## Friday, September 13, 2013

### Pythagorean Stats since 1990

Pythagorean (py) wins (what are py wins?), and Big Wins are interesting stats, but they don't tell us much on their own.  In order to put perspective on them, it's necessary to look at historical data, and see if they have useful, or even any, connection with past seasons.

Py Wins As a Prediction Model

The idea behind the pythagorean expectation formula is that points for and against provide a better indication of team quality than actual wins and losses, and that over time, teams which significantly over or underperform their expectation tend to regress or improve back to expectations.  NFL and MLB statisticians use historical data to provide perspective on what kind of regression or improvement a team a team is likely to show in the next season, or even half season.  I now have data dating back to the 1990 season, which I can use to gather the same data (in the future I will look at pre-1990 seasons, but I expect that as you go back in time, the changes to the game will start to hurt the accuracy of our current data):

Over the past 182 seasons (that's 1 season per team since 1990, including Ottawa twice and the failed American teams), you can see how many teams finished above or below expectation, and how they did in the following season.  Seasons where the team was not in the league the following year have been removed from the table and chart.  The 2012 and 2013 seasons are also not yet included, as they have no follow up season to analyse.

As you can see, the majority of seasons fall into a range quite near to expectation: 41 of 182 fall between -0.5 and 0.5, and 100 between -1 and 1.  That's pretty good; 55% of teams finish within 1 win of expectation, and less than only 28 times in 31 years has a team missed expectations by more +/- 2 wins.

In the ranges where we have more data, the chart follows the line you would expect; teams which miss expectations tend to turn it around the following year, while teams which surpass them end up with a few less wins the next year.

There are of course some outliers in the data at the outer edges where we have poor sample sizes.  In 1997, Montreal finished a full 4.5 wins above expectation, winning 13 games despite a -23 point differential.  Defying the expectations, they won another 12 games in 1998, finishing another 2.7 wins up on expectations.  On the other end of the spectrum, we have the 2010 Blue Bombers, finishing 4.5 wins below expectation.  They had extraordinarily bad luck that year, winning only 4 games despite a point differential better (-21) than those '97 Als.  The next year, Winnipeg won 10 games and made it to the Grey Cup.

Neither one of these examples gives us a good idea what to expect when a team is so far above or below expectation, simply because it's so uncommon.  Were the Bombers lucky to turn it around?  Were the Als lucky to avoid regression?  I think the latter is likely the case based on the ranges where we do have more data, but no one can say for sure.

All in all, I'm comfortable with saying now that as with other sports, Pythagorean Expectation is a good way to predict future performance in the CFL.