luckadjusted

Week 15 2021 · December 19, 2021

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

Bengals at Broncos, Week 15 2021: who deserved to win?

The Bengals beat the Broncos 15–10 and were the better team on the day: replayed with the same form, they win 7 of 10.

Before kickoff the Broncos were 59% favorites. The biggest swing (Q1, 3:44 left): Offensive Holding on the Bengals, 5 yards, wiping out the play, worth 16 points of win probability to the Broncos.

Final

Cincinnati Bengals 15
Denver Broncos 10

December 19, 2021 · Empower Field at Mile High · Closing line: Broncos −3

Luck index +33 Bengals lucky · −33 Broncos

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. Bengals win 7, Broncos win 3.

  1. 1 CIN 55 DEN 31
  2. 2 CIN 26 DEN 10
  3. 3 CIN 30 DEN 17
  4. 4 CIN 37 DEN 27
  5. 5 CIN 37 DEN 30
  6. 6 CIN 20 DEN 16
  7. 7 CIN 19 DEN 17
  8. 8 CIN 21 DEN 24
  9. 9 CIN 10 DEN 17
  10. 10 CIN 0 DEN 16

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

Bengals win 67% of them, Broncos 33%, counting the 2% still level after regulation as half each. The line is what actually happened: Bengals by 5.

Show as a table
Final margin in the replaysShare of replays
Bengals by 17+19.3%
Bengals by 9–1620.8%
Bengals by 1–824.8%
Level after regulation2.3%
Broncos by 1–818.3%
Broncos by 9–169.6%
Broncos 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 +5.0 points to the Bengals: the final margin was Bengals by 5, without the luck even. 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.

  • E. McPherson, 53 yds made · 60% expected
  • B. McManus, 54 yds made · 59% expected
  • B. McManus, 51 yds missed · 65% expected
  • E. McPherson, 58 yds made · 52% expected
  • E. McPherson, 26 yds made · 98% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: Bengals 6 for 38 yards, Broncos 6 for 60 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 3:44 Offensive Holding on the Bengals, 5 yards, wiping out the play +16% DEN +5.0 pts
Q2 13:00 False Start on the Bengals (Tre Flowers), 5 yards · pre-snap +3% DEN +0.5 pts
Q2 9:16 False Start on the Bengals, 5 yards · pre-snap +1% DEN +0.5 pts
Q2 2:00 Neutral Zone Infraction on the Bengals (B.J. Hill), 5 yards · pre-snap +2% DEN +0.7 pts
Q3 9:22 Defensive Holding on the Broncos, 5 yards +2% CIN +0.9 pts
Q3 8:57 Face Mask on the Broncos (McTelvin Agim), 15 yards +5% CIN +1.9 pts
Q3 1:21 Taunting on the Broncos (Tim Patrick), 15 yards +7% CIN +1.7 pts
Q4 13:33 Defensive Pass Interference on the Bengals (Eli Apple), 13 yards +12% DEN +2.1 pts
Q4 6:59 Illegal Block Above the Waist on the Broncos, 5 yards +2% CIN +0.5 pts
Q4 4:09 Offensive Holding on the Broncos, 10 yards +5% CIN +0.6 pts
Q4 1:04 Offensive Holding on the Broncos, 10 yards +6% CIN +0.4 pts
Q4 0:27 Defensive Offside on the Bengals (Trey Hendrickson), 5 yards, wiping out the play · pre-snap +6% CIN +0.7 pts

Bengals penalties, every game · Broncos penalties, every game · All teams, 2021

When it happened

Broncos’ chance of winning

As low as 0% and as high as 68%. 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 Broncos were ahead in it, below while the Bengals were.
#WhenWhat happenedWin probability forNext drive
1 Q1 3:44 Offensive Holding on the Bengals, 5 yards, wiping out the playJudgment calls +16% DEN DEN: Punt
2 Q2 0:14 B. McManus missed 51-yard field goalKicks · 65% expected for him, 29 of 40 from 45+ before +11% CIN DEN: Punt
3 Q3 1:21 Taunting on the Broncos (Tim Patrick), 15 yardsJudgment calls · 2 flags in 1758 snaps before, position avg 1 per 399 +7% CIN CIN: Touchdown
4 Q4 14:50 The Broncos converted 3rd & 83rd & 4th downs · 31% expected +10% DEN DEN: Turnover
5 Q4 13:33 Defensive Pass Interference on the Bengals (Eli Apple), 13 yardsJudgment calls · 12 flags in 1799 snaps before, position avg 1 per 213 +12% DEN DEN: Turnover
6 Q4 12:41 The Broncos converted 3rd & 33rd & 4th downs · 51% expected +8% DEN DEN: Turnover
7 Q4 10:39 The Broncos fumbled and the Bengals recoveredFumble bounces · loose balls are close to 50/50 +12% CIN DEN: Punt
8 Q4 1:04 Offensive Holding on the Broncos, 10 yardsJudgment calls +6% CIN CIN: End of game

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.

  • Dre'Mont Jones (DEN DE), out · 0.5 pts
  • Graham Glasgow (DEN G), out (IR) · 0.4 pts
  • Malik Reed (DEN LB), out (IR) · 0.3 pts
  • Kenny Young (DEN LB), out · 0.2 pts
  • Riley Reiff (CIN T), out (IR) · 0.9 pts
  • Chidobe Awuzie (CIN CB), out (IR) · 0.5 pts
  • Logan Wilson (CIN LB), out · 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

Bengals 47% · Broncos 53%

Final margin
Bengals by 5
Luck in points
5.0 for the Bengals
Luck-adjusted margin
even
Replay with same day's form
Bengals 67% · Broncos 33% 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 Week 15 2021 games · Bengals · Broncos

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