luckadjusted

Wild Card 2021 · January 15, 2022

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

Patriots at Bills, Wild Card 2021: who deserved to win?

The Bills beat the Patriots 47–17, and it was no fluke: replayed with the way both teams actually played, the Bills win 9 of 10.

Before kickoff the Bills were 63% favorites. The biggest swing (Q1, 7:24 left): the Patriots converted 3rd & 14, worth 8 points of win probability to the Patriots.

Final

New England Patriots 17
Buffalo Bills 47

January 15, 2022 · New Era Field · Closing line: Bills −4.5

Luck index +6 Bills about even · −6 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 1, Bills win 9.

  1. 1 NE 26 BUF 20
  2. 2 NE 10 BUF 13
  3. 3 NE 24 BUF 31
  4. 4 NE 17 BUF 27
  5. 5 NE 7 BUF 20
  6. 6 NE 24 BUF 41
  7. 7 NE 13 BUF 33
  8. 8 NE 17 BUF 41
  9. 9 NE 13 BUF 41
  10. 10 NE 14 BUF 48

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 6% of them, Bills 94%, counting the 2% still level after regulation as half each. The line is what actually happened: Bills by 30.

Show as a table
Final margin in the replaysShare of replays
Patriots by 17+0.1%
Patriots by 9–161.2%
Patriots by 1–83.9%
Level after regulation1.7%
Bills by 1–815.4%
Bills by 9–1622.4%
Bills by 17+55.3%

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 +10.1 points to the Patriots: the final margin was Bills by 30, without the luck Bills by 40.1. 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.

  • N. Folk, 44 yds made · 79% expected
  • Extra point missed · 93% expected
  • Extra point missed · 93% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Patriots 5 for 34 yards, Bills 3 for 47 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 8:30 False Start on the Patriots (Jakob Johnson), 5 yards · pre-snap +1% BUF +0.5 pts
Q2 11:50 Illegal Contact on the Patriots (Dont'a Hightower), 5 yards 0% BUF 0.0 pts
Q2 9:56 Face Mask on the Patriots, 15 yards +2% BUF +1.8 pts
Q2 6:26 Defensive Pass Interference on the Bills, 22 yards +2% NE +2.4 pts
Q2 4:49 Delay of Game on the Patriots, 5 yards · pre-snap 0% BUF +0.2 pts
Q3 9:19 Offensive Pass Interference on the Bills (Dawson Knox), 10 yards, wiping out the play 0% NE +2.2 pts
Q3 7:51 Offensive Too Many Men on Field on the Patriots, 4 yards · pre-snap 0% BUF +0.6 pts
Q4 5:19 Roughing the Passer on the Bills (A.J. Epenesa), 15 yards 0% NE +1.7 pts

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

When it happened

Bills’ chance of winning

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 11:18 The Bills converted 3rd & 33rd & 4th downs · 61% expected +5% BUF BUF: Touchdown
2 Q1 7:24 The Patriots converted 3rd & 143rd & 4th downs · 19% expected +8% NE NE: Turnover
3 Q1 6:28 The Patriots converted 3rd & 103rd & 4th downs · 25% expected +6% NE NE: Turnover
4 Q1 3:41 The Bills converted 3rd & 13rd & 4th downs · 81% expected +2% BUF BUF: Touchdown
5 Q1 1:24 The Bills converted 3rd & 43rd & 4th downs · 55% expected +2% BUF BUF: Touchdown
6 Q2 9:56 Face Mask on the Patriots, 15 yardsJudgment calls +2% BUF BUF: Touchdown
7 Q2 7:20 The Bills missed an extra pointKicks · extra points are made about 94% of the time +1% BUF BUF: Touchdown
8 Q2 6:26 Defensive Pass Interference on the Bills, 22 yardsJudgment calls +2% NE NE: Punt

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.

  • Tre'Davious White (BUF CB), out (IR) · 0.8 pts
  • Ike Boettger (BUF G), out (IR) · 0.3 pts
  • Jalen Mills (NE CB), out (IR) · 0.7 pts
  • Isaiah Wynn (NE T), out · 0.6 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 0% · Bills 100%

Final margin
Bills by 30
Luck in points
10.1 for the Patriots
Luck-adjusted margin
Bills by 40.1
Replay with same day's form
Patriots 6% · Bills 94% 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 Wild Card 2021 games · Patriots · Bills

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