luckadjusted

Week 7 2023 · October 22, 2023

Bills at Patriots, Week 7 2023: who deserved to win?

The Patriots stole one. They beat the Bills 29–25, but replayed with the way both teams actually played, the Bills win 8 of 10. Luck ran their way: drops alone were worth 22 points of win probability to the Patriots.

Before kickoff the Bills were 71% favorites. The biggest swing (Q4, 0:54 left): the Patriots converted 3rd & 8, worth 19 points of win probability to the Patriots.

Final

Buffalo Bills 25
New England Patriots 29

October 22, 2023 · Gillette Stadium · Closing line: Bills −7.5

Luck index +82 Patriots very lucky · −82 Bills

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 37 NE 10
  2. 2 BUF 40 NE 20
  3. 3 BUF 23 NE 7
  4. 4 BUF 33 NE 20
  5. 5 BUF 38 NE 27
  6. 6 BUF 30 NE 21
  7. 7 BUF 28 NE 23
  8. 8 BUF 27 NE 24
  9. 9 BUF 24 NE 27
  10. 10 BUF 19 NE 31

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 82% of them, Patriots 18%, counting the 2% still level after regulation as half each. The line is what actually happened: Patriots by 4.

Show as a table
Final margin in the replaysShare of replays
Bills by 17+32.0%
Bills by 9–1621.4%
Bills by 1–826.8%
Level after regulation2.3%
Patriots by 1–810.3%
Patriots by 9–165.2%
Patriots by 17+2.0%

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 4, without the luck Bills by 4.5. 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, 30 yds made · 95% expected
  • T. Bass, 36 yds made · 90% expected
  • C. Ryland, 24 yds made · 98% expected
  • T. Bass, 42 yds missed · 82% expected
  • C. Ryland, 49 yds made · 67% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bills 9 for 46 yards, Patriots 8 for 59 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 5:42 Offensive Offside on the Bills, 4 yards · pre-snap +2% NE +1.2 pts
Q1 3:35 Illegal Contact on the Patriots (Jalen Mills), 5 yards +2% BUF +1.0 pts
Q1 0:06 Offensive Pass Interference on the Bills (Latavius Murray), 10 yards, wiping out the play +10% NE +4.0 pts
Q2 13:14 False Start on the Patriots (Brenden Schooler), 4 yards · pre-snap +4% BUF +0.7 pts
Q2 11:27 Delay of Game on the Bills, 5 yards · pre-snap +2% NE +0.7 pts
Q2 11:01 Neutral Zone Infraction on the Patriots (Deatrich Wise Jr.), 5 yards · pre-snap +2% BUF +0.6 pts
Q3 13:11 Offensive Holding on the Bills (Dalton Kincaid), 10 yards +2% NE +0.8 pts
Q3 12:15 Roughing the Passer on the Patriots (Jack Jones), 15 yards +1% BUF +1.2 pts
Q3 4:23 False Start on the Bills, 5 yards · pre-snap +2% NE +0.7 pts
Q4 11:45 Illegal Contact on the Bills (Taron Johnson), 5 yards, wiping out the play +9% NE +4.0 pts
Q4 9:03 Delay of Game on the Patriots, 5 yards · pre-snap +1% BUF +0.7 pts
Q4 7:36 Defensive Pass Interference on the Bills (Christian Benford), 1 yard 0% NE 0.0 pts
Q4 7:36 Encroachment on the Bills (Jordan Phillips), 0 yards · pre-snap 0% NE +2.8 pts
Q4 6:41 Roughing the Passer on the Patriots (Christian Barmore), 15 yards +2% BUF +1.1 pts
Q4 5:32 Ineligible Downfield Pass on the Patriots, 5 yards, wiping out the play +13% BUF +2.6 pts
Q4 1:58 Defensive Holding on the Patriots (Marte Mapu), 5 yards +9% BUF +1.0 pts
Q4 0:23 Defensive Pass Interference on the Bills (Christian Benford), 6 yards, wiping out the play +11% BUF +0.2 pts

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

When it happened

Patriots’ chance of winning

As low as 35% 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 Patriots were ahead in it, below while the Bills were.
#WhenWhat happenedWin probability forNext drive
1 Q1 0:06 Offensive Pass Interference on the Bills (Latavius Murray), 10 yards, wiping out the playJudgment calls · 2 flags in 1767 snaps before, position avg 1 per 870 +10% NE NE: Punt
2 Q4 5:32 Ineligible Downfield Pass on the Patriots, 5 yards, wiping out the playJudgment calls +13% BUF BUF: Touchdown
3 Q4 2:55 The Bills were stopped on 3rd & 23rd & 4th downs · 54% expected +10% NE BUF: Touchdown
4 Q4 2:50 The Bills converted 4th & 23rd & 4th downs · 54% expected +13% BUF BUF: Touchdown
5 Q4 1:58 The Bills’ two-point try was good3rd & 4th downs · 47% expectedDefensive Holding on the Patriots (Marte Mapu), 5 yardsJudgment calls · 1 flag in 190 snaps before, position avg 1 per 444 +18% BUF BUF: Turnover
6 Q4 0:54 The Patriots converted 3rd & 83rd & 4th downs · 30% expected +19% NE NE: Touchdown
7 Q4 0:23 Defensive Pass Interference on the Bills (Christian Benford), 6 yards, wiping out the playJudgment calls · 4 flags in 677 snaps before, position avg 1 per 216 +11% BUF NE: Touchdown
8 Q4 0:12 S. Diggs dropped a catchable passDrops · 4 drops on 190 catchable balls before this +18% NE BUF: Turnover

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.

  • Christian Gonzalez (NE CB), out (IR) · 1.0 pts
  • JuJu Smith-Schuster (NE WR), out · 0.5 pts
  • Matt Judon (NE LB), out (IR) · 0.4 pts
  • Tre'Davious White (BUF CB), out (IR) · 1.2 pts
  • Matt Milano (BUF LB), out (IR) · 0.6 pts
  • Ed Oliver (BUF DT), out · 0.5 pts
  • DaQuan Jones (BUF DT), 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 67% · Patriots 33%

Final margin
Patriots by 4
Luck in points
8.5 for the Patriots
Luck-adjusted margin
Bills by 4.5
Replay with same day's form
Bills 82% · Patriots 18% 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 7 2023 games · Bills · Patriots

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