Coaches got braver.
Just not on their own half.

A decade of getting braver, and where it stopped

Between 2015 and 2024 the share of fourth downs a team went for rose from 12.4% to 20.0% — a 61% increase. It stopped rising around 2020.

The aggression is not spread evenly across the field. On fourth-and-1 teams go 1% of the time inside the opponent's 40 and 0% from their own 21-40. Same distance, same one yard, opposite behaviour. Everything below is an attempt to find out which of those two numbers is wrong.

How often a team actually converts

A logistic model on splines in yards-to-go and field position, fitted on every third- and fourth-down run or pass since 2015. Test-season log loss 0.6138, AUC 0.702.

Third downs are in the sample on purpose. Coaches choose which fourth downs to go for, so a model fitted on those alone risks learning conversion rate given a coach liked the look. The raw numbers seem to confirm the worry: fourth-down attempts convert +12.2 percentage points more often than third-and-the-same-distance.

Controlled for field position, that gap is zero. The fourth-down coefficient is +0.0154 log-odds (p = 0.65), an average marginal effect of +0.31 points, flat across every distance bucket. The +12.2 was composition — fourth-down attempts happen at different spots on the field. Coach selection is undetectable in the conversion rate, which is also what makes pooling third downs free: ten times the sample at no cost.

The kick, and where the punt lands

Field goals: a spline logistic in kick distance with older seasons down-weighted, because the target is not stationary. Attempts from 51-60 yards went from 61.5% in 2015-2019 to 70.0% in 2023-2024 while everything inside 30 yards sat flat. Test log loss 0.3776.

It still under-predicts by 1.3 points on the test season, and the miss is concentrated at long range — so the engine will be biased against the 50-yard attempt. That bias runs in the same direction as this page's conclusion, which is exactly why it gets tested rather than mentioned: see 7.0.

Punts are not a number but a distribution. The engine needs the spread as well as the mean because win probability bends sharply near both goal lines, and the outcome has a genuine lump in it — a touchback and a fair catch both put the ball on the receiving team's 20. Modelled as a kernel-weighted empirical distribution in net yards, with the touchback carried as its own point mass.

Why win probability and not points

Expected points is the right unit for most of a football game and the wrong one exactly where fourth downs are decided. Down seven with two minutes left, expected points says take the field goal; win probability says a field goal leaves you needing two scores in two minutes.

So every branch is valued in win probability, from a monotone gradient-boosted model fitted on 2015–2024. Test log loss 0.4688 against 0.6915 for a home-field-only baseline, AUC 0.845.

The honest sample size is not the 388,000 plays it was fitted on. Every play in a game shares one label, so the effective sample is closer to the number of games — about 272 a season. Model selection was done with grouped cross-validation on game id for that reason, and every interval quoted here is a game-level bootstrap.

Three branches, one comparison

For any fourth down the engine values all three choices and reports the gap between the best one and the one the coach took.

Go is the conversion probability times the win probability of a first down at the new spot, plus its complement times the win probability of handing over at the line of scrimmage — or a touchdown, when the sticks are past the goal line. Kick is the make probability times a three-point lead and a kickoff, plus a miss giving the opponent the ball at the spot of the kick. Punt is the expectation over the whole landing distribution, not the value at its mean.

There are two implementations: a readable one that handles a single state and is covered by tests pinning every sign convention, and a vectorised one that makes 15,545 decisions tractable. A test runs real fourth downs through both and requires them to agree — a rewrite is exactly where a sign convention quietly stops matching.

Ask it about a situation

Every state below was precomputed — the models cannot run in a browser and there is no server behind this page — so the answer is a lookup over 113,400 situations. Timeouts are fixed at three each, which is why the last two minutes are not offered: that is where timeouts decide the answer.

What the gap is worth, and how sure we are

Run over all 15,545 fourth downs in 2021–2024, the model agrees with the coach 65% of the time. The disagreements total 22 wins a season across the league, or 0.69 per team.

Almost all of it sits in one place. On 1-2 to go from own 21-40 — 682 decisions — coaches go 24% of the time and the model says 88%. That single cell is worth 2.40 wins a season. It is the same asymmetry stage 1.0 opened with, and the model's answer is that the near-side number is the wrong one.

How often the call is actually close

A mean cost on its own would imply a confidence the model does not have. Most disagreements are worth very little: 16% of all decisions are disagreements worth under a single point of win probability, and only 6% are worth more than three.

Does the finding survive its own worst case?

The field-goal model is known to under-rate long attempts, which biases the engine toward going for it — the direction of this page's conclusion. Re-grading with every field goal handed an extra 8 points of make probability, far more than the measured error, moves the share of go recommendations from 45.3% to 43.0% and leaves 36% of the field goals coaches actually kicked still called as go. The conclusion is not an artefact of that bias.

The league table is softer than it looks

A team-season is only a few dozen live fourth downs, so these totals carry real sampling error. Each interval resamples the team's games rather than its decisions, because everything in one game shares an opponent and a score script. The most and least conservative teams do separate — but of the 496 pairs of teams, 429 have overlapping intervals. This table supports "these four teams differ from those four", not a ranking.