Why a 90% favorite every week still goes 17-0 only one time in six

Here is a small calculation that surprises people. A team that is a 90% favorite in every one of seventeen games finishes undefeated with probability 0.9^17 = 16.7%, about one season in six. Most real teams are never 90% favorites every week, so the practical number is much lower.

const perfect = (p, games = 17) => Math.pow(p, games);
[0.7, 0.8, 0.9, 0.95].map(p => [p, (perfect(p) * 100).toFixed(2) + '%']);
// [[0.7,'0.23%'],[0.8,'2.25%'],[0.9,'16.66%'],[0.95,'41.8%']]

Two things matter when you simulate this rather than just compute it. First, weekly win probabilities differ: a 95% game against a bad team and an 70% game on the road average to something that gives a lower perfect-season chance than the same average spread evenly (Jensen's inequality at work, since the product is concave in log space). Second, if you run Monte Carlo seasons, you need thousands of runs to see a rare event stably: at p=0.7 the 0.23% outcome needs roughly 10,000 seasons to appear 20-ish times.

I built a small free browser game around this idea, 17-0 Game: you draft an all-time roster from random teams and eras and simulate a 17-game season to see if you can go undefeated. The calculations above are why most runs end at 13 or 14 wins, and why the occasional 17-0 feels earned.