This year, and henceforth, we're going to try something a little bit different. Every year, a new wrinkle or two is going to be added to the Gus Rankings to attempt to correct for a perceived shortcoming in the original rankings. In keeping with the original spirit of the Gus Rankings, additional adjustments will be 1) objectively defensible to the largest extent possible, and 2) completely transparent in terms of how the calculations are done. Don't know the algorithm that Sagarin uses for his ratings? Don't worry-- that'll never be the case here. The downside is we're losing a bit of the simplicity that made the rankings straight-forward and easy to interpret. I will do my best to arrange to have the original Gus Rankings alongside the new and improved Gus Rankings, so whatever flavor of Gus you enjoy (or ranks your team higher) you can have at the ready.
I had large plans for this year's adjustments-- enough to work on to provide several years of improvements. I think some of them could 1) take some more thought on the objectivity front, and 2) could definitely take some thought on how to implement them so as to minimize the week-to-week effort on my end. So patience here will win out.
Nevertheless, I believe taking a piecemeal approach can prevent anything too drastic from happening on the fly-- after all, I only have so much Excel ability. Further, adding in different features at different times should give a sense for how adjusting for different factors play into the rankings at the end of the day. I view it as an experiment in power rankings-- and since mine are the only ones I know of that straddle the line between silly-in-construction and break-out-the-supercomputer-to-calculate-them, I think there's something to be taken from different aspect of a power ranking.
With that out of the way, here's what's changed to generate this year's rankings-- Gus+.
- I've been struck in the past at how much an end of the game scenario can really swing things for a team. It's not terribly surprising-- after all, when the only thing that counts is your opponents' wins or losses, a flip from one to the other is going to be a big deal. But I don't think that should be such a violent swing. So this year's adjustment deals with that issue.
- Many power rankings deal with margin of victory; Gus+ now does the same. We view close games as part victory and part loss. Now, point differential across the entire spectrum of scores shouldn't all have the same impact. In terms of the chances of winning a game, a field goal to extent a lead to 5 points is much more impactful than a field goal to extent a lead to 53 points. So, all wins over 16 points will be considered 100% wins.
Is 16 arbitrary? Yes. But that's two touchdowns and two two-point conversions, and that's what we're going with.
Games within 16 points are assigned a percent win and a percent loss for each team; one team's percent victory is their opponent's percent loss and vice versa. I considered a range of functional forms to capture this-- something that needed to have a fairly high rate of change around closer scores and then flattening out as it approached 16. The inverse hyperbolic sine provides this form quite nicely-- and is certainly defensible as objective as, conveniently enough, I did not derive the distribution of the inverse hyperbolic sine.
- Overtime games have always bothered me. We judge the vast majority of games on sixty minutes of game play. Why are there a subset of games where we consider more time? That seems arbitrary to me, especially in a power rankings format. So all overtime games, regardless of winner, are now 50% victory and 50% loss. Whether the team ultimately won or lost will play a role in the secondary effects of your other opponents' rankings but not directly within the overtime game. The secondary effects aren't trivial in theory-- maybe these games need to be considered pseudo-ties moving forward, with all of the appropriate adjustments therein-- though in practice there have been exactly three overtime games in the first two weeks. It's something to think about moving forward. That is how ties will be dealt with this year.
- Without further ado, here are this season's first Gus+ Rankings.
- As always, the early portion of the season does not lead to much variation in the rankings. Generally this falls by the wayside after a few weeks; the adjustment for margin of victory should bring about enough variation perhaps a week or two sooner. There is considerably more variation this year as compared to last year's Week 2 rankings.
- It is interesting to me that the largest score is 1; basically, no team has recorded two significant victories over two teams that, in each of their other games, recorded victories themselves. I'm fairly certain I've got everything arranged properly-- there is a team at -2 (Idaho!), and, since the reverse of the above statement could be made, I think the calculations are accurate. And to be fair, only 2 teams had 2 points (or, more accurately, more than 1 point) at this juncture last year, so we're not entirely away from normalcy here.
Comments welcome! I'm excited to see how it all shakes out.
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