luckadjusted

Week 1 2024 · September 8, 2024

Cardinals at Bills, Week 1 2024: who deserved to win?

The Bills beat the Cardinals 34–28, and it was no fluke: replayed with the way both teams actually played, the Bills win 9 of 10. The Cardinals had the bounces: judgment calls alone were worth 12 points of win probability to the Cardinals.

Before kickoff the Bills were 68% favorites. The biggest swing (Q4, 0:44 left): T. McBride dropped a catchable pass, worth 32 points of win probability to the Bills.

Final

Arizona Cardinals 28
Buffalo Bills 34

September 8, 2024 · New Era Field · Closing line: Bills −6.5

Luck index +8 Bills about even · −8 Cardinals

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. Cardinals win 1, Bills win 9.

  1. 1 ARI 24 BUF 19
  2. 2 ARI 15 BUF 17
  3. 3 ARI 30 BUF 35
  4. 4 ARI 20 BUF 28
  5. 5 ARI 16 BUF 27
  6. 6 ARI 10 BUF 24
  7. 7 ARI 20 BUF 37
  8. 8 ARI 16 BUF 36
  9. 9 ARI 13 BUF 38
  10. 10 ARI 0 BUF 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

Cardinals win 8% of them, Bills 92%, 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
Cardinals by 17+0.5%
Cardinals by 9–161.7%
Cardinals by 1–84.8%
Level after regulation1.6%
Bills by 1–817.8%
Bills by 9–1621.8%
Bills by 17+51.8%

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 +3.0 points to the Bills: the final margin was Bills by 6, without the luck Bills by 3. 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.

  • M. Prater, 29 yds made · 95% expected
  • T. Bass, 37 yds made · 87% expected
  • M. Prater, 31 yds made · 94% expected
  • T. Bass, 39 yds made · 84% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Cardinals 5 for 31 yards, Bills 9 for 65 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 9:48 Unnecessary Roughness on the Bills, 10 yards +4% ARI +1.3 pts
Q2 14:57 Defensive Pass Interference on the Cardinals (Sean Murphy-Bunting), 6 yards +1% BUF +0.4 pts
Q2 10:35 Face Mask on the Bills, 15 yards, wiping out the play +11% ARI +4.0 pts
Q2 2:40 False Start on the Bills, 5 yards · pre-snap +1% ARI +0.6 pts
Q2 1:41 False Start on the Bills, 5 yards · pre-snap +1% ARI +0.8 pts
Q2 0:55 Defensive Holding on the Cardinals (Sean Murphy-Bunting), 5 yards +1% BUF +0.8 pts
Q2 0:55 False Start on the Bills, 5 yards · pre-snap +1% ARI +0.6 pts
Q2 0:45 Roughing the Passer on the Cardinals (Zaven Collins), 15 yards, wiping out the play +6% BUF +2.5 pts
Q3 15:00 Offensive Holding on the Bills, 10 yards +3% ARI +0.9 pts
Q3 15:00 Kickoff Short of Landing Zone on the Cardinals, 0 yards · pre-snap 0% BUF 0.0 pts
Q4 11:21 False Start on the Bills, 5 yards · pre-snap +2% ARI +0.7 pts
Q4 7:46 Offensive Holding on the Bills, 10 yards +4% ARI +0.9 pts
Q4 3:52 Defensive Too Many Men on Field on the Cardinals, 5 yards · pre-snap +1% ARI +0.1 pts
Q4 1:56 Kickoff Out of Bounds on the Bills (Tyler Bass), 0 yards · pre-snap 0% ARI 0.0 pts

Cardinals penalties, every game · Bills penalties, every game · All teams, 2024

When it happened

Bills’ chance of winning

As low as 16% 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 Cardinals were.
#WhenWhat happenedWin probability forNext drive
1 Q2 10:35 Face Mask on the Bills, 15 yards, wiping out the playJudgment calls +11% ARI ARI: Touchdown
2 Q3 13:23 The Bills converted 3rd & 113rd & 4th downs · 29% expected +9% BUF BUF: Touchdown
3 Q3 9:55 The Bills converted 3rd & 103rd & 4th downs · 30% expected +15% BUF BUF: Touchdown
4 Q3 8:41 The Cardinals were stopped on 3rd & 63rd & 4th downs · 37% expected +9% BUF ARI: Punt
5 Q4 14:18 The Cardinals were stopped on 3rd & 43rd & 4th downs · 45% expected +9% BUF ARI: Field goal
6 Q4 8:44 Return touchdown by the CardinalsSpecial teams +15% ARI ARI: Touchdown
7 Q4 0:44 T. McBride dropped a catchable passDrops · 3 drops on 127 catchable balls before this +32% BUF ARI: Turnover on downs
8 Q4 0:32 The Cardinals were stopped on 4th & 73rd & 4th downs · 34% expected +13% BUF –

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.

  • Carter O'Donnell (ARI T), out (IR) · 0.5 pts
  • BJ Ojulari (ARI LB), out (IR) · 0.1 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

Cardinals 30% · Bills 70%

Final margin
Bills by 6
Luck in points
3.0 for the Bills
Luck-adjusted margin
Bills by 3.0
Replay with same day's form
Cardinals 8% · Bills 92% 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 1 2024 games · Cardinals · Bills

More from Week 1 2024