luckadjusted

Week 3 2023 · September 25, 2023

Rams at Bengals, Week 3 2023: who deserved to win?

The Bengals beat the Rams 19–16, but the Rams played well enough to win it: they take 7 of 10 replays with the same day's form. Luck ran their way: kicks alone were worth 15 points of win probability to the Bengals.

The Bengals won on an off day: their offense played far below its usual level. In a fresh game against the Rams they would win 62% of the time; with this day’s form, 31%. The numbers

Before kickoff the Bengals were 59% favorites. The biggest swing (Q2, 2:56 left): Offensive Pass Interference on the Bengals (Tee Higgins), 10 yards, wiping out the play, worth 20 points of win probability to the Rams.

Final

Los Angeles Rams 16
Cincinnati Bengals 19

September 25, 2023 · Paycor Stadium · Closing line: Bengals −3

Luck index +69 Bengals very lucky · −69 Rams

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. Rams win 7, Bengals win 3.

  1. 1 LA 44 CIN 17
  2. 2 LA 40 CIN 20
  3. 3 LA 48 CIN 33
  4. 4 LA 33 CIN 21
  5. 5 LA 29 CIN 20
  6. 6 LA 22 CIN 17
  7. 7 LA 20 CIN 18
  8. 8 LA 24 CIN 27
  9. 9 LA 24 CIN 33
  10. 10 LA 21 CIN 41

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.

The Bengals won on an off day

Their offense played far below its usual level. In a fresh game against the Rams they would win 62% of the time; with this day’s form, 31%.

31 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
Rams offenseEPA per play gained −0.09 +0.07 worse by 0.17
Rams defenseEPA per play allowed −0.02 +0.10 better by 0.13
Bengals offenseEPA per play gained −0.02 +0.13 worse by 0.15
Bengals defenseEPA per play allowed −0.09 +0.07 better by 0.17

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

Rams win 69% of them, Bengals 31%, counting the 3% 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
Rams by 17+24.5%
Rams by 9–1620.0%
Rams by 1–823.7%
Level after regulation3.5%
Bengals by 1–814.3%
Bengals by 9–169.3%
Bengals by 17+4.7%

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 +2.1 points to the Rams: the final margin was Bengals by 3, without the luck Bengals by 5.1. 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.

  • E. McPherson, 56 yds missed · 64% expected
  • B. Maher, 30 yds made · 95% expected
  • E. McPherson, 49 yds made · 75% expected
  • B. Maher, 23 yds made · 98% expected
  • E. McPherson, 53 yds made · 68% expected
  • B. Maher, 42 yds made · 83% expected
  • E. McPherson, 48 yds made · 77% expected
  • E. McPherson, 54 yds made · 67% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Rams 4 for 28 yards, Bengals 7 for 49 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 7:23 False Start on the Bengals (Joe Mixon), 5 yards · pre-snap +3% LA +1.0 pts
Q1 6:59 False Start on the Bengals, 5 yards · pre-snap +4% LA +1.0 pts
Q2 14:16 Defensive Holding on the Rams, 5 yards +1% CIN +0.7 pts
Q2 13:23 False Start on the Bengals (Tyler Boyd), 5 yards · pre-snap +6% LA +1.2 pts
Q2 7:11 Illegal Touch Kick on the Bengals, 5 yards +1% LA +0.5 pts
Q2 2:56 Offensive Pass Interference on the Bengals (Tee Higgins), 10 yards, wiping out the play +20% LA +3.8 pts
Q3 14:21 False Start on the Rams, 5 yards · pre-snap +2% CIN +0.7 pts
Q3 12:33 Face Mask on the Bengals (Sam Hubbard), 14 yards, wiping out the play +6% LA +3.4 pts
Q3 4:52 Defensive Pass Interference on the Rams (Quentin Lake), 3 yards +2% CIN +1.0 pts
Q3 1:54 Face Mask on the Rams, 15 yards, wiping out the play +4% CIN +3.1 pts
Q4 5:14 Delay of Game on the Bengals, 5 yards · pre-snap 0% LA +0.3 pts

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

When it happened

Bengals’ chance of winning

As low as 34% 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 Bengals were ahead in it, below while the Rams were.
#WhenWhat happenedWin probability forNext drive
1 Q1 11:31 E. McPherson missed 56-yard field goalKicks · 64% expected for him, 24 of 31 from 45+ before +8% LA CIN: Punt
2 Q2 13:00 E. McPherson made 49-yard field goalKicks · 75% expected for him, 24 of 32 from 45+ before +9% CIN CIN: Punt
3 Q2 2:56 Offensive Pass Interference on the Bengals (Tee Higgins), 10 yards, wiping out the playJudgment calls · 8 flags in 2785 snaps before, position avg 1 per 420 +20% LA LA: Punt
4 Q2 0:03 E. McPherson made 53-yard field goalKicks · 68% expected for him, 25 of 33 from 45+ before +14% CIN CIN: Touchdown
5 Q3 11:24 The Rams were stopped on 3rd & 63rd & 4th downs · 38% expected +9% CIN LA: Field goal
6 Q3 10:42 B. Maher made 42-yard field goalKicks · 83% expected for him +9% LA LA: Turnover
7 Q3 8:29 The Bengals converted 3rd & 103rd & 4th downs · 27% expected +8% CIN CIN: Touchdown
8 Q3 5:01 The Rams were intercepted on a well-placed throwInterceptions · 0% expected to stay out of the defense's hands +11% CIN LA: Punt

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.

  • Jackson Carman (CIN G), out · 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

Rams 28% · Bengals 72%

Final margin
Bengals by 3
Luck in points
2.1 for the Rams
Luck-adjusted margin
Bengals by 5.1
Replay with same day's form
Rams 69% · Bengals 31% 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 3 2023 games · Rams · Bengals

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