On Pythagorean Expectation, luck and a statistically wacky 2015 season

Monday, June 6, 2016 2:24 AM

Pythagoras himself would be proud of Joe PritchardTime for just a bit more math before I make my official predictions for the 2016 CFL season. 

This time, let's take a look at Pythagorean Expectation over the past 10 years, and how it can be used to aid in predictions for this season.

Now, I've based a lot of my work at CFLpass on the fact that teams that underachieve their Pythagorean Expectation (otherwise known as being statistically unlucky) tend to do better the next season, and vice versa. This time around, I took the records and Pythagorean Expectations of all the CFL teams from 2006 onward, and what I found pretty much matched exactly what I was thinking was already true. 

[A quick primer: Wikipedia defines “Pythagorean expectation” as a formula invented by Bill James to estimate how many games a baseball team "should" have won based on the number of runs they scored and allowed. Comparing a team's actual and Pythagorean winning percentage can be used to evaluate how lucky that team was by examining the variation between the two winning percentages. For his analysis, Joe has adapted James’ formula for football. – Ed.]

Teams that underachieved their Pythagorean Expectation by at least a half a win the season before, on average, added over 2.25 wins (2.269, to be precise) the following season. No team that was "unlucky" by over 1.5 wins did any worse than improving by three games the next season.

The biggest positive swing of a team underachieving their Expectation was the 2014 Ottawa RedBlacks, whose record increased by 10 wins the next season, and the biggest negative swing of a team underachieving their Expectation was the 2007 Toronto Argonauts, who dropped 7 wins the next season. 

Teams that overachieved their Pythagorean Expectation by at least a half a win the season before, on average, lost over 1.5 wins (actual number -1.63) the following season. On a whole, these teams had less seasons of huge swings than teams that underachieved the year before.

The biggest positive swing of a team overachieving their Expectation was the 2010 Edmonton Eskimos, who went up 4 wins the next season, and the biggest negative swing of a team overachieving their Expectation was the 2014 Saskatchewan Roughriders, who fell by 7 wins in 2015 after overachieving their expectation by 2.2 games in 2014. 

Teams that came very close to matching their Pythagorean Expectation (by being within a half a win, over or under) averaged out to losing .0278 wins the next season, or basically, staying put. Matter of fact, all teams that fit this category besides the 2007 Calgary Stampeders (who gained 5.5 wins the next season, with ties counted as 0.5 wins in this study) stayed within 3 games of their record the season before.

The teams that fell the most after hitting their Expectation the year before were the 2008 BC Lions and the 2009 Montreal Alouettes, both of who fell by 3 wins the next season.

So where did the 2015 teams fall?

Out West, Edmonton and Calgary were almost dead even, both overachieving their Pythagorean Expectation by around 1.5 wins. BC underachieved by 0.7 wins, the Winnipeg Blue Bombers were almost dead on their expectation, down to the decimal point, and the Riders underachieved by 2.8 wins. 

In the East, Ottawa overachieved their Pythagorean Expectation by nearly 3 wins at 2.7, the Hamilton Tiger-Cats underachieved by 2.5, Toronto overachieved by 2.6, and Montreal underachieved by 2.6. To put this in perspective, in the past 10 years, six teams have been over 2.5 games off their Expectation, and five of those occurred this past season. 

To put this into an easier way of looking at it, here is the order of finish last season and how much they differed from their Expectation.

2015 Eskimos +1.4
2015 Stampeders +1.3
2015 Lions -0.7
2015 Bombers +0.0
2015 Riders -2.8

2015 RedBlacks +2.7
2015 Ti-Cats -2.5
2015 Argos +2.6
2015 Alouttes -2.6

Going back over the past decade, I found that teams that were off their expectation by two or more games had a lot of fluctuation the next season. 

Teams that underachieved their Expectation by that much (like the 2015 Riders, Ti-Cats, and Alouettes) averaged a 5.4-win increase the next season. These teams were the 2010 Bombers, the 2008 Ti-Cats, the 2013 Eskimos, the 2012 Riders, and the 2012 Ti-Cats.

On the flip side, the 2015 RedBlacks and Argos were nos. 1 and 2 as far as teams that finished that much higher than their Expectation. The other five – the 2012 Alouettes, the 2008 Riders, the 2014 Riders, the 2010 Eskimos (who went up 4 wins the next season, the only team in this list to go up and not down), and the 2010 Argos – averaged a 2.1-win decrease the next season. 

Make your 2016 predictions accordingly…

– written by Joe Pritchard