Best NFL Teams Ever: A Mathematical System

I've laid out on this blog before why I think using the Pythagorean formula for NFL team records is stupid.  The season's too short, and going with a linear, rather than quadratic, model shows the results pretty perfectly, ESPECIALLY at the extremes (i.e. Pythagorean will never predict winless or undefeated teams, and not even 1-15 or 15-1 teams, yet they happen ALL THE TIME, relatively speaking).  So I've devised this simple formula:

(TeamPointsScored-TeamPointsAllowed)/(AveragePointsInAnNFLGame)

Then you add that total to a .500 record, however many games that may be.

For the last variable, you take the average number of TOTAL points of an NFL game (usually about 44), not just the average for one team.  It's really simple.  

For example, the Pythagorean formula gives the 2007 Pats an expected W/L in the regular season of 13.8-2.2.  In my method, the Pats scored 589 and allowed 274, for a differential of 315.  In 2007, there were 256 regular season games played and 11104 points scored.  That's a total of 43.375 PPG.  315/43.375=7.26.  Then we add a half-season's worth of wins (8), and we get an expected W/L record of 15.26-0.74... WAY closer to their actual 16-0.

Anyway, I was thinking about this again, and thinking how it would be a good way to compare teams over time.  Except, of course, for the schedule-length issue.  So, I just take the answer and divide by the number of games in a season to get an expected winning percentage.  And that's what we'll go with.  Totally objectively ask the question:  "to what extent did this team dominate their opponents?"

I was initially going to publish the complete list of teams I did.  I took one to five teams from each year in NFL/AFL/APFA/AAFC history.  I'm pretty sure each franchise is represented at least once.  I wound up with 241 teams on the list.  Now, I'm pretty positive they're not the top 241 teams of all-time.  I probably missed as many as 50 or 60 that might be better than the worst team on this list.  But I'm absolutely CERTAIN that the top teams of all-time are represented.

Anyway, I'm not going to publish the full list because it's long.  So I'll start with this post in which I'll look at the early, pre-modern days of the NFL and APFA.  For me, the "modern" NFL starts in 1943.  That's basically when scoring reaches modern levels, and we stop having teams projected to win more than 100% of their games.  Anyway, in this post, I'll have 1920-1942.  In my next post, I'll detail 1943-1969, which includes the AFL and AAFC days.  And my final post will be about the true "modern" NFL, from 1970 to the present.  Here we go.

Before 1950, there is a problem with estmating winning percentages with my method.  That problem is that you will get winning percentages over 1.000.  It happens in more or less every single season.  Sometimes more than one team will be projected to have gone undefeated.  This happens because the gap between the "haves" and "have-nots" is too wide.  If I had looked for the worst teams of all-time, they would all have been from this era; likewise with the best.

You have to keep in mind a few things about this era:  not every team played the same number of games each year (at least until 1936; that's when every team started playing the same number of games, and there was an actual, organized schedule).  Not every team was in the league from year to year.  This creates HUGE gaps between the best an the worst.  Ties were extremely common.  For much of the era, there was no bowl game at the end of the season, so a champion was simply crowned.  It was a mess.  But I present to you (again, based on regular-season only) the greatest teams of the early days of the NFL (including its days as the APFA in 1920 and '21), from 1920-1942:

1923 Canton Bulldogs, 1.695
1925 Pottsville Maroons, 1.559
1922 Rock Island Independents, 1.494
1924 Cleveland Bulldogs, 1.407
1920 Buffalo All-Americans, 1.327
1942 Chicago Bears, 1.320
1929 New York Giants, 1.285
1922 Canton Bulldogs, 1.271
1921 Buffalo All-Americans, 1.269
1927 New York Giants

These ten teams are the greatest ten teams in NFL history, by this method.  Again, this is why we need to split everything that happened up to 1942 separately from the rest of NFL history.  There are a total of 27 teams in NFL history that were projected to win more games than they actually played; all of them are from this era.

You may also have noticed that these team names are not familiar.  Just because these teams were great in their own times, doesn't mean that they stuck around.  Canton/Cleveland, as you can see, was a dynasty.  The Bears of 1942 played in what was the closest to the modern NFL of any of these, and not just because they were the most recent of the bunch.  In 1942, in the average NFL game, the two teams combined for 32.38 points per game.  Scoring was under 30 points per game from 1920 to 1938.  Then in 1939, it reached 30, and hung right around there until 1942.  Then, in 1943, there was an explosion of offense, leading to a 39.65 points per game total.  The lowest it has been since then was in 1977, when it dipped as low as 34.35 points per game.  In other words, still higher than every year up to 1942.

Well, that's all I've got in terms of a history lesson for you tonight.  I'm just gonna keep posting until I get bored, so don't be surprised if there's another one up shortly!