luckadjusted
NFL Week 9 · 2026

Week 4 2023 · October 1, 2023

Bengals at Titans, Week 4 2023: who deserved to win?

The Titans beat the Bengals 27–3, but the replays call it close to a coin flip: with the way both teams played, the Titans win 5 of 10.

Before kickoff the Bengals were 57% favorites. The biggest swing (Q2, 7:56 left): the Titans converted 3rd & 7, worth 9 points of win probability to the Titans.

Final

Cincinnati Bengals 3
Tennessee Titans 27

October 1, 2023 · Nissan Stadium · Closing line: Bengals −2.5

Luck index +55 Titans lucky · −55 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 5, Titans win 5.

  1. 1 CIN 27 TEN 7
  2. 2 CIN 16 TEN 3
  3. 3 CIN 16 TEN 7
  4. 4 CIN 31 TEN 27
  5. 5 CIN 21 TEN 19
  6. 6 CIN 16 TEN 17
  7. 7 CIN 19 TEN 23
  8. 8 CIN 23 TEN 31
  9. 9 CIN 17 TEN 30
  10. 10 CIN 3 TEN 23

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 55% of them, Titans 45%, counting the 7% still level after regulation as half each. The line is what actually happened: Titans by 24.

Show as a table
Final margin in the replaysShare of replays
Bengals by 17+10.2%
Bengals by 9–1616.1%
Bengals by 1–822.7%
Level after regulation7.0%
Titans by 1–822.4%
Titans by 9–1613.8%
Titans by 17+7.9%

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 +9.9 points to the Titans: the final margin was Titans by 24, without the luck Titans by 14.1. 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, 21 yds made · 99% expected
  • N. Folk, 53 yds made · 70% expected
  • N. Folk, 35 yds made · 95% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bengals 5 for 40 yards, Titans 5 for 27 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 0:43 Defensive Pass Interference on the Titans (Roger McCreary), 2 yards +3% CIN +0.9 pts
Q1 0:01 Defensive Offside on the Titans (Arden Key), 5 yards · pre-snap +1% CIN +0.2 pts
Q2 13:35 Illegal Block Above the Waist on the Bengals, 10 yards 0% TEN +0.9 pts
Q2 12:47 False Start on the Titans (Nick Westbrook-Ikhine), 5 yards · pre-snap +1% CIN +0.6 pts
Q2 0:29 Defensive Holding on the Bengals (Germaine Pratt), 5 yards, wiping out the play +1% TEN +1.4 pts
Q3 12:54 Offensive Holding on the Titans, 10 yards, wiping out the play +1% CIN +2.1 pts
Q3 10:52 Unnecessary Roughness on the Bengals (Daxton Hill), 15 yards +1% TEN +1.7 pts
Q3 9:34 Defensive Holding on the Bengals (Chidobe Awuzie), 5 yards 0% TEN +0.9 pts
Q3 5:46 Neutral Zone Infraction on the Bengals (Trey Hendrickson), 5 yards · pre-snap 0% TEN +0.4 pts
Q3 0:36 Ineligible Downfield Pass on the Titans, 5 yards, wiping out the play 0% CIN +2.9 pts

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

When it happened

Titans’ chance of winning

As low as 41% 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 Titans were ahead in it, below while the Bengals were.
#WhenWhat happenedWin probability forNext drive
1 Q1 9:59 The Bengals got away with an interception-worthy throwInterceptions · defenses catch 49% of interception-worthy throws +5% CIN CIN: Field goal
2 Q1 6:00 The Titans were stopped on 3rd & 23rd & 4th downs · 61% expected +4% CIN TEN: Field goal
3 Q1 5:55 The Titans converted 4th & 23rd & 4th downs · 62% expected +8% TEN TEN: Field goal
4 Q1 2:05 The Titans were stopped on 3rd & 33rd & 4th downs · 53% expected +5% CIN TEN: Field goal
5 Q2 14:12 The Bengals were stopped on 3rd & 73rd & 4th downs · 35% expected +4% TEN CIN: Punt
6 Q2 9:39 The Bengals were stopped on 3rd & 43rd & 4th downs · 47% expected +5% TEN CIN: Punt
7 Q2 7:56 The Titans converted 3rd & 73rd & 4th downs · 35% expected +9% TEN TEN: Touchdown
8 Q2 5:34 The Titans fumbled and recovered it themselvesFumble bounces · loose balls are close to 50/50 +5% TEN TEN: Touchdown

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.

  • Nicholas Petit-Frere (TEN T), out (IR) · 0.7 pts
  • Elijah Molden (TEN CB), out · 0.4 pts
  • Treylon Burks (TEN WR), out · 0.3 pts
  • 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

Bengals 2% · Titans 98%

Final margin
Titans by 24
Luck in points
9.9 for the Titans
Luck-adjusted margin
Titans by 14.1
Replay with same day's form
Bengals 55% · Titans 45% 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 4 2023 games · Bengals · Titans

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