luckadjusted
NFL Week 9 · 2026

Week 2 2024 · September 15, 2024

Bengals at Chiefs, Week 2 2024: who deserved to win?

The Chiefs beat the Bengals 26–25, but the replays call it close to a coin flip: with the way both teams played, the Chiefs win 6 of 10. Luck ran their way: kicks alone were worth 16 points of win probability to the Chiefs.

Before kickoff the Chiefs were 68% favorites. The biggest swing (Q4, 0:53 left): Illegal Use of Hands on the Chiefs, 10 yards, wiping out the play, worth 47 points of win probability to the Bengals.

Final

Cincinnati Bengals 25
Kansas City Chiefs 26

September 15, 2024 · GEHA Field at Arrowhead Stadium · Closing line: Chiefs −6.5

Luck index +40 Chiefs lucky · −40 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. Bengals win 4, Chiefs win 6.

  1. 1 CIN 26 KC 7
  2. 2 CIN 20 KC 10
  3. 3 CIN 20 KC 14
  4. 4 CIN 20 KC 17
  5. 5 CIN 10 KC 12
  6. 6 CIN 20 KC 24
  7. 7 CIN 24 KC 31
  8. 8 CIN 6 KC 17
  9. 9 CIN 7 KC 24
  10. 10 CIN 3 KC 27

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 40% of them, Chiefs 60%, counting the 3% still level after regulation as half each. The line is what actually happened: Chiefs by 1.

Show as a table
Final margin in the replaysShare of replays
Bengals by 17+6.1%
Bengals by 9–1612.9%
Bengals by 1–819.9%
Level after regulation2.7%
Chiefs by 1–829.0%
Chiefs by 9–1615.7%
Chiefs by 17+13.8%

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 +0.8 points to the Bengals: the final margin was Chiefs by 1, without the luck Chiefs by 1.8. 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, 22 yds made · 99% expected
  • H. Butker, 19 yds made · 100% expected
  • E. McPherson, 33 yds made · 95% expected
  • E. McPherson, 48 yds made · 77% expected
  • E. McPherson, 53 yds made · 70% expected
  • H. Butker, 51 yds made · 73% expected
  • Extra point missed · 94% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bengals 8 for 79 yards, Chiefs 4 for 44 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 2:07 False Start on the Bengals, 5 yards · pre-snap +2% KC +0.6 pts
Q2 5:21 Defensive Pass Interference on the Chiefs (Trent McDuffie), 14 yards +4% CIN +1.3 pts
Q2 1:50 Offensive Pass Interference on the Bengals (Trenton Irwin), 10 yards +4% KC +1.3 pts
Q2 0:14 Delay of Game on the Bengals, 0 yards · pre-snap 0% KC 0.0 pts
Q3 13:52 Defensive Holding on the Bengals (Jay Tufele), 5 yards +3% KC +0.9 pts
Q3 1:06 Illegal Contact on the Bengals (Daijahn Anthony), 5 yards, wiping out the play +23% KC +4.7 pts
Q3 0:59 Offensive Holding on the Chiefs, 10 yards, wiping out the play +8% CIN +1.6 pts
Q4 11:42 Offensive Holding on the Bengals, 10 yards +7% KC +1.2 pts
Q4 10:43 Unsportsmanlike Conduct on the Bengals (Ja'Marr Chase), 15 yards +7% KC +1.4 pts
Q4 8:14 Offensive Holding on the Chiefs, 10 yards, wiping out the play +31% CIN +4.6 pts
Q4 0:53 Illegal Use of Hands on the Chiefs, 10 yards, wiping out the play +47% CIN +2.3 pts
Q4 0:48 Defensive Pass Interference on the Bengals (Daijahn Anthony), 29 yards +29% KC +1.9 pts

Bengals penalties, every game · Chiefs penalties, every game · All teams, 2024

When it happened

Chiefs’ chance of winning

As low as 25% 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 Chiefs were ahead in it, below while the Bengals were.
#WhenWhat happenedWin probability forNext drive
1 Q3 2:22 The Bengals converted 4th & 33rd & 4th downs · 45% expected +12% CIN CIN: Touchdown
2 Q3 1:06 Illegal Contact on the Bengals (Daijahn Anthony), 5 yards, wiping out the playJudgment calls · 0 flags in 17 snaps before, position avg 1 per 530 +23% KC KC: Turnover
3 Q4 14:52 The Bengals fumbled and the Chiefs recoveredFumble bounces · loose balls are close to 50/50Return touchdown by the ChiefsSpecial teams +45% KC CIN: Field goal
4 Q4 8:14 Offensive Holding on the Chiefs, 10 yards, wiping out the playJudgment calls +31% CIN CIN: Punt
5 Q4 3:27 The Bengals were stopped on 3rd & 63rd & 4th downs · 38% expected +12% KC CIN: Punt
6 Q4 0:53 Illegal Use of Hands on the Chiefs, 10 yards, wiping out the playJudgment calls +47% CIN –
7 Q4 0:48 Defensive Pass Interference on the Bengals (Daijahn Anthony), 29 yardsJudgment calls · 0 flags in 17 snaps before, position avg 1 per 530 +29% KC KC: Field goal
8 Q4 0:03 H. Butker made a 51-yard field goalKicks · 73% expected for him, 43 of 56 from 45+ before +27% KC –

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.

  • Charles Omenihu (KC DE), out (IR) · 0.2 pts
  • Tee Higgins (CIN WR), out · 1.0 pts
  • Brad Robbins (CIN P), out (IR) · 0.1 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 35% · Chiefs 65%

Final margin
Chiefs by 1
Luck in points
0.8 for the Bengals
Luck-adjusted margin
Chiefs by 1.8
Replay with same day's form
Bengals 40% · Chiefs 60% 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 2 2024 games · Bengals · Chiefs

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