luckadjusted
NFL Week 9 · 2026

Week 5 2023 · October 8, 2023

Bengals at Cardinals, Week 5 2023: who deserved to win?

The Bengals beat the Cardinals 34–20, and the replays lean their way: with the same day's form, they win 6 of 10.

Before kickoff the Bengals were 59% favorites. The biggest swing (Q2, 1:30 left): Return touchdown by the Bengals, worth 27 points of win probability to the Bengals.

Final

Cincinnati Bengals 34
Arizona Cardinals 20

October 8, 2023 · State Farm Stadium · Closing line: Bengals −3

Luck index +36 Bengals lucky · −36 Cardinals

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 6, Cardinals win 4.

  1. 1 CIN 35 ARI 10
  2. 2 CIN 24 ARI 6
  3. 3 CIN 30 ARI 17
  4. 4 CIN 16 ARI 7
  5. 5 CIN 16 ARI 10
  6. 6 CIN 23 ARI 20
  7. 7 CIN 32 ARI 35
  8. 8 CIN 17 ARI 24
  9. 9 CIN 15 ARI 26
  10. 10 CIN 15 ARI 35

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 64% of them, Cardinals 36%, counting the 2% still level after regulation as half each. The line is what actually happened: Bengals by 14.

Show as a table
Final margin in the replaysShare of replays
Bengals by 17+19.3%
Bengals by 9–1619.4%
Bengals by 1–823.6%
Level after regulation1.6%
Cardinals by 1–816.8%
Cardinals by 9–1611.8%
Cardinals by 17+7.6%

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 +1.1 points to the Bengals: the final margin was Bengals by 14, without the luck Bengals by 12.9. 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, 40 yds made · 90% expected
  • E. McPherson, 40 yds made · 90% expected
  • Extra point missed · 94% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bengals 4 for 40 yards, Cardinals 2 for 16 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 13:28 Player Out of Bounds on Kick on the Cardinals (Joey Blount), 5 yards +1% CIN +0.3 pts
Q2 10:55 Unnecessary Roughness on the Bengals (Devin Harper), 15 yards +3% ARI +1.1 pts
Q2 0:01 Delay of Game on the Bengals, 5 yards · pre-snap 0% ARI 0.0 pts
Q4 10:26 Offensive Holding on the Bengals, 10 yards +4% ARI +1.4 pts
Q4 8:38 Defensive Pass Interference on the Cardinals (Kyzir White), 11 yards +3% CIN +1.1 pts
Q4 6:58 Illegal Use of Hands on the Bengals, 10 yards, wiping out the play +3% ARI +3.3 pts

Bengals penalties, every game · Cardinals penalties, every game · All teams, 2023

When it happened

Cardinals’ chance of winning

As low as 0% and as high as 69%. 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 Cardinals were ahead in it, below while the Bengals were.
#WhenWhat happenedWin probability forNext drive
1 Q2 12:30 The Cardinals converted 3rd & 93rd & 4th downs · 29% expected +6% ARI ARI: Touchdown
2 Q2 7:19 The Cardinals got away with an interception-worthy throwInterceptions · defenses catch 50% of interception-worthy throws +6% ARI ARI: Punt
3 Q2 3:16 The Bengals converted 3rd & 83rd & 4th downs · 35% expected +8% CIN CIN: Turnover on downs
4 Q2 1:37 The Bengals were stopped on 4th & 13rd & 4th downs · 71% expected +11% ARI CIN: Opp touchdown
5 Q2 1:30 The Cardinals threw an interception-worthy pass, and it was pickedInterceptions · defenses catch 50% of interception-worthy throwsReturn touchdown by the BengalsSpecial teams +27% CIN ARI: Punt
6 Q2 0:56 The Bengals got away with an interception-worthy throwInterceptions · defenses catch 49% of interception-worthy throws +7% CIN CIN: Turnover on downs
7 Q3 2:28 The Cardinals were stopped on 3rd & 73rd & 4th downs · 33% expected +5% CIN ARI: Turnover on downs
8 Q3 1:49 The Cardinals were stopped on 4th & 13rd & 4th downs · 74% expected +10% CIN ARI: 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.

  • Budda Baker (ARI SS), out (IR) · 0.9 pts
  • Jonathan Ledbetter (ARI DE), out · 0.4 pts
  • Tee Higgins (CIN WR), out · 1.1 pts
  • Chidobe Awuzie (CIN CB), out · 0.5 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 99% · Cardinals 1%

Final margin
Bengals by 14
Luck in points
1.1 for the Bengals
Luck-adjusted margin
Bengals by 12.9
Replay with same day's form
Bengals 64% · Cardinals 36% 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 5 2023 games · Bengals · Cardinals

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