luckadjusted
NFL Week 9 · 2026

Week 5 2021 · October 10, 2021

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

Bills at Chiefs, Week 5 2021: who deserved to win?

The Bills beat the Chiefs 38–20, but the replays lean toward the Chiefs: they take 6 of 10 with the same day's form.

Before kickoff the Chiefs were 57% favorites. The biggest swing (Q4, 11:50 left): Roughing the Passer on the Chiefs (Frank Clark), 15 yards, wiping out the play, worth 16 points of win probability to the Bills.

Final

Buffalo Bills 38
Kansas City Chiefs 20

October 10, 2021 · GEHA Field at Arrowhead Stadium · Closing line: Chiefs −2.5

Luck index +60 Bills very lucky · −60 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 4, Chiefs win 6.

  1. 1 BUF 45 KC 24
  2. 2 BUF 47 KC 34
  3. 3 BUF 34 KC 27
  4. 4 BUF 29 KC 27
  5. 5 BUF 44 KC 47
  6. 6 BUF 44 KC 50
  7. 7 BUF 26 KC 35
  8. 8 BUF 27 KC 41
  9. 9 BUF 30 KC 49
  10. 10 BUF 7 KC 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

Bills win 40% of them, Chiefs 60%, counting the 2% still level after regulation as half each. The line is what actually happened: Bills by 18.

Show as a table
Final margin in the replaysShare of replays
Bills by 17+7.2%
Bills by 9–1611.7%
Bills by 1–818.7%
Level after regulation2.3%
Chiefs by 1–823.2%
Chiefs by 9–1618.9%
Chiefs by 17+18.0%

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 +1.7 points to the Bills: the final margin was Bills by 18, without the luck Bills by 16.3. 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, 38 yds made · 93% expected
  • T. Bass, 30 yds made · 96% expected
  • H. Butker, 54 yds made · 72% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bills 10 for 103 yards, Chiefs 7 for 55 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 12:12 Defensive Offside on the Bills (A.J. Epenesa), 4 yards · pre-snap +7% KC +0.9 pts
Q1 10:41 Defensive Holding on the Bills (Tre'Davious White), 5 yards +6% KC +1.3 pts
Q1 10:37 Offensive Holding on the Chiefs (Demarcus Robinson), 10 yards +3% BUF +0.8 pts
Q1 9:01 False Start on the Chiefs, 5 yards · pre-snap +2% BUF +0.8 pts
Q1 3:49 Offensive Holding on the Bills, 10 yards, wiping out the play +7% KC +3.4 pts
Q1 3:21 Intentional Grounding on the Bills (Josh Allen), 18 yards +4% KC +1.3 pts
Q1 3:14 Defensive Offside on the Chiefs, 5 yards, wiping out the play · pre-snap +8% KC +2.9 pts
Q1 0:23 False Start on the Chiefs (Travis Kelce), 5 yards · pre-snap +3% BUF +0.5 pts
Q2 14:23 Defensive Holding on the Bills (Siran Neal), 5 yards +5% KC +1.2 pts
Q2 2:20 False Start on the Chiefs, 5 yards · pre-snap +3% BUF +0.7 pts
Q2 0:31 Offensive Pass Interference on the Chiefs, 10 yards, wiping out the play +7% BUF +2.6 pts
Q3 5:40 Roughing the Passer on the Bills (Ed Oliver), 15 yards +2% KC +3.0 pts
Q3 0:07 Defensive Pass Interference on the Bills (Tre'Davious White), 18 yards +1% KC +1.3 pts
Q4 12:13 Offensive Holding on the Bills, 8 yards, wiping out the play +4% KC +1.9 pts
Q4 11:50 Roughing the Passer on the Chiefs (Frank Clark), 15 yards, wiping out the play +16% BUF +5.6 pts
Q4 4:25 Unnecessary Roughness on the Bills (Jordan Poyer), 15 yards 0% KC +1.9 pts
Q4 4:20 Neutral Zone Infraction on the Bills (Jerry Hughes), 5 yards · pre-snap 0% KC +0.5 pts

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

When it happened

Chiefs’ chance of winning

As low as 0% and as high as 85%. 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 12:12 Defensive Offside on the Bills (A.J. Epenesa), 4 yardsPre-snap flags · 2 flags in 602 snaps before, position avg 1 per 266 +7% KC KC: Field goal
2 Q1 4:36 The Chiefs fumbled and the Bills recoveredFumble bounces · loose balls are close to 50/50 +7% BUF KC: Touchdown
3 Q1 3:49 Offensive Holding on the Bills, 10 yards, wiping out the playJudgment calls +7% KC KC: Touchdown
4 Q1 3:21 The Bills were stopped on 3rd & 113rd & 4th downs · 31% expectedIntentional Grounding on the Bills (Josh Allen), 18 yardsJudgment calls · 6 flags in 2577 snaps before, position avg 1 per 711 +6% KC BUF: Punt
5 Q1 3:14 Defensive Offside on the Chiefs, 5 yards, wiping out the playPre-snap flags +8% KC BUF: Punt
6 Q2 0:31 Offensive Pass Interference on the Chiefs, 10 yards, wiping out the playJudgment calls +7% BUF BUF: End of half
7 Q3 7:20 Return touchdown by the BillsSpecial teams +9% BUF BUF: Opp touchdown
8 Q4 11:50 Roughing the Passer on the Chiefs (Frank Clark), 15 yards, wiping out the playJudgment calls · 9 flags in 1857 snaps before, position avg 1 per 266 +16% BUF 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.

  • Chris Jones (KC DT), out · 0.8 pts
  • Charvarius Ward (KC CB), out · 0.6 pts
  • Matt Milano (BUF LB), out · 0.6 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 100% · Chiefs 0%

Final margin
Bills by 18
Luck in points
1.7 for the Bills
Luck-adjusted margin
Bills by 16.3
Replay with same day's form
Bills 40% · Chiefs 60% 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 (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 Week 5 2021 games · Bills · Chiefs

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