Bears Field Goal Decision Methodology
Methods and sources for "A Toss-Up From 58 Yards." It asks which of Chicago's three choices on 4th and 15 at the New England 40, with 1:39 left and a 27-21 lead, gave the best chance to win, judged only on what was known before the snap. The data window is through Oct. 22, 2026: the game itself, with every model and estimate built from games played before it.
- The question and the decision state
- Where each number comes from
- How the options are valued
- The historical drives check
- Uncertainty and labels
- Limits
The question and the decision state
On Oct. 22, 2026, Chicago led New England 27-21 with 1:39 (99 seconds) left and faced 4th and 15 at the New England 40, after a 10-yard sack on third down. New England had used its last timeout; Chicago had two. Cairo Santos kicked a 58-yard field goal, and Chicago won 30-24. We compared kicking, punting and going for it, using only information available before the snap. The state comes from nflverse play-by-play (game 2026_07_NE_CHI, play 3945) and was checked against ESPN's game story. A missed kick beyond the 20 returns the ball to the spot of the kick, 8 yards behind the line, so a miss would have given New England the ball at its own 48.
The owner asked for this review on Oct. 23, 2026, and the brief was written in the same session as the analysis, so the question and acceptance criteria were not fixed before the numbers were seen. The labels for the size of a gap were carried over unchanged from our earlier review of Tampa Bay and Dallas, where they were fixed before any data was seen.
Where each number comes from
Every number is produced by the scripts in research/nfl-bears-patriots-field-goal/ in the site repository and collected in results/key_numbers.csv. The pipeline is adapted from the research behind "Not All Field Goals Weigh the Same."
| Numbers in the article | Source | Script or output |
|---|---|---|
| Clock, score, field position, timeouts, weather, the earlier 53-yard miss, and Santos's record before the kick | nflverse play-by-play 2014 to 2026, checked against ESPN | 02_case.py, results/case_reconstruction.csv, results/kicker_history.csv |
| Win probability for each option, after a make, a miss, a punt or a failed fourth down; break-even make probabilities | Our win-probability model, fit on games before Oct. 22, 2026 | 03_fit_models.py, 05_decisions.py, results/decision_values.csv |
| Make probability at 58 yards (65%, range 59% to 69%) and the Santos-adjusted 64% | Field-goal model on every attempt from 2016 to Oct. 19, 2026 | 04_components.py, results/fg_estimates.csv |
| Fourth-and-long conversion (20%), punt landing spots, kickoff starts and late-game clock use | nflverse play-by-play before Oct. 22, 2026 | 04_components.py, results/conv_empirical.csv, results/punt_outcomes.csv, results/transition_timing.csv |
| Touchdown rates on late drives, Chicago's answer rate, and the model-free decision values | nflverse drives, 2016 to Oct. 19, 2026 | 06_empirical.py, results/empirical_td_rate.csv, results/empirical_decision.csv |
| Refit ranges and the share of refits favoring each option | 50 refits of the win-probability model on resampled games | 05_decisions.py, results/decision_uncertainty.csv, results/decision_shares.csv |
| Figures 1 and 2 | The result files above | 09_web_figures.py, figures/web/source/ |
08_key_numbers.py checks the information boundary: the win-probability model's training data end on Oct. 19, 2026, before the game. The case game is read only for the decision state, and its outcome rows are marked as hindsight.
How the options are valued
Win-probability model. A gradient-boosted classifier (XGBoost) predicts whether the team with the ball wins from score, time, field position, down and distance, timeouts, home field and the pregame point spread, decayed over the game. It was trained on 390,323 plays from Sept. 8, 2016 to Oct. 19, 2026. On the 2025 season, held out, its Brier score was 0.159, close to nflfastR's 0.158 on the same plays. A second version without the point spread is reported as an alternative.
Field goal. A logistic model of makes on distance (a spline), season trend, roof, wind and cold, fit on attempts from 2016 to Oct. 19, 2026, estimated a 64.6% make chance for 58 yards outdoors at 61 degrees with a 3 mph wind. Its 95% confidence interval was 59% to 69%. A kicker adjustment, shrunk toward the league with empirical Bayes using Santos's 106 attempts of 45 yards or more since 2014, moved it to 64%. A make is followed by a kickoff, valued over 2025 and 2026 kickoff starts; a miss gives New England the ball at its own 48.
Punt. We used 738 punts from the opponent 36 to 44 since 2021, with each landing spot re-centred on the 40 and touchbacks kept at the 20. Go for it. Teams converted 46 of 235 fourth downs needing 13 to 17 yards from 2016 on. A conversion is valued as a win, because three kneel-downs would run out the clock against a defense without timeouts. A failure is valued over the spots where New England took over after failed attempts.
Each option's value is the probability-weighted average of the win probabilities after its outcomes. The break-even make probability against the punt is the value of the punt minus the value after a miss, divided by the value after a make minus the value after a miss.
The historical drives check
General win-probability models are fit mostly on situations far from the end of a game. As a check that does not rely on the model, we took fourth-quarter drives that started with 45 to 150 seconds left by an offense trailing by 4 to 8 points, which needed a touchdown. From their own 1 to 15, 10 of 67 scored a touchdown (15%); from their own 40 to 60, 21 of 57 did (37%). Teams trailing by 1 to 3 points with 15 to 60 seconds left scored on 35 of 136 drives (26%), our stand-in for Chicago answering a New England touchdown.
New England's chance to win after a punt or a miss was approximated as the touchdown rate times the chance Chicago did not answer. The made-kick branch keeps the model's value, because no team in the sample came back from 9 to 11 points down in that window. This puts the punt at 88.9% and the kick at 88.5%, with a break-even of 66%. Using only drives by offenses without timeouts, the two are tied at 90.3% and the break-even is 65%. The approximation ignores the extra point, overtime, and the exact clock, and the samples are small.
Uncertainty and labels
We refit the win-probability model 50 times on game-level resamples. The kick's edge over the punt ranged from -0.8 to 2.0 points across 95% of refits, the kick was ahead in 66% of them, and the break-even ranged from 46% to 73%. Without the point spread, the kick was ahead by 1.1 points, with a break-even of 56%, in 88% of refits. The kick beat going for it in all 50 refits of both versions. We label a gap of 2 points or more as clear, 1 to 2 points as a lean, and less than 1 point as a toss-up; the labels describe the size of a gap, not whether a choice was right.
Limits
- Model levels. Our model gave Chicago 92.9% for its best option, while nflfastR's pre-snap estimate was 97.3%. The two measure different things (nflfastR does not compare options), but the gap shows that end-game levels differ across models.
- What the models cannot see. No tracking or personnel data, the wind at the snap rather than at kickoff, or the staff's read of Santos that night. ESPN reported that Johnson first planned to punt and that Santos asked for the kick; our estimates cannot judge what that request said about his chances.
- Small samples. Santos's 0 for 6 from 56 yards or longer, and the historical drive groups of 20 to 67 drives, are too small to stand alone.
- Simplifications. A converted fourth down is valued as a certain win, punt and kick timings are late-game medians, and a punt return touchdown is valued with a typical kickoff start.