Believe it or not, the system was able to chug its way through the entire 2005 NBA season without a lot of pain. And the graph looks cool, too. I’m pleasantly surprised. MLB might work pretty well, after all.

Here’s the 2005 beatpath graph after San Antonio won the championship:

Now here’s the more interesting one. Check out this beatpath graph for 2005 when I run the beatflukes variant. This one cancels out a ton of loops. Again, I’m still not sure I’m handling beatflukes correctly, but the vertical nature of this graph is pretty fascinating.

Over a long season where teams play each other a lot, the teams have pretty clear chances to assert dominance over each other, and the home field advantage largely cancels out. The benefit of these tall graphs is that there are many fewer possible power rankings orderings. Out of all the teams, it appears that only Minnesota and the Clippers have a pretty wide variance of where they could be placed in the rankings.

(It’s pretty amazing what some performance enhancements can do. Earlier tonight, generating this graph took over 45 minutes and led to my first ever out-of-memory errors on my powerbook. A few unique sorts later, and this took less than sixty seconds.)

That’s pretty impressive. NHL now?

Or how about last seasons English Premier League:

http://soccernet.espn.go.com/grid?league=eng.1&year=2004&view=n&cc=5739

Twenty teams all in one grouping. Each team plays every other team twice: once home and once away. I imagine the end result would look very much like the final standings for the season:

http://soccernet.espn.go.com/tables?league=eng.1&season=2004&column=none&order=false&cc=5739

So how many of the beatpath links are “multiple” ones? That is, you’ve got one arrow from San Antonio to Phoenix – does that represent one excess win, or three, or four? (Where “excess wins” means after all the beatloops are cancelled out)

Does graphviz allow for changing the arrow size on a per-link basis? I can’t remember. If so, you could increase the arrow size to indicate the number of “hidden/excess wins”.

I forget how many multiple wins are there. It would basically be the season series minus any beatloops.

I could play with arrow size, but I’m a bit torn about it. Really the only purpose of the graph to keep it simple is to say that Team A is “better” than Team B (or has proven themselves better through win/loss behavior). The question of “how much better” can be answered in so many different ways, that if I started weighing it in one way, it sort of opens it up to interpretation arguments. (“Sure, they won four games and lost two, but in those two games they got absolutely destroyed so that should count for something!”)

Eventually I’m going to store each graph’s supporting data in a database somehow so that people can choose to draw the graph in different ways – with or without redundant wins, for instance. What’ll be even cooler is when I can dynamically draw subgraphs for only the data emanating from a particular team, or a time-based graph of where a team is in the rankings, … tons of possibilities here. I have to figure out how to get paid for this.

Well, there

isa clear benefit to the multiple wins, in that it provides them with insurance against losses. I just figured it’d be nice to see on the graph how protected a team is against the team below it.Yeah, that’s true… it would help tell how stable the team is against the one immediately below it. It isn’t the whole story because it doesn’t communicate how stable the team is over other teams. (For instance, in this week’s NFL graph, both DEN and IND have a similarly unstable/unprotected win over Jacksonville – but losing it would hurt Denver a lot more because it doesn’t have any direct wins over CIN, PIT, etc.) But I’ll play with the idea some more.

It’s cool to see this work for different sports.

After next year’s World cup is over, I think it would be cool to see a World Soccer beatpath graph that includes all mathces both in the world cup finals, and in world cup qualifying.

This could be the ultimate back of the envelope ranking system for MLB.

I’m interested in seeing how the NBA regular season beatpath graph corresponds with the winners in the postseason.

Good question.

At the end of the 2005 regular season, the normal variant had the top six as:

San Antonio

Phoenix

Dallas

Miami

Sacramento

Detroit

(Houston #10)

The beatfluke variant had the top five as:

Phoenix

Dallas

Miami

Houston

Detroit

San Antonio

(Sacramento #7)

Whereas after the playoffs, the normal variant had the top six as:

San Antonio

Phoenix

Dallas

Seattle

Detroit

Miami

(Houston #9)

And the beatflukes variant had the top six as:

San Antonio

Phoenix

Detroit

Dallas

Houston

Seattle

(Miami #7)

In the NFL, the beatflukes variant ends up slightly more accurate, but I haven’t tested accuracy for the NBA yet.