Week 4 2025 · September 20, 2025
Boise State at Air Force, Week 4 2025: who deserved to win?
Boise State beat Air Force 49–37, and the replays lean its way: with the same day's form, it wins 8 of 10.
Before kickoff Boise State was a 75% favorite.
Final
 Boise State Broncos | 49 |
|---|---|
 Air Force Falcons | 37 |
Replay with same day's form
Luck index +25 Boise State about even · −25 Air Force
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. Boise State wins 8, Air Force wins 2.
- 1 BOIS 55 AF 17
- 2 BOIS 49 AF 21
- 3 BOIS 35 AF 14
- 4 BOIS 49 AF 31
- 5 BOIS 52 AF 38
- 6 BOIS 45 AF 35
- 7 BOIS 28 AF 21
- 8 BOIS 45 AF 42
- 9 BOIS 31 AF 35
- 10 BOIS 20 AF 34
Three other ways to ask
Each answers a different question, so none of them replaces the replay above.
Before kickoff
The closing betting line, turned into a probability. What everyone knew before the game.
Same teams, fresh 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.
Only coin-flips re-rolled
Every kick, fumble bounce, conversion and judgment call redrawn; everything else fixed. The narrowest view of luck.
How 4,000 replays ended
Boise State wins 75% of them, Air Force 25%, counting the 5% still level after regulation as half each. The line is what actually happened: Boise State by 12.
Show as a table
| Final margin in the replays | Share of replays |
|---|---|
| Boise State by 17+ | 34.3% |
| Boise State by 9–16 | 19.2% |
| Boise State by 1–8 | 18.2% |
| Level after regulation | 5.2% |
| Air Force by 1–8 | 13.9% |
| Air Force by 9–16 | 5.7% |
| Air Force by 17+ | 3.6% |
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.
Penalties: Boise State 11 for 97 yards, Air Force 6 for 35 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
| When | Flag | Win probability for |
|---|---|---|
| Q1 7:45 | Personal Foul on Air Force, 8 yards | +1% BOIS +0.5 pts |
| Q1 6:28 | Roughing the Passer on Boise State, 15 yards | +4% AF +2.4 pts |
| Q1 6:23 | Holding on Air Force, 10 yards | +3% BOIS +1.7 pts |
| Q1 4:24 | False Start on Boise State, 5 yards · pre-snap | +1% AF +0.7 pts |
| Q1 1:55 | Holding on Boise State, 10 yards | 0% AF 0.0 pts |
| Q2 12:57 | False Start on Boise State, 5 yards · pre-snap | 0% AF +0.4 pts |
| Q2 12:47 | False Start on Boise State, 5 yards · pre-snap | 0% AF +0.4 pts |
| Q2 9:54 | Offside on Air Force, 5 yards · pre-snap | +1% BOIS +0.7 pts |
| Q2 6:28 | Penalty on Boise State, 7 yards | +1% AF +1.2 pts |
| Q2 3:29 | Holding on Boise State, 10 yards | +1% AF +0.8 pts |
| Q2 2:47 | Penalty on Boise State, 15 yards | +1% AF +0.9 pts |
| Q2 1:05 | Holding on Air Force, 0 yards | 0% BOIS 0.0 pts |
| Q2 0:43 | Illegal Formation on Boise State, 5 yards · pre-snap | +1% AF +0.5 pts |
| Q2 0:26 | Pass Interference on Air Force, 7 yards | +2% BOIS +1.7 pts |
| Q2 0:20 | Holding on Boise State, 10 yards | +1% AF +1.3 pts |
| Q3 7:35 | False Start on Air Force, 5 yards · pre-snap | +2% BOIS +1.1 pts |
| Q4 8:21 | Penalty on Boise State, 10 yards | +2% AF +1.3 pts |
When it happened
Air Force’s chance of winning
Numbers mark the biggest luck moments, listed below.
| # | When | What happened | Win probability for | Next drive |
|---|---|---|---|---|
| 1 | Q1 10:33 | Boise State converted 3rd & 73rd & 4th downs · 41% expected | +4% BOIS | BOIS: Touchdown |
| 2 | Q1 6:28 | Roughing the Passer on Boise State, 15 yardsJudgment calls | +4% AF | AF: Punt |
| 3 | Q2 14:57 | Air Force was stopped on 4th & 23rd & 4th downs · 68% expected | +4% BOIS | AF: Touchdown |
| 4 | Q3 12:29 | Boise State converted 3rd & 63rd & 4th downs · 46% expected | +5% BOIS | BOIS: Touchdown |
| 5 | Q3 7:19 | Air Force converted 3rd & 83rd & 4th downs · 37% expected | +5% AF | AF: Field goal |
| 6 | Q3 5:56 | Air Force converted 3rd & 93rd & 4th downs · 35% expected | +5% AF | AF: Field goal |
| 7 | Q3 4:06 | Air Force was stopped on 3rd & 33rd & 4th downs · 60% expected | +4% BOIS | AF: Field goal |
| 8 | Q3 1:41 | Air Force was stopped on 3rd & 33rd & 4th downs · 52% expected | +4% BOIS | AF: Field goal |
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
Boise State 96% · Air Force 4%
- Final margin
- Boise State by 12
- Luck in points
- 3.8 for Boise State
- Luck-adjusted margin
- Boise State by 8.2
- Replay with same day's form
- Boise State 75% · Air Force 25% unchanged: why
About these numbers
Play-by-play and expected points from CollegeFootballData.com via cfbfastR; win probability from our own model of the score, the possession and the betting line; kicks valued against each kicker’s own record. College play-by-play has no charting of drops or interception-worthy throws and no injury reports, so those kinds of luck aren’t counted here.
Methodology and validation · All Week 4 2025 games · 
Boise State · 
Air Force
More from Week 4 2025
- Fresno State at Hawai'i FRES 23–21 · replay 24% for the winner
- UTSA at Colorado State UTSA 17–16 · replay 40% for the winner
- UNLV at Miami (OH) UNLV 41–38 · replay 50% for the winner
- Nevada at Western Kentucky WKU 31–16 · replay 73% for the winner
- Wyoming at Colorado COLO 37–20 · replay 91% for the winner
- Idaho at San José State SJSU 31–28 · replay 91% for the winner
- California at San Diego State SDSU 34–0 · replay 92% for the winner
- McNeese at Utah State USU 48–7 · replay 97% for the winner
- Troy at Buffalo TROY 21–17 · replay 30% for the winner
- Arkansas at Memphis MEM 32–31 · replay 30% for the winner
- Syracuse at Clemson SYR 34–21 · replay 34% for the winner
- NC State at Duke DUKE 45–33 · replay 35% for the winner