chiefs were stopped on 3rd & 53rd & 4th downs · 49% expected +8% CIN KC: Field goal
7 Q4 3:19 The Bengals converted 3rd & 273rd & 4th downs · 15% expected +17% CIN CIN: Field goal
8 Q4 0:50 Illegal Use of Hands on the Chiefs (L'Jarius Sneed), 0 yardsJudgment calls · 11 flags in 1425 snaps before, position avg 1 per 213 +6% CIN CIN: Field goal

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.

  • Riley Reiff (CIN T), out (IR) · 0.9 pts
  • Germaine Pratt (CIN LB), out · 0.6 pts
  • Trae Waynes (CIN CB), 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

Chiefs 74% · Bengals 26%

Final margin
Bengals by 3
Luck in points
4.4 for the Bengals
Luck-adjusted margin
Chiefs by 1.4
Replay with same day's form
Chiefs 83% · Bengals 17% 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 17 2021 games · Chiefs · Bengals

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