luckadjusted

Week 17 2023 · December 31, 2023

Patriots at Bills, Week 17 2023: who deserved to win?

The Bills beat the Patriots 27–21 and were the better team on the day: replayed with the same form, they win 8 of 10.

Before kickoff the Bills were 87% favorites. The biggest swing (Q1, 15:00 left): Return touchdown by the Patriots, worth 24 points of win probability to the Patriots.

Final

New England Patriots 21
Buffalo Bills 27

December 31, 2023 · New Era Field · Closing line: Bills −15

Luck index +23 Bills about even · −23 Patriots

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 2, Bills win 8.

  1. 1 NE 16 BUF 3
  2. 2 NE 26 BUF 22
  3. 3 NE 10 BUF 12
  4. 4 NE 19 BUF 24
  5. 5 NE 15 BUF 23
  6. 6 NE 9 BUF 20
  7. 7 NE 13 BUF 27
  8. 8 NE 13 BUF 31
  9. 9 NE 9 BUF 31
  10. 10 NE 20 BUF 50

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 23% of them, Bills 77%, counting the 2% still level after regulation as half each. The line is what actually happened: Bills by 6.

Show as a table
Final margin in the replaysShare of replays
Patriots by 17+2.6%
Patriots by 9–166.9%
Patriots by 1–811.9%
Level after regulation2.1%
Bills by 1–824.1%
Bills by 9–1620.6%
Bills by 17+31.7%

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 +6.1 points to the Bills: the final margin was Bills by 6, without the luck Patriots by 0.1. 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.

  • T. Bass, 35 yds made · 92% expected
  • T. Bass, 24 yds made · 98% expected
  • C. Ryland, 47 yds missed · 71% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Patriots 2 for 20 yards, Bills 4 for 32 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 0:54 Unnecessary Roughness on the Patriots (Jalen Mills), 15 yards +1% BUF +1.2 pts
Q2 6:09 Offensive Holding on the Bills (Khalil Shakir), 10 yards +2% NE +1.2 pts
Q3 3:09 Delay of Game on the Patriots, 5 yards · pre-snap 0% BUF +0.9 pts
Q3 2:09 False Start on the Bills (Dalton Kincaid), 5 yards · pre-snap 0% NE +0.6 pts
Q4 11:35 Unnecessary Roughness on the Bills (Jordan Poyer), 7 yards +2% NE +1.1 pts
Q4 11:01 Offensive Holding on the Bills, 10 yards +1% NE +0.9 pts

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

When it happened

Bills’ chance of winning

As low as 32% 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 Bills were ahead in it, below while the Patriots were.
#WhenWhat happenedWin probability forNext drive
1 Q1 15:00 Return touchdown by the PatriotsSpecial teams +24% NE NE: Touchdown
2 Q1 12:14 The Bills were stopped on 3rd & 63rd & 4th downs · 40% expectedJ. Cook dropped a catchable passDrops · 6 drops on 68 catchable balls before this +9% NE BUF: Field goal
3 Q1 10:38 The Patriots were stopped on 3rd & 53rd & 4th downs · 35% expected +5% BUF NE: Punt
4 Q1 8:41 The Patriots threw an interception-worthy pass, and it was pickedInterceptions · 47% expected to stay out of the defense's hands +5% BUF NE: Turnover
5 Q1 5:57 The Patriots fumbled and the Bills recoveredFumble bounces · loose balls are close to 50/50 +5% BUF NE: Punt
6 Q2 12:47 The Patriots were stopped on 3rd & 113rd & 4th downs · 21% expectedThe Patriots threw an interception-worthy pass, and it was pickedInterceptions · 48% expected to stay out of the defense's handsReturn touchdown by the BillsSpecial teams +22% BUF NE: Touchdown
7 Q2 8:33 The Bills converted 3rd & 83rd & 4th downs · 34% expected +4% BUF BUF: Turnover
8 Q2 1:54 C. Ryland missed 47-yard field goalKicks · 71% expected for him, 5 of 10 from 45+ before +5% BUF NE: End of half

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 (IR) · 0.8 pts
  • J.C. Jackson (NE CB), out (IR) · 0.5 pts
  • Jabrill Peppers (NE SS), out · 0.5 pts
  • Cole Strange (NE G), out (IR) · 0.3 pts
  • Rhamondre Stevenson (NE RB), 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 26% · Bills 74%

Final margin
Bills by 6
Luck in points
6.1 for the Bills
Luck-adjusted margin
Patriots by 0.1
Replay with same day's form
Patriots 23% · Bills 77% 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 17 2023 games · Patriots · Bills

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