Western Michigan vs Central Michigan

Who takes over matters more than that he is out. Among 1,101 games where a starter was absent, the side’s margin came in −0.54 ± 0.67 points when the presumed backup had 150+ career attempts (n = 530) and −2.19 ± 0.69 when he had fewer (n = 534). The ordering is better established than either number on its own.

With no replacement named the penalty is 1.41 points — the average over every absence, measured as the coefficient on “last week’s starter attempted no passes” (t = −2.91). Deliberately not the −3.91 of the raw figure, four fifths of which is a starter being pulled because the game was already lost.

None of this is a validated improvement. The effect on the predicted margin is real — −0.91 points per adjusted yard of downgrade, t = −2.43, and it survives a permutation control at z = −3.12. The effect on the probability is not statistically significant: pooled over 4,899 games it is −0.00045 of log loss at t = −0.87, against the 0.00103 it would need. On the flagged games alone it is −0.0019 at t = −0.60.

Treat these controls as an aid to judgement, not as a better model. The measurement says the crude proxy behind them captures too little — not that the information is absent, since identifying the right replacement after the fact is worth four times as much. Whether naming the announced starter lands nearer that figure is untested, and the only clean way to find out is to fix the numbers now and score them on a season this fit never saw.