When Super Bowl XLIX Starts to Bore You…

I appreciate that the Super Bowl unites all Americans in their inability to read Roman numerals.

(Caution — oxymoron ahead!) If you’re a smart football fan, then you’ve invited folks to your house to watch the game, so you don’t have to drive home drunk on a cold Sunday night in February.

If this year’s Super Bowl is like last year’s, your guests will be bored by halftime, with the Seahawks leading 22‑0.

Or if deflated balls are used, the Patriots could be leading 38‑7 at the end of the third quarter, like when they played the Colts two weeks ago.

In either case, you’ll need something to keep your guests entertained between commercials and after the Katy Perry halftime show. I suggest the following problem.

Imagine that the NFL has eliminated divisions, and there are just two conferences with 16 teams each. To simplify things, every team plays the other 15 teams in their conference exactly once each. At the end of the regular season, what is probability that every team within a conference has a different record? (Assuming, of course, that each team is equally likely to win on any given Sunday, and assuming that ties are not possible.)

It’s not a trivial problem, so I’ll give you some time to think about it. The answer will be revealed on Monday, February 2, 2015; that is, after the game.