Week 15 2023 · December 16, 2023
Vikings at Bengals, Week 15 2023: who deserved to win?
The Bengals beat the Vikings 27–24, but the Vikings played well enough to win it: they take 7 of 10 replays with the same day's form. Luck ran their way: 3rd & 4th downs alone were worth 2.1 points to the Bengals.
The Bengals won on an off day: their defense played far below its usual level. In a fresh game against the Vikings they would win 58% of the time; with this day’s form, 26%. The numbers
Before kickoff the Bengals were 59% favorites. The biggest swing (QOT, 5:31 left): the Bengals converted 3rd & 9, worth 45 points of win probability to the Bengals.
Final (OT)
 Minnesota Vikings | 24 |
|---|---|
 Cincinnati Bengals | 27 |
Replay with same day's form
Luck index +74 Bengals very lucky · −74 Vikings
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. Vikings win 7, Bengals win 3.
- 1 MIN 34 CIN 10
- 2 MIN 31 CIN 13
- 3 MIN 31 CIN 17
- 4 MIN 31 CIN 20
- 5 MIN 28 CIN 20
- 6 MIN 15 CIN 10
- 7 MIN 34 CIN 31
- 8 MIN 24 CIN 27
- 9 MIN 9 CIN 16
- 10 MIN 9 CIN 24
Three other ways to ask
Each answers a different question, so none of them replaces the replay above.
Before kickoff
The closing betting line, turned into a probability. What everyone knew before the game.
Same teams, fresh 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.
Only coin-flips re-rolled
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 defense played far below its usual level. In a fresh game against the Vikings they would win 58% of the time; with this day’s form, 26%.
Same teams, fresh game
Replay with same day's form
32 points apart for the Bengals: the gap is how differently this game went from what the two teams usually are.
| Unit | This game | Usual level | Better or worse than usual |
|---|---|---|---|
| Vikings offenseEPA per play gained | +0.26 | +0.09 | better by 0.16 |
| Vikings defenseEPA per play allowed | +0.21 | +0.07 | worse by 0.14 |
| Bengals offenseEPA per play gained | +0.21 | +0.13 | better by 0.08 |
| Bengals defenseEPA per play allowed | +0.26 | +0.11 | worse by 0.15 |
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
Vikings win 74% of them, Bengals 26%, 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 replays | Share of replays |
|---|---|
| Vikings by 17+ | 25.0% |
| Vikings by 9–16 | 21.6% |
| Vikings by 1–8 | 24.6% |
| Level after regulation | 3.0% |
| Bengals by 1–8 | 14.4% |
| Bengals by 9–16 | 7.6% |
| Bengals by 17+ | 3.8% |
Where the luck was
Take the luck out
The final margin was Bengals by 3. Remove the luck, one kind at a time, and it becomes Bengals by 1.8.
The kicks
How likely each kicker was to make that kick (his own record, the distance and the weather), and what happened.
- E. McPherson, 34 yds made · 95% expected
- G. Joseph, 39 yds made · 88% expected
- E. McPherson, 29 yds made · 98% expected
When it happened
Bengals’ chance of winning
As low as 7% and as high as 100%. Numbers mark the biggest luck moments, listed below.
| # | When | What happened | Win probability for | Next drive |
|---|---|---|---|---|
| 1 | Q2 4:14 | The Vikings were stopped on 3rd & 93rd & 4th downs · 32% expectedThe Vikings threw an interception-worthy pass, and it was pickedInterceptions · 49% expected to stay out of the defense's hands | +18% CIN | MIN: Turnover |
| 2 | Q2 0:31 | The Vikings were stopped on 3rd & 73rd & 4th downs · 37% expectedThe Vikings were intercepted on a well-placed throwInterceptions · 0% expected to stay out of the defense's hands | +21% CIN | MIN: Touchdown |
| 3 | Q2 0:11 | The Bengals were stopped on 3rd & 103rd & 4th downs · 28% expectedThe Bengals fumbled and recovered it themselvesFumble bounces · loose balls are close to 50/50 | +14% CIN | CIN: Turnover |
| 4 | Q4 11:19 | The Bengals converted 3rd & 213rd & 4th downs · 17% expected | +14% CIN | CIN: Touchdown |
| 5 | Q4 7:49 | The Bengals converted 4th & 13rd & 4th downs · 66% expected | +22% CIN | CIN: Touchdown |
| 6 | Q4 6:29 | Defensive Offside on the Bengals (Trey Hendrickson), 5 yards, wiping out the playPre-snap flags · 15 flags in 3502 snaps before, position avg 1 per 295 | +35% MIN | MIN: Touchdown |
| 7 | QOT 6:36 | The Vikings were stopped on 3rd & 13rd & 4th downs · 76% expected | +17% CIN | MIN: Turnover on downs |
| 8 | QOT 5:31 | The Bengals converted 3rd & 93rd & 4th downs · 30% expected | +45% CIN | CIN: 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.
- Joe Burrow (CIN QB), out (IR), replaced by j.browning · 4.3 pts
- Cam Taylor-Britt (CIN CB), out (IR) · 0.6 pts
- Kirk Cousins (MIN QB), out (IR), replaced by n.mullens · 3.7 pts
- Brian O'Neill (MIN T), out · 1.1 pts
- Jordan Hicks (MIN LB), out (IR) · 0.5 pts
- Alexander Mattison (MIN RB), out · 0.2 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
Vikings 30% · Bengals 70%
- Final margin
- Bengals by 3
- Luck in points
- 1.2 for the Bengals
- Luck-adjusted margin
- Bengals by 1.8
- Replay with same day's form
- Vikings 74% · Bengals 26% unchanged: why
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 15 2023 games · 
Vikings · 
Bengals
More from Week 15 2023
- Chargers at Raiders LV 63–21 · replay 87% for the winner
- Steelers at Colts IND 30–13 · replay 96% for the winner
- Broncos at Lions DET 42–17 · replay 88% for the winner
- Falcons at Panthers CAR 9–7 · replay 56% for the winner
- Bears at Browns CLE 20–17 · replay 88% for the winner
- Texans at Titans HOU 19–16 · replay 84% for the winner
- Chiefs at Patriots KC 27–17 · replay 92% for the winner
- Giants at Saints NO 24–6 · replay 98% for the winner
- Jets at Dolphins MIA 30–0 · replay 100% for the winner
- Buccaneers at Packers TB 34–20 · replay 75% for the winner
- 49ers at Cardinals SF 45–29 · replay 99% for the winner
- Commanders at Rams LA 28–20 · replay 75% for the winner
- Cowboys at Bills BUF 31–10 · replay 95% for the winner
- Ravens at Jaguars BAL 23–7 · replay 96% for the winner
- Eagles at Seahawks SEA 20–17 · replay 18% for the winner