How many perfect seasons should a 32-team league expect? A quick binomial estimate

Perfect NFL seasons are rare, but how rare should they be if you only know the per-game win probability? A binomial model gives a surprisingly clear answer.

One team

If a team wins each game independently with probability p, the chance it wins all 17 is p^17:

p per game	P(17-0)
0.80	2.3%
0.85	6.3%
0.90	16.7%
0.95	41.8%

A whole league

Now take a league of 32 teams. If the average team is a 50% favorite each week, the chance any specific team goes 17-0 is 0.5^17, about 0.0008%, or 1 in 131,072. Across 32 teams the chance that at least one is perfect by pure luck is about 32 / 131,072, roughly 0.024%, or about once in 4,100 seasons.

Real leagues are not made of coin flips, of course: a few teams are much stronger than average, which is why perfect seasons occasionally happen. But the model shows why they are so exceptional: you need a team that is a heavy favorite every week, not just most weeks.

Try it yourself

def p_perfect(p, games=17):
    return p ** games

for p in (0.80, 0.85, 0.90, 0.95):
    print(p, round(p_perfect(p) * 100, 1))

If you would rather draft a roster and simulate the season than do the arithmetic, 17-0 Game is a free browser sim built around exactly this question.