luckadjusted

Week 15 2023 · December 17, 2023

Cowboys at Bills, Week 15 2023: who deserved to win?

The Bills beat the Cowboys 31–10, and it was no fluke: replayed with the way both teams actually played, the Bills win 10 of 10. The Cowboys had the bounces: drops alone were worth 9 points of win probability to the Cowboys.

Before kickoff the Bills were 56% favorites. The biggest swing (Q1, 0:25 left): Roughing the Kicker on the Cowboys (Sam Williams), 15 yards, worth 10 points of win probability to the Bills.

Final

Dallas Cowboys 10
Buffalo Bills 31

December 17, 2023 · New Era Field · Closing line: Bills −2

Luck index +5 Bills about even · −5 Cowboys

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. Cowboys win 0, Bills win 10.

  1. 1 DAL 28 BUF 31
  2. 2 DAL 14 BUF 20
  3. 3 DAL 19 BUF 27
  4. 4 DAL 17 BUF 27
  5. 5 DAL 6 BUF 20
  6. 6 DAL 10 BUF 27
  7. 7 DAL 7 BUF 26
  8. 8 DAL 23 BUF 45
  9. 9 DAL 7 BUF 34
  10. 10 DAL 6 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

Cowboys win 5% of them, Bills 95%, counting the 1% still level after regulation as half each. The line is what actually happened: Bills by 21.

Show as a table
Final margin in the replaysShare of replays
Cowboys by 17+0.1%
Cowboys by 9–160.8%
Cowboys by 1–83.3%
Level after regulation1.4%
Bills by 1–815.0%
Bills by 9–1620.6%
Bills by 17+58.8%

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 +0.3 points to the Bills: the final margin was Bills by 21, without the luck Bills by 20.7. 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.

  • B. Aubrey, 32 yds made · 96% expected
  • T. Bass, 23 yds made · 98% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Cowboys 5 for 48 yards, Bills 1 for 15 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 9:00 Roughing the Passer on the Cowboys (DeMarcus Lawrence), 3 yards +4% BUF +1.3 pts
Q1 6:02 Offensive Holding on the Cowboys, 10 yards +3% BUF +0.9 pts
Q1 0:25 Roughing the Kicker on the Cowboys (Sam Williams), 15 yards +10% BUF +2.7 pts
Q2 12:15 Unnecessary Roughness on the Bills, 15 yards +3% DAL +1.8 pts
Q2 4:23 Unnecessary Roughness on the Cowboys (Jayron Kearse), 15 yards +2% BUF +1.2 pts
Q4 12:53 Defensive Too Many Men on Field on the Cowboys, 5 yards · pre-snap 0% BUF +0.6 pts

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

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 Cowboys were.
#WhenWhat happenedWin probability forNext drive
1 Q1 9:00 Roughing the Passer on the Cowboys (DeMarcus Lawrence), 3 yardsJudgment calls · 16 flags in 3016 snaps before, position avg 1 per 295 +4% BUF BUF: Touchdown
2 Q1 7:25 The Cowboys converted 3rd & 63rd & 4th downs · 40% expected +5% DAL DAL: Punt
3 Q1 4:50 The Cowboys were stopped on 3rd & 143rd & 4th downs · 25% expected +3% BUF DAL: Punt
4 Q1 3:15 The Bills were stopped on 3rd & 33rd & 4th downs · 57% expected +4% DAL BUF: Punt
5 Q1 3:04 The Cowboys got away with an interception-worthy throwInterceptions · 48% expected to stay out of the defense's hands +5% DAL DAL: Punt
6 Q1 0:35 D. Kincaid dropped a catchable passDrops · 0 drops on 63 catchable balls before this +4% DAL BUF: Touchdown
7 Q1 0:25 Roughing the Kicker on the Cowboys (Sam Williams), 15 yardsJudgment calls · 10 flags in 1056 snaps before, position avg 1 per 295 +10% BUF BUF: Touchdown
8 Q1 0:14 D. Kincaid dropped a catchable passDrops · 1 drops on 64 catchable balls before this +4% DAL BUF: Touchdown

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.

  • Micah Hyde (BUF FS), out · 0.7 pts
  • Kaiir Elam (BUF CB), out (IR) · 0.2 pts
  • Malik Hooker (DAL FS), out · 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

Cowboys 0% · Bills 100%

Final margin
Bills by 21
Luck in points
0.3 for the Bills
Luck-adjusted margin
Bills by 20.7
Replay with same day's form
Cowboys 5% · Bills 95% 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 15 2023 games · Cowboys · Bills

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