Tuesday, December 11, 2007

How Many Teams Could Go Undefeated in One Season?

This comes from an e-mail conversation I had at work with the guys I watch the games with. One of them posed the question of how many undefeated teams can there be in the same season. Below is an informal proof answering the question.

An undefeated team will have won all of their divisional games. So the maximum possible number is ≤8.

Each team in conference A will play all the teams in one of the divisions in conference B. So if there are 8 teams with that have won all of their divisional games, then there will be 4 matchups between otherwise undefeated teams. There are 3 possible outcomes: all 4 matchups are won by conference A teams (4 undefeated teams in conference A, 0 in B), 3 are won by conference A teams (3 in A, 1 in B), 2 are won by conference A teams (2 in A, 2 in B).

Now there are the intraconference games to consider. The 4 divisions within each conference are paired up so that each team in division C plays each team in division D. If there are 2 undefeated teams within the conference after interconference and divisional play, they will not necessarily play each other in intraconference play, leaving 2 undefeated teams in each conference for a total of 4. If there are 3 remaining undefeated teams within the conference, then 2 are guaranteed to meet each other in intraconference play, leaving 2 undefeated teams (as one will lose) in that conference but only one in the other conference for a total of 3. If there all 4 remaining undefeated teams are in the same conference, then there will be 2 undefeated teams remaining after intraconference play.

Therefore, 4 teams could have perfect seasons in the same year at most, but only 2 are possible in each conference.

Here's an example of such a scenario using 2007 matchups.

New England, Pittsburgh, Jacksonville, San Diego, Dallas, Green Bay, Tampa Bay, and Seattle all go 6-0 in divisional play.

INTERCONFERENCE
AFC East vs. NFC East
AFC North vs. NFC West
AFC South vs. NFC South
AFC West vs. NFC North

New England vs. Dallas. New England wins.
Pittsburgh vs. Seattle. Seattle wins.
Jacksonville vs. Tampa Bay. Jacksonville wins.
San Diego vs. Green Bay. Green Bay wins.


INTRACONFERENCE
AFC East vs. AFC North
AFC South vs. AFC West
NFC East vs. NFC North
NFC South vs. NFC West

New England and Jacksonville do not play each other and can win out.
Green Bay and Seattle do not play each other and can win out.

3 comments:

Brian Burke said...

Interesting. I guess the opposite is true. Only 4 teams could go winless, 2 from each conference.

Roger said...

Technically, the correct answer is 32 since every game could end in a tie. That's a useless answer, granted, and I found the discussion interesting regardless.

Derek said...

I did have some indecision regarding whether to use perfect or undefeated. I guess I should say perfect, but ties count as half a win when calculating winning percentage. So an 0-0-16 team would be .500. In a way, ties are half-losses.