Monday, July 7, 2014

/r/CFL Mathematical Rankings explained (And the Week 2 Math Rankings)

Many of the readers here were originally introduced to this blog via, a great CFL-based community of which I am a regular participant.

One of the ways I participate is as one of the 10 voters (technically 9 currently, as we have no Edmonton voter) for the official /r/CFL Power Rankings.

The /r/CFL Power Rankings work in the usual way, we have a group of voters, and each voter ranks the teams at the end of each week.  The average of the votes determines a team's position on the list.  Most of the rankers vote from a team standpoint; they are designated as the official voter for their team, and they will contribute a short note regarding their team for the rankings.

My contribution is different, however.  The folks organizing the rankings decided that they would like to include my voice as well, and I'm happy to have the opportunity to contribute.  My rankings, as I'm not designated as a team ranker, are intended to be an unbiased vote, so as per my nature, my votes are math based.

For my vote, I've opted to use the Simple Ranking System, a new system I haven't talked about on this blog before (you can see each team's SRS rank on the standings page of

Simple Ranking System, or SRS, follows the same concept as Pythagorean Expectation and is based on the theory that points for and against are a better indicator of team strength than a team's actual record.  However, what Pythagorean Expectation and points for/against lack are adjustment's based on matchup.  The best team in the league beating the worst team in the league in a close game is both less impressive for the best team, and more impressive for the worst team.  SRS attempts to adjust results based on opponent rankings.

In basic terms, the formula for SRS is a team's average point margin, plus the average of their opponent's ratings.

I'll quote for this part:

So every team's rating is their average point margin, adjusted up or down depending on the strength of their opponents. Thus an average team would have a rating of zero. Suppose a team plays a schedule that is, overall, exactly average. Then the sum of the terms in parentheses would be zero and the team's rating would be its average point margin. If a team played a tougher-than-average schedule, the sum of the terms in parentheses would be positive and so a team's rating would be bigger than its average point margin.
You can figure out any team's rating if you know their opponent ratings. Which sounds easy, except you can't know an opponent rating until you've figured out their own opponent rating.  Which brings you back to the first opponent, and leaves you in an infinite loop.

Fortunately, the loop will stabilize after a number of iterations.  On, SRS is calculated first with an opponent adjustment of 0, then again once we've calculated them all once.  And then again and again, until the ratings stop changing.  Once the ratings stop changing, you have your ratings for the week.

How does this apply to the Power Rankings?

Simple.  My votes are simply the order of the teams ranked by SRS on  It's bias-free because I have no direct input on the process, and it provides a good way to contextualize a team's perfomance, especially in the early parts of the season when there aren't too many common opponents.

There's one caveat though: with a small sample size, the usefulness of a stat like this is reduced, as a single game makes up a significant portion of the rating and may be an outlier in the teams actual season.  Over time, those even out, but early on, they count too heavily.  So I have introduced an element of human intervention for the early part of the season.  It's not based on any tested math, it's just a means to avoid wild swings to a certain extent.  

Going into the season, I ranked the teams based on their expected win total change (from historical Pythagorean Expectation data).  After 1 game, a team's movement was capped at +/- 3 spots on the list (ie: the 9th place team on the list was limited to no higher than 6th position).  After 2 games, the cap was raised to +/- 6 positions.  After 3 games, the limit will be removed and SRS will be used directly.

The Week 2 Math Rankings

1) Winnipeg (SRS rank 1)
2) Toronto (SRS rank 3)
3) Calgary (SRS rank 4)
4) Saskatchewan (SRS rank 5)
5) Montreal (SRS rank 6)
6) Ottawa (SRS rank 2)
7) Edmonton (SRS rank 7)
8) Hamilton (SRS rank 8)
9) Montreal (SRS rank 9)

With the movement cap up to 6 for most teams this week (Calgary and Ottawa were restricted to +/- 3), the cap was mostly a non-issue, and only Ottawa was affected.  They started the season in 9th and weren't moved in the bye week, so despite a strong performance against what SRS thinks is the best team in the league, Winnipeg, they were moved down to 6th by the cap.

Some might find the rankings of 1-1 Toronto and 2-0 Edmonton to be rather odd, but they can be explained by opponent adjustments.  Toronto dominated a Saskatchewan team which had a very strong week 1 ranking, and that makes Winnipeg look that much better in week 1, and subsequently Toronto's loss to a strong Winnipeg team no longer hurts as much.  Likewise, while Edmonton is sitting pretty at 2-0, their two wins have come against the 8th and 9th ranked teams, both 0-2 with an average point differential of -23.5 between them.

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