Tuesday, November 08, 2005

Big Ten Beatpath Rankings Week 8

I came across an interesting idea for ranking teams based on "unambiguous beatpaths" here. The idea is pretty simple - you have an "unambiguous beatwin" over another team if there's a chain of wins to that team, and no team on that chain has beaten you.

So, for instance, Penn State has beaten Ohio State who has beaten Iowa who has beaten Purdue who has beaten Michigan State who has beaten Indiana who has beaten Illinois. That's the longest current beatpath in the Big Ten (though not the only one of that length).

These rankings aren't subjective. They're automatic, just based purely on wins and losses, with no ambiguity. Here's the beatpath rankings for the Big Ten as of Week 8 (of the Big Ten season).

Beatpath Rankings for Week 8

Wow. What's interesting is it falls out exactly as you'd expect, although maybe some people wouldn't put Purdue that high. But hey, they beat Michigan State, and Michigan State has beaten - well, no one in the Big Ten. But look at it: it puts Penn State at the top, and Wisconsin/Northwestern/Ohio State/Michigan all at about the same level.

The interesting thing about beatpaths is how to handle beatpath loops. Like, for instance, the fact that Penn State has beaten Wisconsin, who beat Michigan, who beat Penn State. In any ranking where you say "I won't put someone over someone else they've beaten" this is a problem. In the methodology of beatpaths.com, you simply delete all of those games.

Curiously, in the Big Ten, there's only one beatloop graph, all involving Michigan's win over Penn State, and Michigan's win over Northwestern. Those snarky Wolverines! Here's the loop graph.

Big Ten beatloops

If you look, you can tell that this graph actually has three smaller loops - Michigan->NW->Wisconsin, Michigan->Penn State->Minnesota, and Michigan->Penn State->Wisconsin. The beatpath methodology says we delete the smallest loops first, so all of those games go poof. From this graph, this leaves us with one beatpath: PSU->NW, so that's what this graph entirely resolves to.

One interesting problem with these rankings is that Michigan is essentially immune to moving down on the graph, thanks to its win over Penn State. Even if OSU beats Michigan, they can't move down, as that would put them under Penn State, whom they beat. This type of problem usually resolves itself in the NFL due to teams playing each other multiple times. But still, it's interesting.

Thanks to tunesmith of beatpaths.com for this idea!

Update: Well, I've now computed power rankings based on a similar methodology to that on Beatpaths.com, although in my case, instead of the number of unique teams in beatloops, I use the number of teams in independent beatloops only (This avoids penalizing Penn State for Michigan being wacko). Rankings go from 1.0 to -1.0.

1: Penn State 0.723
2: Ohio State 0.714
3: Wisconsin 0.555
4: Michigan 0.500
5: Northwestern 0.444
6: Minnesota 0.111
7: Iowa 0.000
8: Purdue -0.400
9: Michigan State -0.600
10: Indiana -0.800
11: Illinois -1.000

3 Comments:

Anonymous Anonymous said...

hrm, if psu beat wis, then that's not a beatloop. psu should come out of that graph with a beatpath of psu->nw->wis.

2:29 PM

 
Anonymous Anonymous said...

whoops, I'm wrong. misread a team abbreviation.

2:30 PM

 
Blogger Pat said...

Yah, once I figure out a good template that includes the team's abbreviations, I'll use that one instead.

4:27 PM

 

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