luckadjusted
NFL Week 9 · 2026

Week 14 2023 · December 10, 2023

Bills at Chiefs, Week 14 2023: who deserved to win?

The Bills beat the Chiefs 20–17, but the replays call it close to a coin flip: with the way both teams played, the Bills win 5 of 10. Luck ran their way: 3rd & 4th downs alone were worth 9 points of win probability to the Bills.

Before kickoff the Chiefs were 56% favorites. The biggest swing (Q4, 1:25 left): Offensive Offside on the Chiefs (Kadarius Toney), 5 yards, wiping out the play, worth 67 points of win probability to the Bills.

Final

Buffalo Bills 20
Kansas City Chiefs 17

December 10, 2023 · GEHA Field at Arrowhead Stadium · Closing line: Chiefs −2

Luck index +46 Bills lucky · −46 Chiefs

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 5, Chiefs win 5.

  1. 1 BUF 37 KC 13
  2. 2 BUF 31 KC 16
  3. 3 BUF 44 KC 35
  4. 4 BUF 13 KC 7
  5. 5 BUF 27 KC 24
  6. 6 BUF 22 KC 24
  7. 7 BUF 19 KC 24
  8. 8 BUF 17 KC 27
  9. 9 BUF 10 KC 24
  10. 10 BUF 21 KC 43

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 54% of them, Chiefs 46%, counting the 6% still level after regulation as half each. The line is what actually happened: Bills by 3.

Show as a table
Final margin in the replaysShare of replays
Bills by 17+11.8%
Bills by 9–1615.5%
Bills by 1–822.1%
Level after regulation5.8%
Chiefs by 1–820.6%
Chiefs by 9–1613.7%
Chiefs by 17+10.5%

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 +3.6 points to the Bills: the final margin was Bills by 3, without the luck Chiefs by 0.6. 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.

  • T. Bass, 31 yds made · 95% expected
  • H. Butker, 27 yds made · 99% expected
  • T. Bass, 39 yds made · 89% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bills 4 for 35 yards, Chiefs 7 for 45 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 half toward luck; pre-snap fouls, which repeat, don’t count. How calls are valued

WhenFlagWin probability for
Q1 3:05 False Start on the Chiefs (Marquez Valdes-Scantling), 5 yards · pre-snap +2% BUF +0.9 pts
Q2 11:50 Defensive Holding on the Bills (Tim Settle), 5 yards 0% KC +0.3 pts
Q2 10:53 Offensive Pass Interference on the Chiefs (Travis Kelce), 10 yards +1% BUF +0.8 pts
Q2 2:23 Offensive Holding on the Chiefs, 10 yards, wiping out the play +6% BUF +1.6 pts
Q2 2:00 False Start on the Chiefs, 5 yards · pre-snap 0% BUF +0.4 pts
Q3 11:11 Offensive Holding on the Bills (Dawson Knox), 10 yards +3% KC +1.1 pts
Q3 9:27 Neutral Zone Infraction on the Chiefs (Chris Jones), 5 yards · pre-snap +1% BUF +0.4 pts
Q4 9:46 Offensive Holding on the Bills, 10 yards, wiping out the play +13% KC +2.1 pts
Q4 9:10 Offensive Holding on the Bills, 10 yards, wiping out the play +10% KC +1.7 pts
Q4 2:17 Illegal Contact on the Chiefs (Jaylen Watson), 5 yards +17% BUF +1.7 pts
Q4 1:25 Offensive Offside on the Chiefs (Kadarius Toney), 5 yards, wiping out the play · pre-snap +67% BUF +5.7 pts

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

When it happened

Chiefs’ chance of winning

As low as 0% and as high as 67%. 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 Chiefs were ahead in it, below while the Bills were.
#WhenWhat happenedWin probability forNext drive
1 Q4 10:42 The Bills converted 3rd & 93rd & 4th downs · 34% expected +9% BUF BUF: Punt
2 Q4 9:46 Offensive Holding on the Bills, 10 yards, wiping out the playJudgment calls +13% KC KC: Punt
3 Q4 9:10 Offensive Holding on the Bills, 10 yards, wiping out the playJudgment calls +10% KC KC: Punt
4 Q4 5:41 The Bills converted 3rd & 63rd & 4th downs · 42% expected +11% BUF BUF: Field goal
5 Q4 2:17 Illegal Contact on the Chiefs (Jaylen Watson), 5 yardsJudgment calls · 3 flags in 1301 snaps before, position avg 1 per 216 +17% BUF BUF: Field goal
6 Q4 1:25 Offensive Offside on the Chiefs (Kadarius Toney), 5 yards, wiping out the playPre-snap flags · 1 flag in 693 snaps before, position avg 1 per 420 +67% BUF BUF: End of game
7 Q4 1:05 The Chiefs were stopped on 3rd & 153rd & 4th downs · 25% expected +10% BUF KC: Turnover on downs
8 Q4 1:01 The Chiefs were stopped on 4th & 153rd & 4th downs · 26% expected +9% 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.

  • Donovan Smith (KC T), out · 1.2 pts
  • Bryan Cook (KC FS), out (IR) · 0.4 pts
  • Drue Tranquill (KC LB), out · 0.4 pts
  • Isiah Pacheco (KC RB), out · 0.3 pts
  • Kaiir Elam (BUF CB), out (IR) · 0.4 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 70% · Chiefs 30%

Final margin
Bills by 3
Luck in points
3.6 for the Bills
Luck-adjusted margin
Chiefs by 0.6
Replay with same day's form
Bills 54% · Chiefs 46% unchanged: why
How much of each is luck?

0% treats it as skill, 100% as pure luck. The tick is our fit.

What counts

None by default: our tests measured no carryover after a lucky break. Slide it up to count a break for more than its own swing. 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 14 2023 games · Bills · Chiefs

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