What a first-year head coach costs

A program that fires its coach and hires a new one loses about 2.3 rating points in our preseason college football model before a single snap is played. That is not a guess about culture fit or a new playbook. It is one fitted coefficient, minus 2.2511, sitting inside the same six-input formula that produces every number on our board.

Where the flag sits in the model

The rating is a linear composite. Six things about a team going into a season turn into one number, points against an average opponent on a neutral field. The six inputs are prior season SP plus (performance carried forward), a four year blue chip ratio (talent), returning production, net portal flow, the average star rating of incoming transfers, and a flag for a first year head coach, labeled coaching continuity inside the model.

That flag is a plain 0 or 1, set to 1 if the program has a first year head coach that season. The source is a single field, is_first_year_at_program, in our coaching intelligence table, and it defaults to false when that table has no row. Everything else in the formula is a continuous measurement. This one is a switch.

The formula

The whole thing fits on one line:

rating = -10.716
         + 0.5634 * prior_sp
         + 19.2118 * bcr
         + 5.8729 * ret_ppa
         - 0.0947 * portal_net
         + 1.7239 * tin_stars
         - 2.2511 * new_hc

It was fit by ordinary least squares, regressing actual end of season SP plus on these six preseason inputs, trained on the 2021 through 2023 seasons only, 389 team seasons, in sample R squared 0.657. The new_hc weight is the last term, and it is the only one of the six that ever takes just two values.

A fixed cost, not a scaled one

The other five weights move on a sliding scale, because the inputs they multiply move too. Prior season SP plus swings across tens of points from the top of the sport to the bottom, which makes performance carryover the biggest lever overall even though its per point weight is modest. Blue chip ratio carries the heaviest coefficient per unit, a 0.10 gap in four year blue chip ratio is worth roughly 1.9 rating points on its own. Returning production lands third, and the portal terms are smaller adjustments on top of those three.

The coaching flag does not scale with anything. No partial credit for a coach in year one versus year two, no adjustment for how the hire was received. The flag is on or off, and when it is on the team loses about 2.3 points, full stop. Walk that through the same math that turns a rating into a win total, a per game win probability from the normal curve of the rating gap, standard deviation 17 points, home field worth 2.5, non FBS opponents pinned at minus 22, and the cost tops out at about six tenths of an expected win over a 12 game season. That is its ceiling, reached only if every game on the schedule is a true coin flip before the penalty is applied, because the normal curve is steepest at the middle and flattens out toward the blowouts. A realistic Power Five schedule, a mix of competitive games and lopsided ones, lands closer to half a win. We are not attaching that swing to a specific team here. The point is the shape of the cost, fixed, not sliding, and capped well under a full win even at its ceiling.

Getting the flag right

Here is why we treat this input carefully instead of trusting it blindly. Our coaching intelligence snapshots from August 4 carried a null value for is_first_year_at_program on a batch of programs. A naive dedupe that just grabbed the latest snapshot row would have read that null as false, silently marking real first year hires, including the ones at Michigan and Southern Miss, as returning continuity instead of a coaching change.

A null flag reads as false, and false is worth 2.3 points more than true, so getting this one field wrong does not throw a small error into the rating. It moves a team by nearly the same amount as a real coaching change would, in the wrong direction. The loader now prefers the latest non null flag it can find and, failing that, checks whether the coach’s start year matches the season being rated. A field worth this much does not get to default silently.

Did it hold up out of sample

The coaching term is not tested alone, it rides inside the full formula, so this is the whole model’s record. Train on 2021 through 2023, then compare each held out season’s expected wins to actual results, for every team with at least eight graded games, against a baseline of last year’s SP plus walked through the schedule.

Season	Teams	Composite MAE	SP plus baseline
2024	133	1.844	2.012
2025	134	1.915	1.919
Average		1.880	1.966

The composite wins clearly in 2024, by about 0.17 of a win, and 2025 is a statistical tie, a gap of 0.004. Averaged, the edge is about 0.09 of a win, winning the average without giving a season back. That is a real improvement and a modest one.

What this does not do is claim anything about the market. The composite validates predicting actual wins, nothing about beating a spread or a total. We have no archive of preseason win total lines going back far enough to grade closing line value, so no market claim is on the table. An average miss of about 1.9 wins per team means any single number this formula produces, coaching flag included, is a lean, not a lock.

What it powers

This formula, coaching flag and all, is the engine behind our expected wins and win total leans for 2026. The full field lives at edgelabs.bet/cfb/power-ratings, and the win total board that comes out of it is at edgelabs.bet/cfb/win-total-predictions. Members get the leans first, with the sample and the error attached to each one. Founding access is open at edgelabs.bet/join.