luckadjusted

Week 2 2024 · September 15, 2024

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

The Chiefs beat the Bengals 26–25 and were the better team on the day: replayed with the same form, they win 7 of 10. The Bengals had the bounces: judgment calls alone were worth 17 points of win probability to the Bengals.

Before kickoff the Chiefs were 68% favorites. The game turned on a luck play (Q4, 0:48 left): Defensive Pass Interference on the Bengals (Daijahn Anthony), 29 yards, worth 29 points of win probability to the Chiefs. The biggest single swing (Q4, 14:52 left): Return touchdown by the Chiefs.

Final

Cincinnati Bengals 25
Kansas City Chiefs 26

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

Luck index +25 Chiefs lucky · −25 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 3, Chiefs win 7.

  1. 1 CIN 37 KC 21
  2. 2 CIN 26 KC 19
  3. 3 CIN 13 KC 10
  4. 4 CIN 10 KC 12
  5. 5 CIN 13 KC 17
  6. 6 CIN 17 KC 26
  7. 7 CIN 7 KC 19
  8. 8 CIN 7 KC 23
  9. 9 CIN 17 KC 37
  10. 10 CIN 10 KC 37

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 25% of them, Chiefs 75%, counting the 4% 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+2.6%
Bengals by 9–167.1%
Bengals by 1–814.7%
Level after regulation4.0%
Chiefs by 1–824.5%
Chiefs by 9–1621.6%
Chiefs by 17+25.5%

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 +2.2 points to the Chiefs: the final margin was Chiefs by 1, without the luck Bengals by 1.2. 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, 22 yds made · 100% expected
  • H. Butker, 19 yds made · 100% expected
  • E. McPherson, 33 yds made · 95% expected
  • E. McPherson, 48 yds made · 78% expected
  • E. McPherson, 53 yds made · 70% expected
  • H. Butker, 51 yds made · 74% expected
  • Extra point missed · 93% 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 toward luck, pre-snap fouls mostly don’t. 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 +1.7 pts
Q2 1:50 Offensive Pass Interference on the Bengals (Trenton Irwin), 10 yards +4% KC +1.7 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 +1.0 pts
Q3 1:06 Illegal Contact on the Bengals (Daijahn Anthony), 5 yards, wiping out the play +23% KC +4.8 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 Q1 12:14 The Bengals converted 4th & 33rd & 4th downs · 50% expected +19% CIN CIN: Field goal
2 Q3 2:22 The Bengals converted 4th & 33rd & 4th downs · 42% expected +16% CIN CIN: Touchdown
3 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
4 Q4 14:52 The Bengals were stopped on 3rd & 103rd & 4th downs · 27% expectedThe Bengals fumbled and the Chiefs recoveredFumble bounces · loose balls are close to 50/50Return touchdown by the ChiefsSpecial teams +74% KC CIN: Field goal
5 Q4 8:14 Offensive Holding on the Chiefs, 10 yards, wiping out the playJudgment calls +31% CIN 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 The game turned hereDefensive 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 51-yard field goalKicks · 74% expected for him, 43 of 56 from 45+ before +37% 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 50% · Chiefs 50%

Final margin
Chiefs by 1
Luck in points
2.2 for the Chiefs
Luck-adjusted margin
Bengals by 1.2
Replay with same day's form
Bengals 25% · Chiefs 75% 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; injuries from snap counts and injury reports.

Methodology and validation · All Week 2 2024 games · Bengals · Chiefs

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