Beatpaths! Beatpaths! Beatpaths!

For those that are new visitors this year, here’s a quick description of what we’re all about.

A few years back, I was reading one of those websites that purports to power-rank sports teams based off of every single in-game stat in the book. And, being a Broncos homer, I was peeved that the Broncos were ranked so low.

My gut-based thought – completely lacking in any evidence and data – was that wins aren’t always linked to stats. Sometimes it’s heart! And guts! Or the intelligence of a team’s scheme – sometimes they just play the matchup game better. But really, I was just thinking about how it all comes down to wins and losses, and damn the rest of the data.

The advanced ranking schemes pay attention to a lot of data – all the data except for wins and losses. So my perverse idea was to do the inverse. Focus only on wins and losses.

Turns out there are other schemes that also only pay attention to wins and losses – they use big words and probability and math and statistical theory.

I decided to use graphs. Here’s how the idea came about.

I started graphing the NFL season based off of one simple rule – if a team beats another, you draw a line from the winner to the loser. The End.

Soon, you start seeing long sequences of wins and losses – The Broncos beat the Steelers, who beat the Patriots, who beat the Giants — oh wait, they didn’t beat the Giants. Anyway, those sequences of wins become what I call a beatpath.

Now, early in the season, you see sportswriters try in vain to structure their own power rankings by always having teams ranked ahead of other teams they’ve beaten.

But soon, you notice that contradictions start appearing. Every year, there’s some silly article over in college football land about how Captain Doohickey Tech is better than Ohio State, since they beat Team A, who beat Team B, who beat Team C…. who beat Team X, who upset Ohio State back in week 2. When you know just as well that Ohio State has demolished someone who has in turn demolished the Raiders, I mean, Captain Doohickey Tech.

That contradiction is called a beatloop.

And so we, that is the Royal We, not to be confused with Eddie Royal, worked out a system to resolve these beatloops and come up with automatic power rankings. And surprisingly, it’s ended up weirdly accurate. Well, sometimes just weird. But a hell of a lot of fun.

Every week I’ll post graphs that are a snapshot of the NFL season so far. And the automatic power rankings that come from the graph. And we’ll be continuing to discuss ways to tweak the algorithm – commenters often come up with variants to the algorithm that might even be more accurate. And we’ll have arguments about whether the beatpath algorithm is actually predictive (when it’s doing well), or merely descriptive of the season so far (when there are lots of upsets). And there will probably be some subtle Broncos homerism littered throughout, until someone calls me out on it.

Welcome to the site (redesign coming soon!), and enjoy your stay!

7 Responses to Beatpaths! Beatpaths! Beatpaths!

  1. The MOOSE says:

    I don’t think your homerism is subtle, not that it needs to be. But cheap shot on the Pats there, like we haven’t suffered enough in our last two games.

    Anywho, since it may be helpful for any new reader that passes along, last year your lovely host TT ran his base system which simply eliminated beatloops from smallest to largest until none remained and those were the graphs. If there was a season split between two division rivals, they’d both lose their wins and that was the end of it.

    Some commented that if a team won huge but lost a close second game, that they shouldn’t cancel each other out, and therefore the score of the game should be part of the evaluation. From this idea the “weighted” system was created where each loop was broken by removing the closest victory first and reducing the value of remaining links in the loop. This typically produced a very different graph that often contradicted conventional wisdom due to outlying blowouts, but the method still performed well at postseason predictions relative to the other format.

    Finally, one frequent commenter named Doktarr suggested that instead of simply eliminating loops altogether, each link should be given a weight based on how many times it appears in other loops. This means if several loops are being held together by a single game, it can be considered that the one game is a fluke or else the other loops wouldn’t collapse. This process was named the “iterative” method and often led to much less ambiguity amongst the teams (i.e. taller graphs) but occasionally favored a team most would consider weak.

    What I brought to the table was a different way to “tiebreak” teams that are near the same level to determine the rankings. For each method I evaluated each team’s total paths in and out and gave them a score based on the lengths of the paths. The formula rated each team on a scale from -10 to 10 so that most teams would be near 0 and reaching numbers beyond 5 would require having most of the teams in the league connected to the graph beneath that team. No team, not even last year’s Patriots, reached 10, which essentially requires having a direct win over every team in the league.

  2. ThunderThumbs says:

    Well, all right – I do officially feel bad for Pats and Pats fans (and Brady) about Brady’s injury.

    And that injury certainly does do a lot to help the Patriots look like an underdog again – and the winning underdog is something that suits the Patriots better (at least in my mind).

    But I still don’t think they’re quite in underdog territory yet. Maybe if they lose some games due to Brady’s absence. Not that I’m rooting for that. But if they just keep winning with Cassell or whoever, it’s just still a juggernaut in a slightly different form.

  3. ThunderThumbs says:

    So, what would make it easier for others to try out their own tiebreaking variants? I suppose I could make some sort of data file available for download each week.

  4. JT says:

    A data file of some kind could be useful, in a nice format like csv, xml, or whatever you’ve got. The question becomes what to put in it. I wouldn’t put anything more than the results of each game, Teams involved and sores, and date. It shouldn’t be too hard to read that to try other variations.

  5. Justin says:

    So are you going to show us the week 1 graph? 🙂

  6. The MOOSE says:

    A data file sounds good to me. It’d be nice to have something in a more standard format. Previously I’d just copy the schedule results into a .txt file from the NFL official site and had my program parse that out. Something more structured would require a little work though.

  7. The MOOSE says:

    As excited as I was to get back into drawing the graphs, the week 1 graphs are so utterly boring that it’s not even worth publishing as they will all be the same. In case TT doesn’t bother and Justin still wants it, just imagine 16 columns side by side with the opponents from each game as each column. The winning team is on top with an arrow to the losing team on the bottom. You probably already knew that since you’re a returning visitor, but anyone new might not know that it takes at least 2 weeks for the graphs to get going and around 5 before it gets really interesting.

    For anyone who cared about the results from my runs:

    In both the Standard and Iterative methods, there is a 16-way tie for first place with a score of 3.54, and a 16-way tie for last place with a score of -3.54. That’s how it works after one week.

    Since the Weighted method takes score into account, the #1 team is PHI with a 5.76, and conversely the #32 team is STL with -5.76. Teams are ranked exactly by their point differential after week 1.

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