luckadjusted

Week 14 2021 · December 12, 2021

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

49ers at Bengals, Week 14 2021: who deserved to win?

The 49ers beat the Bengals 26–23, but the Bengals played well enough to win it: they take 6 of 10 replays with the same day's form. Luck ran their way: fumble bounces alone were worth 13 points of win probability to the 49ers.

Before kickoff the 49ers were 57% favorites. The game turned on a luck play (QOT, 6:19 left): E. McPherson made 41-yard field goal, worth 29 points of win probability to the 49ers.

Final (OT)

San Francisco 49ers 26
Cincinnati Bengals 23

December 12, 2021 · Paul Brown Stadium · Closing line: 49ers −2.5

Luck index +63 49ers very lucky · −63 Bengals

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. 49ers win 4, Bengals win 6.

  1. 1 SF 22 CIN 3
  2. 2 SF 40 CIN 27
  3. 3 SF 27 CIN 20
  4. 4 SF 33 CIN 30
  5. 5 SF 32 CIN 34
  6. 6 SF 17 CIN 23
  7. 7 SF 9 CIN 19
  8. 8 SF 20 CIN 34
  9. 9 SF 20 CIN 40
  10. 10 SF 16 CIN 45

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

49ers win 37% of them, Bengals 63%, counting the 2% still level after regulation as half each. The line is what actually happened: 49ers by 3.

Show as a table
Final margin in the replaysShare of replays
49ers by 17+6.5%
49ers by 9–1611.2%
49ers by 1–818.4%
Level after regulation2.1%
Bengals by 1–823.0%
Bengals by 9–1618.8%
Bengals by 17+20.1%

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 +4.8 points to the Bengals: the final margin was 49ers by 3, without the luck 49ers 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.

  • R. Gould, 33 yds made · 93% expected
  • E. McPherson, 37 yds made · 90% expected
  • E. McPherson, 28 yds made · 97% expected
  • R. Gould, 24 yds made · 98% expected
  • E. McPherson, 46 yds missed · 79% expected
  • R. Gould, 47 yds missed · 73% expected
  • E. McPherson, 41 yds made · 85% expected
Bar: expected chance of a make. Filled dot: made. Open dot: missed or blocked.

Penalties: 49ers 6 for 40 yards, Bengals 2 for 19 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 7:49 Offensive Holding on the 49ers, 10 yards, wiping out the play +7% CIN +1.9 pts
Q1 1:17 False Start on the Bengals (Tee Higgins), 5 yards · pre-snap +4% SF +0.7 pts
Q2 5:53 Illegal Use of Hands on the 49ers (Ambry Thomas), 5 yards, wiping out the play +16% CIN +4.6 pts
Q2 1:27 Offensive Holding on the 49ers (Jauan Jennings), 10 yards +4% CIN +1.0 pts
Q2 0:30 Taunting on the Bengals (Vonn Bell), 14 yards +6% SF +1.8 pts
Q2 0:18 Delay of Game on the 49ers, 5 yards · pre-snap 0% CIN 0.0 pts
Q3 7:43 Illegal Use of Hands on the 49ers (Ambry Thomas), 5 yards +1% CIN +0.5 pts
QOT 5:35 False Start on the 49ers (George Kittle), 5 yards · pre-snap +8% CIN +0.9 pts

49ers penalties, every game · Bengals penalties, every game · All teams, 2021

When it happened

Bengals’ chance of winning

As low as 0% and as high as 88%. 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 Bengals were ahead in it, below while the 49ers were.
#WhenWhat happenedWin probability forNext drive
1 Q1 9:20 The Bengals fumbled and the 49ers recoveredFumble bounces · loose balls are close to 50/50 +9% SF CIN: Field goal
2 Q2 5:53 Illegal Use of Hands on the 49ers (Ambry Thomas), 5 yards, wiping out the playJudgment calls · 0 flags in 116 snaps before, position avg 1 per 213 +16% CIN CIN: Field goal
3 Q2 1:07 The Bengals fumbled and the 49ers recoveredFumble bounces · loose balls are close to 50/50 +10% SF CIN: End of half
4 Q4 1:31 The Bengals converted 3rd & 103rd & 4th downs · 27% expected +9% CIN CIN: Touchdown
5 Q4 0:20 The 49ers converted 3rd & 103rd & 4th downs · 28% expected +22% SF SF: Missed field goal
6 Q4 0:04 R. Gould missed 47-yard field goalKicks · 73% expected for him, 17 of 26 from 45+ before +27% CIN SF: Touchdown
7 QOT 6:19 The game turned hereE. McPherson made 41-yard field goalKicks · 85% expected for him +29% SF –
8 QOT 2:34 The 49ers converted 3rd & 53rd & 4th downs · 42% expected +9% SF SF: 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.

  • Logan Wilson (CIN LB), out · 0.4 pts
  • Mike McGlinchey (SF T), out (IR) · 0.9 pts
  • Emmanuel Moseley (SF CB), out (IR) · 0.6 pts
  • Elijah Mitchell (SF RB), out · 0.1 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

49ers 79% · Bengals 21%

Final margin
49ers by 3
Luck in points
4.8 for the Bengals
Luck-adjusted margin
49ers by 7.8
Replay with same day's form
49ers 37% · Bengals 63% 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 14 2021 games · 49ers · Bengals

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