NFL Graphs

So, I’m bored, and I like social choice and vote theory.

One of the things that has a lot in common with voting is ranking sports teams. Each game is like a vote between two candidates.

Most of the team ranking systems out there have lots of controversy because inevitably, one team is ranked above another team that has beaten them. It’s less rare in College, but it happens all the time in the NFL, which is pretty incestuous. Ha ha. I love describing things as incestuous when they’re really not. Anyway.

Just to illustrate, I’m using one of my homegrown graphing applications to show a “beatpath map” to all the NFL games. I’ll update this entry as I create a graph for each week.

Basically, you draw a bubble for each team. Then you draw an arrow from a team, to another team it beat. You keep the unbeaten teams up high, so the beatpath always goes down.

Week one is boring because you just have a row of sixteen teams, with another row of the sixteen teams they beat immediately underneath.

But it already starts to get complicated in Week 2 (click to enlarge):


More below the fold, as I create them.

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Here’s Week 3. Only four undefeated teams remain. It’s getting complicated, obviously. Now, I don’t really control the placement of the bubbles, other than to say that defeats go downward, so undefeated teams are on top. The rest of the bubble placement is controlled by AT&T (my application uses their graphviz open source package). But here you’ll see we have our first circular beatpath. Miami->Denver->KC->Jets->Miami. Miami being on top is arbitrary.


And here is Week 4. Good God. At this point I’m not sure it’s really even worth continuing on throughout the season. I will do at least one more week, though.


Week 5. I can’t even make sense of this.


But here’s something interesting. You can start to play with removing circular beatpaths. The theory goes, if Denver and KC play each other twice and split the series, it’s really unclear which one of them is better. So rather than snarl up the graph, just remove both arrows, as if they didn’t play each other.

You remove all the smallest circles first. So for week five, I removed the smallest circles in order until there were no circular beatpaths left. The beatpaths I removed in order were:

– philly -> oakland -> dallas -> philly
– new orleans -> carolina -> green bay -> new orleans
– san diego -> new england -> pittsburgh -> san diego
– arizona -> san fran -> st. louis -> arizona
– baltimore -> jets -> tampa bay -> detroit -> baltimore
– miami -> denver -> KC -> jets -> miami
– atlanta -> buffalo -> miami -> carolina -> new england -> atlanta

yes, it gets pretty snarled. But by the end of it, you have something much clearer: a graph of all the unambiguous beatpaths so far this season:


One interesting side effect of this is that Miami’s record is pretty much obliterated. Every single beatpath it had was ambiguous and circular, so it’s not even on the graph. What that means is if you were to try and make a 32-team ranking out of this graph, you could have a defensible reason for putting Miami anywhere you wanted.

Given that graph and my new, probably very flawed theory, here are my picks for Week 6. First, my gut picks, then my system picks (which are supposed to be more accurate):

* CAROLINA at Detroit: Carolina’s a tough team.
* CINCINNATI at Tennessee: The Titans are improving, but the Bengals are better.
* Jacksonville at PITTSBURGH: The Steelers are at home.
* Miami at TAMPA BAY: The Bucs won’t lose two in a row.
* Minnesota at CHICAGO: The Bears are playing well.
* NEW ENGLAND at Denver: I want Denver to win, but I think the Pats will win it late in the game.
* JETS at Buffalo: The AFC East is destined to be a snarl.
* SAN DIEGO at Oakland: San Diego is destined to be a snarl.

And my system picks:
* ATLANTA at New Orleans: Atlanta should bounce back from their loss to the Pats.
* CLEVELAND at Baltimore: Cleveland’s better than you think.
* Giants at DALLAS: Parcells beats one of his old teams.
* WASHINGTON at Kansas City: My surprise pick of the week.
* Houston at SEATTLE: Seattle builds more confidence.
* St. Louis at INDY: Indy will be tested, but will win.

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