luckadjusted

Divisional round 2023 · January 21, 2024

Chiefs at Bills, Divisional round 2023: who deserved to win?

The Chiefs beat the Bills 27–24 and were the better team on the day: replayed with the same form, they win 6 of 10. The Bills had the bounces: 3rd & 4th downs alone were worth 11 points of win probability to the Bills.

Before kickoff the Bills were 57% favorites. The biggest swing (Q4, 1:47 left): T. Bass missed 44-yard field goal, worth 30 points of win probability to the Chiefs.

Final

Kansas City Chiefs 27
Buffalo Bills 24

January 21, 2024 · New Era Field · Closing line: Bills −2.5

Luck index +37 Chiefs lucky · −37 Bills

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. Chiefs win 6, Bills win 4.

  1. 1 KC 35 BUF 13
  2. 2 KC 34 BUF 17
  3. 3 KC 27 BUF 16
  4. 4 KC 28 BUF 20
  5. 5 KC 24 BUF 19
  6. 6 KC 19 BUF 17
  7. 7 KC 35 BUF 38
  8. 8 KC 21 BUF 26
  9. 9 KC 16 BUF 26
  10. 10 KC 7 BUF 26

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

Chiefs win 63% of them, Bills 37%, counting the 2% still level after regulation as half each. The line is what actually happened: Chiefs by 3.

Show as a table
Final margin in the replaysShare of replays
Chiefs by 17+16.1%
Chiefs by 9–1620.3%
Chiefs by 1–826.4%
Level after regulation2.3%
Bills by 1–820.5%
Bills by 9–169.5%
Bills by 17+4.9%

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 +7.0 points to the Chiefs: the final margin was Chiefs by 3, without the luck Bills by 4. 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, 27 yds made · 96% expected
  • H. Butker, 47 yds made · 75% expected
  • H. Butker, 29 yds made · 97% expected
  • T. Bass, 44 yds missed · 76% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Chiefs 2 for 15 yards, Bills 5 for 28 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 14:52 Illegal Bat on the Bills (Dalton Kincaid), 10 yards +2% KC +0.8 pts
Q2 11:45 Defensive Holding on the Bills (Rasul Douglas), 5 yards 0% KC +0.3 pts
Q2 0:20 Offensive Holding on the Chiefs, 10 yards 0% BUF +0.1 pts
Q3 7:54 Illegal Use of Hands on the Chiefs (Trent McDuffie), 5 yards +4% BUF +1.2 pts
Q3 3:29 Delay of Game on the Bills, 5 yards · pre-snap +4% KC +0.6 pts
Q4 14:20 Encroachment on the Bills (Tim Settle), 5 yards · pre-snap 0% KC 0.0 pts
Q4 9:31 Defensive Pass Interference on the Bills (Dorian Williams), 3 yards +6% KC +1.0 pts

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

When it happened

Bills’ chance of winning

As low as 0% and as high as 70%. 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 Chiefs were.
#WhenWhat happenedWin probability forNext drive
1 Q3 3:29 The Bills converted 3rd & 133rd & 4th downs · 26% expectedDelay of Game on the Bills, 5 yardsPre-snap flags +11% BUF BUF: Touchdown
2 Q4 12:57 The Bills were stopped on 4th & 53rd & 4th downs · 44% expected +8% KC BUF: Punt
3 Q4 8:23 S. Diggs dropped a catchable passDrops · 9 drops on 262 catchable balls before this +9% KC BUF: Missed field goal
4 Q4 5:47 The Bills got away with an interception-worthy throwInterceptions · 48% expected to stay out of the defense's hands +14% BUF BUF: Missed field goal
5 Q4 4:52 The Bills converted 4th & 33rd & 4th downs · 54% expected +17% BUF BUF: Missed field goal
6 Q4 3:20 The Bills converted 3rd & 43rd & 4th downs · 49% expected +9% BUF BUF: Missed field goal
7 Q4 1:55 The Bills were stopped on 3rd & 93rd & 4th downs · 33% expected +10% KC BUF: Missed field goal
8 Q4 1:47 T. Bass missed 44-yard field goalKicks · 76% expected for him +30% KC –

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.

  • Christian Benford (BUF CB), out · 0.8 pts
  • Terrel Bernard (BUF LB), out · 0.4 pts
  • Wanya Morris (KC T), out · 0.5 pts
  • Bryan Cook (KC FS), out (IR) · 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

Chiefs 28% · Bills 72%

Final margin
Chiefs by 3
Luck in points
7.0 for the Chiefs
Luck-adjusted margin
Bills by 4.0
Replay with same day's form
Chiefs 63% · Bills 37% 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 Divisional round 2023 games · Chiefs · Bills

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