luckadjusted

Week 1 2024 · September 8, 2024

Patriots at Bengals, Week 1 2024: who deserved to win?

The Patriots beat the Bengals 16–10, but it was a coin flip: replayed with the way both teams played, the Patriots win 5 of 10. Luck ran their way: drops alone were worth 13 points of win probability to the Patriots.

Before kickoff the Bengals were 72% favorites. The biggest swing (Q2, 5:19 left): the Bengals were stopped on 3rd & 11, worth 10 points of win probability to the Patriots.

Final

New England Patriots 16
Cincinnati Bengals 10

September 8, 2024 · Paycor Stadium · Closing line: Bengals −8

Luck index +53 Patriots lucky · −53 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. Patriots win 5, Bengals win 5.

  1. 1 NE 24 CIN 7
  2. 2 NE 29 CIN 17
  3. 3 NE 13 CIN 5
  4. 4 NE 24 CIN 20
  5. 5 NE 16 CIN 14
  6. 6 NE 14 CIN 16
  7. 7 NE 13 CIN 17
  8. 8 NE 9 CIN 17
  9. 9 NE 10 CIN 23
  10. 10 NE 6 CIN 24

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

Patriots win 47% of them, Bengals 53%, counting the 7% still level after regulation as half each. The line is what actually happened: Patriots by 6.

Show as a table
Final margin in the replaysShare of replays
Patriots by 17+6.1%
Patriots by 9–1615.5%
Patriots by 1–823.1%
Level after regulation7.3%
Bengals by 1–823.5%
Bengals by 9–1616.0%
Bengals by 17+8.4%

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 +8.5 points to the Patriots: the final margin was Patriots by 6, without the luck Bengals by 2.5. 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.

  • J. Slye, 32 yds made · 95% expected
  • J. Slye, 35 yds made · 92% expected
  • J. Slye, 37 yds made · 91% expected
  • E. McPherson, 51 yds made · 74% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Patriots 5 for 40 yards, Bengals 2 for 10 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 15:00 Illegal Formation on the Patriots, 5 yards · pre-snap +1% CIN +0.5 pts
Q1 2:38 False Start on the Patriots, 5 yards · pre-snap +2% CIN +0.9 pts
Q2 9:04 Defensive Offside on the Patriots (Joshua Uche), 5 yards · pre-snap +1% CIN +0.5 pts
Q2 2:01 Defensive Offside on the Bengals, 5 yards · pre-snap 0% NE +0.7 pts
Q3 5:37 Defensive Pass Interference on the Patriots (Marco Wilson), 20 yards +4% CIN +1.3 pts
Q4 3:14 Delay of Game on the Patriots, 5 yards · pre-snap +2% CIN +0.5 pts
Q4 2:26 Illegal Substitution on the Bengals, 5 yards · pre-snap +3% NE +0.5 pts

Patriots penalties, every game · Bengals penalties, every game · All teams, 2024

When it happened

Bengals’ chance of winning

As low as 0% and as high as 57%. 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 Patriots were.
#WhenWhat happenedWin probability forNext drive
1 Q1 14:20 The Bengals fumbled and recovered it themselvesFumble bounces · loose balls are close to 50/50 +6% CIN CIN: Punt
2 Q1 4:34 The Patriots converted 3rd & 83rd & 4th downs · 28% expected +8% NE NE: Touchdown
3 Q2 15:00 The Patriots converted 3rd & 33rd & 4th downs · 40% expected +7% NE NE: Touchdown
4 Q2 13:27 The Bengals were stopped on 3rd & 33rd & 4th downs · 51% expected +5% NE CIN: Punt
5 Q2 9:51 Z. Moss dropped a catchable passDrops · 5 drops on 47 catchable balls before this +5% NE CIN: Turnover
6 Q2 5:19 The Bengals were stopped on 3rd & 113rd & 4th downs · 25% expectedThe Bengals fumbled and the Patriots recoveredFumble bounces · loose balls are close to 50/50 +10% NE CIN: Turnover on downs
7 Q3 7:12 The Bengals were stopped on 3rd & 23rd & 4th downs · 60% expectedT. Hudson dropped a catchable passDrops · 1 drops on 58 catchable balls before this +7% NE CIN: Turnover on downs
8 Q4 7:05 The Bengals were stopped on 3rd & 53rd & 4th downs · 40% expected +5% NE 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.

  • Tee Higgins (CIN WR), out · 1.0 pts
  • Brad Robbins (CIN P), out (IR) · 0.1 pts
  • Sidy Sow (NE T), out · 0.4 pts
  • Cole Strange (NE G), out (IR) · 0.3 pts
  • Christian Barmore (NE DT), out (IR) · 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

Patriots 34% · Bengals 66%

Final margin
Patriots by 6
Luck in points
8.5 for the Patriots
Luck-adjusted margin
Bengals by 2.5
Replay with same day's form
Patriots 47% · Bengals 53% 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 1 2024 games · Patriots · Bengals

More from Week 1 2024