luckadjusted

AFC Championship 2021 · January 30, 2022

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

Bengals at Chiefs, AFC Championship 2021: who deserved to win?

The Bengals stole one. They beat the Chiefs 27–24, but replayed with the way both teams actually played, the Chiefs win 8 of 10. Luck ran their way: 3rd & 4th downs alone were worth 14 points of win probability to the Bengals.

Before kickoff the Chiefs were 70% favorites. The biggest swing (Q4, 15:00 left): the Chiefs were stopped on 3rd & 3, worth 12 points of win probability to the Bengals.

Final (OT)

Cincinnati Bengals 27
Kansas City Chiefs 24

January 30, 2022 · GEHA Field at Arrowhead Stadium · Closing line: Chiefs −7

Luck index +80 Bengals very lucky · −80 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. Bengals win 2, Chiefs win 8.

  1. 1 CIN 40 KC 28
  2. 2 CIN 31 KC 28
  3. 3 CIN 36 KC 38
  4. 4 CIN 24 KC 29
  5. 5 CIN 28 KC 36
  6. 6 CIN 26 KC 38
  7. 7 CIN 19 KC 34
  8. 8 CIN 13 KC 31
  9. 9 CIN 31 KC 55
  10. 10 CIN 13 KC 45

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 20% of them, Chiefs 80%, counting the 2% 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
Bengals by 17+2.5%
Bengals by 9–166.0%
Bengals by 1–811.4%
Level after regulation2.0%
Chiefs by 1–824.1%
Chiefs by 9–1619.7%
Chiefs by 17+34.4%

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 +0.2 points to the Chiefs: the final margin was Bengals by 3, without the luck Bengals by 3.2. 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, 32 yds made · 96% expected
  • E. McPherson, 31 yds made · 97% expected
  • E. McPherson, 52 yds made · 72% expected
  • H. Butker, 44 yds made · 84% expected
  • E. McPherson, 31 yds made · 97% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bengals 4 for 30 yards, Chiefs 2 for 11 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
Q2 9:26 Defensive Offside on the Bengals (Khalid Kareem), 5 yards · pre-snap +2% KC +0.8 pts
Q2 0:13 Defensive Pass Interference on the Bengals (Eli Apple), 14 yards +2% KC +1.4 pts
Q3 11:13 Delay of Game on the Bengals, 6 yards · pre-snap +1% KC +0.9 pts
Q3 5:02 Defensive Pass Interference on the Chiefs (Rashad Fenton), 6 yards +1% CIN +1.0 pts
Q4 8:47 Defensive Offside on the Chiefs (Frank Clark), 5 yards · pre-snap +2% CIN +0.4 pts
Q4 7:36 False Start on the Bengals, 5 yards · pre-snap +4% KC +0.6 pts

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

When it happened

Chiefs’ chance of winning

As low as 0% and as high as 95%. 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 Chiefs were ahead in it, below while the Bengals were.
#WhenWhat happenedWin probability forNext drive
1 Q3 0:14 The Bengals’ two-point try was good3rd & 4th downs · 47% expected +8% CIN CIN: Turnover
2 Q4 15:00 The Chiefs were stopped on 3rd & 33rd & 4th downs · 57% expected +12% CIN KC: Punt
3 Q4 13:14 The Chiefs were stopped on 3rd & 63rd & 4th downs · 42% expected +10% CIN KC: Punt
4 Q4 9:35 The Bengals converted 3rd & 73rd & 4th downs · 34% expected +7% CIN CIN: Field goal
5 Q4 6:07 E. McPherson made 52-yard field goalKicks · 72% expected for him, 15 of 19 from 45+ before +10% CIN CIN: Field goal
6 Q4 3:29 The Chiefs converted 3rd & 13rd & 4th downs · 79% expected +11% KC KC: Field goal
7 Q4 0:39 The Chiefs were stopped on 3rd & 93rd & 4th downs · 28% expectedThe Chiefs fumbled and recovered it themselvesFumble bounces · loose balls are close to 50/50 +10% CIN KC: Field goal
8 Q4 0:03 H. Butker made 44-yard field goalKicks · 84% expected for him +12% KC KC: Turnover

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.

  • Larry Ogunjobi (CIN DT), out (IR) · 0.4 pts
  • Joe Bachie (CIN LB), out (IR) · 0.2 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 72% · Chiefs 28%

Final margin
Bengals by 3
Luck in points
0.2 for the Chiefs
Luck-adjusted margin
Bengals by 3.2
Replay with same day's form
Bengals 20% · Chiefs 80% 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 (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 Conference championships 2021 games · Bengals · Chiefs

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