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 3.4 points 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 26 BUF 21
  2. 2 ARI 19 BUF 21
  3. 3 ARI 15 BUF 20
  4. 4 ARI 20 BUF 28
  5. 5 ARI 20 BUF 31
  6. 6 ARI 6 BUF 20
  7. 7 ARI 6 BUF 23
  8. 8 ARI 17 BUF 37
  9. 9 ARI 13 BUF 38
  10. 10 ARI 7 BUF 38

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

Take the luck out

The final margin was Bills by 6. Remove the luck, one kind at a time, and it becomes Bills by 3.0.

Each row takes one kind of luck out of the margin. Color shows which team it helped. Luck shares are the fitted ones (how much of each component 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.

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

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