luckadjusted
NFL Week 9 · 2026

Week 5 2019 · October 6, 2019

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

Cardinals at Bengals, Week 5 2019: who deserved to win?

The Cardinals beat the Bengals 26–23, and the replays lean their way: with the same day's form, they win 8 of 10.

An off day for the Bengals: their defense played far below its usual level. In a fresh game against the Cardinals they would win 53% of the time; with this day’s form, 23%. The numbers

Before kickoff the Bengals were 59% favorites. The biggest swing (Q2, 7:55 left): the Cardinals converted 3rd & 10, worth 9 points of win probability to the Cardinals.

Final

Arizona Cardinals 26
Cincinnati Bengals 23

October 6, 2019 · Paul Brown Stadium · Closing line: Bengals −3

Luck index +23 Cardinals about even · −23 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. Cardinals win 8, Bengals win 2.

  1. 1 ARI 44 CIN 17
  2. 2 ARI 51 CIN 31
  3. 3 ARI 34 CIN 18
  4. 4 ARI 33 CIN 20
  5. 5 ARI 20 CIN 10
  6. 6 ARI 30 CIN 23
  7. 7 ARI 16 CIN 13
  8. 8 ARI 19 CIN 17
  9. 9 ARI 20 CIN 23
  10. 10 ARI 14 CIN 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.

An off day for the Bengals

Their defense played far below its usual level. In a fresh game against the Cardinals they would win 53% of the time; with this day’s form, 23%.

30 points apart for the Bengals: the gap is how differently this game went from what the two teams usually are.

UnitThis gameUsual levelBetter or worse than usual
Cardinals offenseEPA per play gained +0.28 +0.00 better by 0.28
Cardinals defenseEPA per play allowed +0.02 +0.15 better by 0.13
Bengals offenseEPA per play gained +0.02 +0.07 worse by 0.05
Bengals defenseEPA per play allowed +0.28 +0.18 worse by 0.10

EPA (expected points added) per play on competitive snaps, turnovers left out because they are valued as luck. Usual level: the team’s earlier games this season plus half of last season, pulled toward the league average. One team’s defense and the other team’s offense are the same snaps, so one game can’t fully say whose day it was; it shows how far this one was from both teams’ norms.

How 4,000 replays ended

Cardinals win 77% of them, Bengals 23%, counting the 3% still level after regulation as half each. The line is what actually happened: Cardinals by 3.

Show as a table
Final margin in the replaysShare of replays
Cardinals by 17+27.9%
Cardinals by 9–1621.1%
Cardinals by 1–827.5%
Level after regulation2.8%
Bengals by 1–812.0%
Bengals by 9–166.4%
Bengals by 17+2.3%

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 +6.1 points to the Bengals: the final margin was Cardinals by 3, without the luck Cardinals by 9.1. 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.

  • R. Bullock, 23 yds made · 98% expected
  • Z. Gonzalez, 37 yds missed · 91% expected
  • Z. Gonzalez, 23 yds made · 98% expected
  • R. Bullock, 48 yds made · 72% expected
  • Z. Gonzalez, 20 yds made · 98% expected
  • R. Bullock, 23 yds made · 98% expected
  • Z. Gonzalez, 22 yds made · 98% expected
  • Z. Gonzalez, 31 yds made · 95% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Cardinals 12 for 96 yards, Bengals 7 for 60 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 7:53 Ineligible Downfield Pass on the Cardinals, 5 yards +2% CIN +0.7 pts
Q1 7:14 Face Mask on the Bengals (Dre Kirkpatrick), 15 yards +5% ARI +1.8 pts
Q1 5:33 False Start on the Cardinals, 5 yards · pre-snap +2% CIN +0.5 pts
Q1 2:27 Offensive Holding on the Cardinals, 10 yards +3% CIN +0.9 pts
Q2 6:44 Roughing the Passer on the Bengals (Geno Atkins), 10 yards +4% ARI +1.3 pts
Q2 5:01 Unnecessary Roughness on the Cardinals (Deionte Thompson), 15 yards +5% CIN +1.8 pts
Q2 3:27 Illegal Block Above the Waist on the Cardinals, 10 yards, wiping out the play +8% CIN +1.8 pts
Q2 0:14 Defensive Offside on the Bengals (Geno Atkins), 2 yards · pre-snap +1% ARI +0.4 pts
Q3 13:03 Illegal Use of Hands on the Cardinals, 5 yards +1% CIN +0.3 pts
Q3 9:52 False Start on the Bengals, 5 yards · pre-snap +3% ARI +0.7 pts
Q3 4:55 False Start on the Cardinals (Rodney Gunter), 5 yards · pre-snap +2% CIN +1.1 pts
Q3 3:28 Defensive Pass Interference on the Cardinals (Deionte Thompson), 6 yards +4% CIN +1.3 pts
Q3 3:24 Illegal Use of Hands on the Bengals, 10 yards, wiping out the play +8% ARI +2.0 pts
Q4 15:00 Illegal Block Above the Waist on the Cardinals (Larry Fitzgerald), 10 yards +1% ARI +0.8 pts
Q4 13:25 Illegal Double-Team Block on the Bengals (Andrew Brown), 8 yards +1% ARI +0.6 pts
Q4 12:16 Illegal Block Above the Waist on the Bengals, 10 yards, wiping out the play +4% ARI +1.6 pts
Q4 10:35 Illegal Block Above the Waist on the Cardinals, 10 yards +2% CIN +0.9 pts
Q4 9:39 Illegal Block Above the Waist on the Cardinals, 10 yards +3% CIN +0.9 pts
Q4 4:08 Delay of Game on the Cardinals, 5 yards · pre-snap +1% CIN +0.6 pts

Cardinals penalties, every game · Bengals penalties, every game · All teams, 2019

When it happened

Bengals’ chance of winning

As low as 0% and as high as 74%. 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 Cardinals were.
#WhenWhat happenedWin probability forNext drive
1 Q1 3:46 The Cardinals converted 4th & 23rd & 4th downs · 56% expected +6% ARI ARI: Touchdown
2 Q2 13:04 The Cardinals were stopped on 3rd & 63rd & 4th downs · 41% expected +6% CIN ARI: Missed field goal
3 Q2 13:00 Z. Gonzalez missed a 37-yard field goalKicks · 91% expected for him +7% CIN ARI: Field goal
4 Q2 7:55 The Cardinals converted 3rd & 103rd & 4th downs · 30% expected +9% ARI ARI: Field goal
5 Q2 3:27 Illegal Block Above the Waist on the Cardinals, 10 yards, wiping out the playJudgment calls +8% CIN CIN: Field goal
6 Q3 14:18 The Bengals converted 3rd & 103rd & 4th downs · 30% expected +6% CIN CIN: Field goal
7 Q3 3:24 Illegal Use of Hands on the Bengals, 10 yards, wiping out the playJudgment calls +8% ARI ARI: Field goal
8 Q3 1:05 The Cardinals converted 3rd & 73rd & 4th downs · 38% expected +6% ARI ARI: 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.

  • Cordy Glenn (CIN T), out · 0.9 pts
  • John Ross (CIN WR), out (IR) · 0.4 pts
  • Christian Kirk (ARI WR), out · 1.0 pts
  • Zach Allen (ARI DE), out · 0.7 pts
  • Damiere Byrd (ARI WR), out · 0.7 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

Cardinals 96% · Bengals 4%

Final margin
Cardinals by 3
Luck in points
6.1 for the Bengals
Luck-adjusted margin
Cardinals by 9.1
Replay with same day's form
Cardinals 77% · Bengals 23% 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 5 2019 games · Cardinals · Bengals

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