luckadjusted

Divisional round 2021 · January 23, 2022

No FTN charting for this game (drops and interception-worthy throws are not modelled).

Bills at Chiefs, Divisional round 2021: who deserved to win?

The Chiefs beat the Bills 42–36 and were the better team on the day: replayed with the same form, they win 7 of 10.

Before kickoff the Chiefs were 57% favorites. The biggest swing (Q4, 2:00 left): the Bills converted 4th & 13, worth 35 points of win probability to the Bills.

Final (OT)

Buffalo Bills 36
Kansas City Chiefs 42

January 23, 2022 · GEHA Field at Arrowhead Stadium · Closing line: Chiefs −2.5

Luck index +28 Chiefs lucky · −28 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. Bills win 3, Chiefs win 7.

  1. 1 BUF 56 KC 38
  2. 2 BUF 31 KC 23
  3. 3 BUF 27 KC 24
  4. 4 BUF 24 KC 26
  5. 5 BUF 35 KC 40
  6. 6 BUF 24 KC 31
  7. 7 BUF 21 KC 33
  8. 8 BUF 28 KC 44
  9. 9 BUF 17 KC 38
  10. 10 BUF 20 KC 51

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 28% of them, Chiefs 72%, counting the 4% still level after regulation as half each. The line is what actually happened: Chiefs by 6.

Show as a table
Final margin in the replaysShare of replays
Bills by 17+3.3%
Bills by 9–167.8%
Bills by 1–815.6%
Level after regulation3.9%
Chiefs by 1–824.5%
Chiefs by 9–1620.8%
Chiefs by 17+24.1%

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 +1.8 points to the Bills: the final margin was Chiefs by 6, without the luck Chiefs by 7.8. 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.

  • H. Butker, 50 yds missed · 72% expected
  • H. Butker, 39 yds made · 88% expected
  • H. Butker, 28 yds made · 98% expected
  • H. Butker, 49 yds made · 73% expected
  • Extra point missed · 93% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bills 3 for 15 yards, Chiefs 1 for 10 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
Q2 2:37 Defensive Holding on the Bills (Dane Jackson), 5 yards, wiping out the play +7% KC +2.9 pts
Q2 0:37 Defensive Holding on the Bills, 5 yards +1% KC +0.1 pts
Q3 8:06 Offensive Holding on the Chiefs, 10 yards, wiping out the play +7% BUF +1.8 pts
Q4 12:44 False Start on the Bills (Dawson Knox), 5 yards · pre-snap +3% KC +0.8 pts

Bills penalties, every game · Chiefs penalties, every game · All teams, 2021

When it happened

Chiefs’ chance of winning

As low as 14% 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 Chiefs were ahead in it, below while the Bills were.
#WhenWhat happenedWin probability forNext drive
1 Q1 2:36 The Chiefs converted 3rd & 53rd & 4th downs · 40% expected +10% KC KC: Touchdown
2 Q2 11:16 The Chiefs were stopped on 3rd & 93rd & 4th downs · 36% expected +11% BUF KC: Punt
3 Q2 0:03 H. Butker missed 50-yard field goalKicks · 72% expected for him, 24 of 31 from 45+ before +11% BUF KC: Field goal
4 Q3 10:06 The Chiefs converted 4th & 13rd & 4th downs · 80% expected +10% KC KC: Field goal
5 Q4 2:48 The Bills converted 4th & 43rd & 4th downs · 51% expected +19% BUF BUF: Touchdown
6 Q4 2:31 The Bills were stopped on 3rd & 63rd & 4th downs · 43% expected +20% KC BUF: Touchdown
7 Q4 2:00 The Bills converted 4th & 133rd & 4th downs · 28% expected +35% BUF BUF: Touchdown
8 Q4 1:39 The Chiefs converted 3rd & 103rd & 4th downs · 34% expected +11% KC KC: 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.

  • Rashad Fenton (KC CB), out · 0.2 pts
  • Ike Boettger (BUF G), 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

Bills 10% · Chiefs 90%

Final margin
Chiefs by 6
Luck in points
1.8 for the Bills
Luck-adjusted margin
Chiefs by 7.8
Replay with same day's form
Bills 28% · Chiefs 72% 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 (not available for this game); injuries from snap counts and injury reports. No FTN charting for this game (drops and interception-worthy throws are not modelled).

Methodology and validation · All Divisional round 2021 games · Bills · Chiefs

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