luckadjusted

Week 4 2023 · October 1, 2023

Cardinals at 49ers, Week 4 2023: who deserved to win?

The 49ers beat the Cardinals 35–16, and it was no fluke: replayed with the way both teams actually played, the 49ers win 9 of 10.

Before kickoff the 49ers were 87% favorites.

Final

Arizona Cardinals 16
San Francisco 49ers 35

October 1, 2023 · Levi's Stadium · Closing line: 49ers −15

Luck index +7 49ers about even · −7 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, 49ers win 9.

  1. 1 ARI 17 SF 13
  2. 2 ARI 21 SF 24
  3. 3 ARI 24 SF 29
  4. 4 ARI 24 SF 31
  5. 5 ARI 17 SF 27
  6. 6 ARI 28 SF 42
  7. 7 ARI 24 SF 41
  8. 8 ARI 17 SF 38
  9. 9 ARI 13 SF 38
  10. 10 ARI 3 SF 34

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 7% of them, 49ers 93%, counting the 2% still level after regulation as half each. The line is what actually happened: 49ers by 19.

Show as a table
Final margin in the replaysShare of replays
Cardinals by 17+0.3%
Cardinals by 9–161.6%
Cardinals by 1–83.8%
Level after regulation1.8%
49ers by 1–817.2%
49ers by 9–1623.9%
49ers by 17+51.5%

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 +4.1 points to the 49ers: the final margin was 49ers by 19, without the luck 49ers by 14.9. Luck shares are the fitted ones (how much of each kind is luck).

Penalties: Cardinals 9 for 55 yards, 49ers 4 for 21 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 13:34 False Start on the Cardinals (Owen Pappoe), 5 yards · pre-snap +4% SF +0.6 pts
Q1 11:39 Defensive Holding on the Cardinals (Kyzir White), 5 yards 0% SF +0.2 pts
Q1 10:09 Face Mask on the Cardinals (Zeke Turner), 2 yards +1% SF +0.5 pts
Q1 8:59 Defensive Holding on the 49ers (Javon Hargrave), 5 yards +2% ARI +1.1 pts
Q1 8:40 False Start on the Cardinals, 5 yards · pre-snap +2% SF +0.6 pts
Q2 12:54 Defensive Pass Interference on the 49ers, 6 yards +1% ARI +1.3 pts
Q2 12:16 Offensive Holding on the Cardinals, 10 yards +2% SF +0.9 pts
Q2 5:22 Unnecessary Roughness on the Cardinals (Kris Boyd), 12 yards 0% SF +0.8 pts
Q2 4:51 False Start on the Cardinals, 5 yards · pre-snap 0% SF +0.8 pts
Q3 6:58 Defensive Offside on the 49ers (Arik Armstead), 5 yards · pre-snap +1% ARI +0.6 pts
Q4 14:22 Offensive Holding on the Cardinals (Trey McBride), 10 yards +1% SF +0.8 pts
Q4 2:23 Defensive Holding on the Cardinals (Marco Wilson), 1 yard 0% SF +1.6 pts
Q4 1:59 False Start on the 49ers, 5 yards · pre-snap 0% ARI 0.0 pts

Cardinals penalties, every game · 49ers penalties, every game · All teams, 2023

When it happened

49ers’ 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 49ers were ahead in it, below while the Cardinals were.
#WhenWhat happenedWin probability forNext drive
1 Q1 13:34 False Start on the Cardinals (Owen Pappoe), 5 yardsPre-snap flags · 0 flags in 30 snaps before, position avg 1 per 444 +4% SF SF: Touchdown
2 Q1 7:02 The Cardinals converted 3rd & 83rd & 4th downs · 30% expected +4% ARI ARI: Punt
3 Q1 6:21 The Cardinals fumbled and recovered it themselvesFumble bounces · loose balls are close to 50/50 +5% ARI ARI: Punt
4 Q1 1:04 The 49ers were stopped on 3rd & 43rd & 4th downs · 51% expected +3% ARI SF: Touchdown
5 Q1 0:26 The 49ers converted 4th & 43rd & 4th downs · 50% expected +6% SF SF: Touchdown
6 Q2 11:25 The Cardinals converted 4th & 73rd & 4th downs · 32% expected +3% ARI ARI: Field goal
7 Q2 10:20 The Cardinals converted 3rd & 73rd & 4th downs · 33% expected +4% ARI ARI: Field goal
8 Q4 9:59 The Cardinals were stopped on 3rd & 103rd & 4th downs · 27% expected +3% SF ARI: 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.

  • Budda Baker (ARI SS), out (IR) · 0.9 pts
  • Jonathan Ledbetter (ARI DE), out · 0.4 pts
  • Krys Barnes (ARI LB), out · 0.2 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 0% · 49ers 100%

Final margin
49ers by 19
Luck in points
4.1 for the 49ers
Luck-adjusted margin
49ers by 14.9
Replay with same day's form
Cardinals 7% · 49ers 93% 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 4 2023 games · Cardinals · 49ers

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