luckadjusted

Week 16 2021 · December 26, 2021

No FTN charting for this game (drops and interception-worthy throws are not modelled).

Bills at Patriots, Week 16 2021: who deserved to win?

The Bills beat the Patriots 33–21 and were the better team on the day: replayed with the same form, they win 8 of 10.

Before kickoff it was a pick’em. The biggest swing (Q2, 4:51 left): the Bills were stopped on 4th & 1, worth 11 points of win probability to the Patriots.

Final

Buffalo Bills 33
New England Patriots 21

December 26, 2021 · Gillette Stadium · Closing line: Patriots −1

Luck index +22 Bills about even · −22 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. Bills win 8, Patriots win 2.

  1. 1 BUF 34 NE 10
  2. 2 BUF 27 NE 7
  3. 3 BUF 24 NE 9
  4. 4 BUF 21 NE 10
  5. 5 BUF 31 NE 24
  6. 6 BUF 23 NE 17
  7. 7 BUF 17 NE 14
  8. 8 BUF 14 NE 12
  9. 9 BUF 20 NE 23
  10. 10 BUF 3 NE 15

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

Bills win 78% of them, Patriots 22%, counting the 5% still level after regulation as half each. The line is what actually happened: Bills by 12.

Show as a table
Final margin in the replaysShare of replays
Bills by 17+23.2%
Bills by 9–1623.9%
Bills by 1–826.7%
Level after regulation5.1%
Patriots by 1–813.9%
Patriots by 9–165.5%
Patriots by 17+1.8%

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 +5.1 points to the Patriots: the final margin was Bills by 12, without the luck Bills by 17.1. 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, 25 yds made · 97% expected
  • T. Bass, 34 yds made · 91% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bills 5 for 45 yards, Patriots 3 for 30 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 1:51 Offensive Holding on the Patriots (Jonnu Smith), 10 yards, wiping out the play +8% BUF +2.2 pts
Q2 2:15 Encroachment on the Patriots (Christian Barmore), 5 yards · pre-snap +2% BUF +1.0 pts
Q2 1:35 Roughing the Passer on the Bills, 15 yards +4% NE +1.1 pts
Q2 1:22 Unsportsmanlike Conduct on the Patriots, 15 yards +5% BUF +1.0 pts
Q2 1:00 Offensive Pass Interference on the Bills (Emmanuel Sanders), 10 yards +3% NE +0.3 pts
Q3 10:21 Ineligible Downfield Pass on the Bills, 5 yards, wiping out the play +5% NE +2.7 pts
Q3 10:15 Offensive Holding on the Bills (Dawson Knox), 10 yards +3% NE +1.5 pts
Q4 10:25 Defensive Holding on the Bills (Taron Johnson), 5 yards +1% NE +0.9 pts

Bills penalties, every game · Patriots penalties, every game · All teams, 2021

When it happened

Patriots’ chance of winning

As low as 0% and as high as 55%. 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 Patriots were ahead in it, below while the Bills were.
#WhenWhat happenedWin probability forNext drive
1 Q1 6:43 The Bills converted 4th & 23rd & 4th downs · 55% expected +8% BUF BUF: Touchdown
2 Q1 1:51 Offensive Holding on the Patriots (Jonnu Smith), 10 yards, wiping out the playJudgment calls · 12 flags in 2164 snaps before, position avg 1 per 269 +8% BUF BUF: Field goal
3 Q2 15:00 The Patriots converted 4th & 13rd & 4th downs · 73% expected +9% NE NE: Touchdown
4 Q2 9:04 T. Bass made 25-yard field goalKicks · 97% expected for him +7% BUF BUF: Turnover on downs
5 Q2 4:51 The Bills were stopped on 4th & 13rd & 4th downs · 69% expected +11% NE BUF: Touchdown
6 Q2 2:15 The Bills converted 4th & 23rd & 4th downs · 63% expectedEncroachment on the Patriots (Christian Barmore), 5 yardsPre-snap flags · 0 flags in 536 snaps before, position avg 1 per 273 +9% BUF BUF: Touchdown
7 Q2 1:48 The Bills converted 3rd & 113rd & 4th downs · 29% expected +8% BUF BUF: Touchdown
8 Q4 7:26 The Bills converted 3rd & 103rd & 4th downs · 31% expected +7% BUF BUF: 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.

  • Nelson Agholor (NE WR), out · 0.5 pts
  • Tre'Davious White (BUF CB), out (IR) · 1.1 pts
  • Cole Beasley (BUF WR), out (IR) · 0.5 pts
  • Star Lotulelei (BUF DT), out · 0.3 pts
  • Cody Ford (BUF G), out (IR) · 0.3 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

Bills 100% · Patriots 0%

Final margin
Bills by 12
Luck in points
5.1 for the Patriots
Luck-adjusted margin
Bills by 17.1
Replay with same day's form
Bills 78% · Patriots 22% 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 (not available for this game); injuries from snap counts and injury reports. No FTN charting for this game (drops and interception-worthy throws are not modelled).

Methodology and validation · All Week 16 2021 games · Bills · Patriots

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