Friday, July 24, 2009

NFL: Pythagorean Projection I: 1994-2008


Those of you who have spent much time reading footballoutsiders may have noticed they often talk about something called a 'Pythagorean projection', and seem to take it pretty seriously.

Pythagorean projection is a technique (full details here) of taking, for each team, the number of points they score and allow, and using that to project the winning percentage for the next season.

The result is a number in the range from 0.000 to 1.000, which is taken as the predicted winning percentage (0.000 would mean predicting no games won; 1.000 would mean predicting all games won).

Every Season since 1993

I'm going to go back to 1993, since at or just before 1993 is when a lot of important features of the current NFL system were adopted:

  • Free agency
  • Salary Cap
  • 6 teams (per conference) playoff format
  • Bye week

This results in 461 projections, with 461 actual results to compare to. (Note that for some teams and seasons, like the Browns in 1999, or the Texans in 2002, there was no 'previous season' to provide a projection, and so are not included in this data set.)

The Full Data Set

The graph below displays the 461 projections compared with the corresponding actual result. Here is how the data points were produced:

For each season from 1994 to 2008, for each team with PF/PA values from the previous season:

  1. The actual winning percentage was computed for the team for that season.

  2. The projected winning percentage was computed using the Pythagorean method.

  3. The difference between actual and projected winning percentage is computed (using absolute value, since a miss below isn't better than a miss above).

  4. The values are then sorted from lowest (values near 0% indicate a near-perfect projection) to highest (high values indicate... well, situations where Pythagorean projection didn't work so well).

Here is what a plot of these numbers looks like:

Click for full size

Some details:

Range# of Data Points% of 461Classification
0.0≤δ≤ 12.520143.6% Reasonably Close
12.5<δ≤ 25.015934.5% Moderately Close
25.0<δ≤ 50.09721.0% Wrong
50.040.9% Yikes!


As a predictive method, Pythagorean Projection isn't something to bet the farm on. However, it can be interesting to look at the teams it missed on. Below are the 4 teams in the above data set where the projected and actual winning percentages differed by more than 50%.

  • 1994 Houston Oilers (actual: 2-14 projected 11.8 wins)
    In 1993, the Oilers won the AFC Central with a 12-4 record. This is before I paid very close attention to the game, but Wikipedia does indicate that there was serious conflict on the coaching staff in 1993. In 1994, head coach Jack Pardee was fired after a 1-9 start to the season, and Jeff Fisher was brought in as the new head coach.

  • 1999 Indianapolis Colts (actual: 13-3 projected 4.8 wins)
    The Colts were a doormat team for a long time after Unitas left. That didn't really change until 1999, which was Peyton Manning's second season.

  • 2001 Chicago Bears (actual 13-3 projected 4.8 wins)
    2002 Chicago Bears (actual 4-12 projected 12.3 wins)
    From 1996-2004 (inclusive), the Bears didn't win more than 7 games in a season, except for 2001. Part of it was fluke wins (including a couple improbable OT victories), part of it was the Bears' defense showing signs of what would take them to the Super Bowl a few years later.

Coming up

In part 2, I'll take a look at how Pythagorean Projection performed on the 2008 season.