Professional Football Researchers Association Forum

Rupert Patrick wrote:I'm not exactly sure how the odds would work out, but from 1970-2001 you had 74 four-team divisions (1982 excepted) and in those 74 divisions there were zero situations where there was a less than .500 team making the postseason. From 2002-14 there have been a total of 104 four-team divisions, and two had a less than .500 team winning the division. I'm guessing there is between a one and one and a half percent chance of a less than .500 team winning a four-team division, and with eight four-team divisions per season, there is approximately an eight to ten percent chance of it happening in a particular season.

The odds of a less than .500 division winner in a five team division has to be about one in a thousand. The only time we came really close to seeing it, I think, was in the 1978 NFC Central when Minnesota and Green Bay both finished 8-7-1, and there have been some 9-7 division winners in divisions with five teams.

I need to do a quick study of this to figure out the historical percentages and see if I can extrapolate the data to estimate the odds for this happening for a five-team division.

I put together an analysis of 4, 5 and 6 team divisions and determined two things - the average winning percentage of each place (second place in a four team division, fourth place in a five team division) and I charted the winning percentage of every division winner.

Winning percentage by finish: First of all, if two teams finished 10-6 for the division lead, both the division winner and runner up were credited with a 10-6 record. Also, I threw out the 1982 and 1987 seasons because of the strikes, and eliminated 1933-35 because teams played an unequal number of games. I also removed 1942-44 from the study because of the war, and otherwise used the 1936-2014 data.

There have been a total of 195 four-team divisions (such as the 1936 NFL West, 1968 AFL West and 2001 AFC East). The average winning percentage of the division winners was .7283, runner ups averaged .5758, third place .4362 and last place .2682.

There have been 146 five team divisions (such as the 1947 NFL East and 1977 AFC West). Teams who won these divisions average a .7393 winning percentage, second place averaged .6283, third place .4968, fourth place .3808 and fifth place .2422.

There have been 23 six-team divisions (1959 NFL East or 2000 AFC Central) with the division winner averaging a .7826 winning percentage, second place at .6839, third place .5562, fourth place .4583, fifth at .3261 and last place at .2201.

Conclusions: The more teams in the league, the more the winning percentages of the various teams spread out or disperse. An example is the winning percentages of second place teams:

Four team divisions: average second place winning percentage .5758
Five team divisions: average .6283
Six team divisions: average .6839

Probability of a .500 or below .500 division winner:

In four team divisions, there have been two below .500 winners and four .500 division winners in 196 divisions, for an average of one percent of below .500 and two percent of .500. With eight four team divisions in the league, those figures increase eight times for an eight percent chance of a below .500 winner and a 16 percent chance of a .500 division winner.

In five team divisions, there have been no .500 winners, and the lowest winning percentage of a five-team division winner (there have been 146 five team divisions) was the 1978 Vikings who finished 8-7-1. I think my ballpark guess of a below .500 winner in a five team division at one in a thousand is probably not a bad estimate.

The lowest winning percentage of a six-team division is .6667, and I would guess the odds of a below .500 division champion with six teams in the division is probably about a million to one.

Conclusions: The fewer teams in the division, the much higher the probability is that there is not at least an average team in the division, and thus, it is much more likely that you will see teams win the division with below .500 records.

Rupert Patrick wrote:

Rupert Patrick wrote: The lowest winning percentage of a six-team division is .6667, and I would guess the odds of a below .500 division champion with six teams in the division is probably about a million to one.

But in a six team division in a 16 game season, wouldn't it be possible for all six teams to finish at 5-11-0 (.312)? That's assuming that they all went split their divisional games 5-5-0, and lost the other six outside the division or conference.

Rupert Patrick wrote:
Rupert Patrick wrote:
The lowest winning percentage of a six-team division is .6667, and I would guess the odds of a below .500 division champion with six teams in the division is probably about a million to one.


But in a six team division in a 16 game season, wouldn't it be possible for all six teams to finish at 5-11-0 (.312)? That's assuming that they all went split their divisional games 5-5-0, and lost the other six outside the division or conference.

Yes, definitely possible. Ridiculously unlikely though. All the teams in the division would need to go a combined 0-36 outside the division. If every game is a 50/50 coin flip of going either way, there's a 1 in 6,871,946,736 of the 6 teams at 5-11 scenario happening.

So Rupert's estimate was only about 6.7 billion off.

But then again, if that division was that BAD, those teams would most definitely have less than a 50% chance of winning each game.

Mark L. Ford wrote:

Rupert Patrick wrote:

Rupert Patrick wrote: The lowest winning percentage of a six-team division is .6667, and I would guess the odds of a below .500 division champion with six teams in the division is probably about a million to one.

But in a six team division in a 16 game season, wouldn't it be possible for all six teams to finish at 5-11-0 (.312)? That's assuming that they all went split their divisional games 5-5-0, and lost the other six outside the division or conference.

(updated numbers - I had some of the math wrong)

It is theoretically possible, but the odds of 36 games outside the division falling just right, and along with all six teams breaking even at the same time in their division, the odds are astronomical. If such a team would be expected to beat a 5-11 team 68.75 percent of the time (which is what it probably would be as a 5-11 team has a .3125 winning percentage, meaning they lose 68.75 percent of the time) but win 36 times straight, the odds are 721 thousand to one, or .6875 to the 36th power. On the other hand, the odds of a team going 5-5 in ten division games is ten factorial divided by five factorial divided by five factorial times .5 to the tenth power (which equals .2461) and take that to the sixth power is .000222 or 4502 to one. Multiply the 721 thousand to one times the 4502 to one and you get 3.25 billion to one. You have about a twenty times better chance than hitting the Powerball.

Nice work putting together the numbers, Rupert. Good stuff.

Interesting, but not surprising. The conclusions are essentially what many of us have said for years in the various threads regarding league structure.

I'll second what Reaser said, Rupert, and appreciate the explanation of how the math works on that. I never could grasp probability and statistics, though I did great in things like calculus.