luckadjusted
NFL Week 9 · 2026

Week 16 2023 · December 24, 2023

Patriots at Broncos, Week 16 2023: who deserved to win?

The Patriots beat the Broncos 26–23, and the replays lean their way: with the same day's form, they win 7 of 10.

An off day for the Broncos: they played far below what the matchup promised. In a fresh game against the Patriots they would win 65% of the time; with this day’s form, 31%. The numbers

Before kickoff the Broncos were 70% favorites. The biggest swing (Q4, 0:07 left): C. Ryland made a 56-yard field goal, worth 24 points of win probability to the Patriots.

Final

New England Patriots 26
Denver Broncos 23

December 24, 2023 · Empower Field at Mile High · Closing line: Broncos −7

Luck index +31 Patriots lucky · −31 Broncos

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 7, Broncos win 3.

  1. 1 NE 36 DEN 7
  2. 2 NE 30 DEN 9
  3. 3 NE 23 DEN 7
  4. 4 NE 37 DEN 25
  5. 5 NE 19 DEN 10
  6. 6 NE 20 DEN 14
  7. 7 NE 12 DEN 10
  8. 8 NE 6 DEN 10
  9. 9 NE 3 DEN 13
  10. 10 NE 19 DEN 38

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 Broncos

They played far below what the matchup promised. In a fresh game against the Patriots they would win 65% of the time; with this day’s form, 31%.

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

UnitThis gameUsual levelBetter or worse than usual
Patriots offenseEPA per play gained +0.09 +0.04 better by 0.05
Patriots defenseEPA per play allowed −0.06 +0.07 better by 0.13
Broncos offenseEPA per play gained −0.06 +0.04 worse by 0.10
Broncos defenseEPA per play allowed +0.09 +0.09 better by 0.00

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

Patriots win 69% of them, Broncos 31%, counting the 3% still level after regulation as half each. The line is what actually happened: Patriots by 3.

Show as a table
Final margin in the replaysShare of replays
Patriots by 17+24.8%
Patriots by 9–1619.9%
Patriots by 1–821.3%
Level after regulation2.9%
Broncos by 1–814.8%
Broncos by 9–1610.8%
Broncos by 17+5.4%

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 +4.5 points to the Broncos: the final margin was Patriots by 3, without the luck Patriots by 7.5. 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.

  • C. Ryland, 33 yds made · 92% expected
  • C. Ryland, 47 yds missed · 69% expected
  • W. Lutz, 57 yds missed · 55% expected
  • C. Ryland, 56 yds made · 54% expected
  • Extra point missed · 94% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Patriots 3 for 25 yards, Broncos 2 for 25 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
Q2 5:59 Unnecessary Roughness on the Broncos, 15 yards, wiping out the play +6% NE +2.4 pts
Q2 0:51 Offensive Holding on the Patriots, 10 yards +11% DEN +1.4 pts
Q3 2:57 Offensive Holding on the Patriots, 10 yards, wiping out the play +5% DEN +1.6 pts
Q4 3:51 Offensive Holding on the Broncos, 10 yards +2% NE +1.2 pts
Q4 1:58 Player Out of Bounds on Kick on the Patriots (Chris Board), 5 yards 0% DEN +0.4 pts

Patriots penalties, every game · Broncos penalties, every game · All teams, 2023

When it happened

Broncos’ chance of winning

As low as 0% and as high as 80%. 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 Broncos were ahead in it, below while the Patriots were.
#WhenWhat happenedWin probability forNext drive
1 Q1 13:23 The Broncos were stopped on 4th & 23rd & 4th downs · 52% expected +10% NE DEN: Punt
2 Q2 0:51 Offensive Holding on the Patriots, 10 yardsJudgment calls +11% DEN DEN: Missed field goal
3 Q3 1:41 The Patriots converted 3rd & 93rd & 4th downs · 26% expected +10% NE NE: Touchdown
4 Q3 1:34 The Broncos fumbled and the Patriots recoveredFumble bounces · loose balls are close to 50/50Return touchdown by the PatriotsSpecial teams +18% NE DEN: Punt
5 Q4 2:59 The Broncos converted 3rd & 43rd & 4th downs · 44% expected +11% DEN DEN: Touchdown
6 Q4 2:53 The Broncos’ two-point try was good3rd & 4th downs · 47% expected +14% DEN DEN: Punt
7 Q4 0:47 The Patriots converted 3rd & 33rd & 4th downs · 49% expected +17% NE NE: Field goal
8 Q4 0:07 C. Ryland made a 56-yard field goalKicks · 54% expected for him, 4 of 9 from 45+ before +24% NE –

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.

  • Hunter Henry (NE TE), out · 0.8 pts
  • JuJu Smith-Schuster (NE WR), out · 0.8 pts
  • J.C. Jackson (NE CB), out (IR) · 0.6 pts
  • Kendrick Bourne (NE WR), out (IR) · 0.6 pts
  • Jabrill Peppers (NE SS), out · 0.5 pts
  • Rhamondre Stevenson (NE RB), out · 0.3 pts
  • Cole Strange (NE G), out (IR) · 0.3 pts
  • Conor McDermott (NE T), 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 71% · Broncos 29%

Final margin
Patriots by 3
Luck in points
4.5 for the Broncos
Luck-adjusted margin
Patriots by 7.5
Replay with same day's form
Patriots 69% · Broncos 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

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 16 2023 games · Patriots · Broncos

More from Week 16 2023