Notropis asked this question in last night’s Ace of Spades HQ MNF open thread:
Here’s a fun math question (or not):
Examine the NFL schedule, and determine what the maximum number of undefeated teams could be, at any point in the season.
Ex: after week 1, I’d guess it’d be 16, unless someone had a week 1 bye.
Since the order of the NFL schedule is too random to properly assign victories between Weeks 2 and 16 (e.g., a team that won in Week 1 may or may not face another 1-0 team in Week 2), it is impossible to answer that without a Cray supercomputer.
However, since the content of the NFL schedule is entirely predictable, we can figure out how many teams can finish 16-0. The schedule of every NFL team is made up of the following:
– A home-and-home series against each of the other three division rivals.
– A game apiece against the four teams of a single division in the other conference.
– A game apiece against the three teams in the same conference that finished in the same divisional order the prior season (i.e. the NFC North champion will face the NFC East champion, the NFC South champion, and the NFC West champion).
– A game apiece against the other three teams of a single division in the same conference.
A single team that goes 16-0 (Team A) eliminates from a 16-0 possibility the other three teams in its division, all four teams of its “interconference” division schedule, the three teams that finished in the same divisional spot the prior season, and the other three teams of its “intraconference” division schedule. That leaves 6 teams in that same conference and 12 teams in the other conference that could go 16-0.
A second team in the same conference that goes 16-0 (Team B) eliminates from a 16-0 possibility its two division rivals that didn’t face Team A, all four teams of its “interconference” division schedule, the two teams that finished in the same divisional spot the previous season that didn’t face Team A, and the team of its “intraconference” division schedule that didn’t face Team A. That leaves just 8 teams in the other conference that could go 16-0.
The first team in the other conference that goes 16-0 (Team C) eliminates from a 16-0 possibility, at a minimum, its three division rivals and the team that finished in the same divisional spot the previous season that didn’t face Team A or Team B. If the “intraconference” division opponents for Team C are not the same as the “interconference” division opponents for Team A or Team B, Team C also eliminates the other 3 teams of that division.
If, however, they are the same, a fourth team (Team D) could go 16-0.
