USCL team ratings

Last year, I attempted to do some numerical analysis of the league, but this was perhaps not too interesting as it just verified what anyone would expect anyway: those with higher records tended to have higher ratings (!!!). This year, however, my programming skills have increased sufficiently that this might be a more interesting representation, largely because this time I've taken margin of victory into account and ran the simulation to its equilibrium state.

Some methodology notes: 

• Each team began with a 2400 rating
• For convenience, a constant K-factor of 14 was used
• In order to take margin of victory into account, each of the four games in a match was basically treated independently; e.g. a 4-0 victory would count as defeating the opponent 4 times. More formally, the expected winrate was simply scaled by a factor of 4. This isn't the most accurate treatment -- particularly in cases of 3-1 vs. 2.5-1.5 matches -- but I don't have a better heuristic at the moment.
• One major pitfall from last year is that it began every team at a uniform rating and ran the season once, thus not allowing time for ratings to normalize. In other words, beating a weak team early would be worth a large number of rating points, while beating the same team later on would be worth much less. This time, to combat this, the season was run 10000 times, which approximates the equilibrium state almost perfectly.
• Since I'm sure you're all burning to know, the code I used is here if anyone wants to make adaptations. Fair warning: it's god awful, but seems to get the job done.

Or in a more interesting format:

Eastern Division

Western Division

Nothing here is too surprising -- as expected, the ratings correlate very well with the number of game points. But some interesting things remain; for example, New York actually significantly outperformed New England (boo) under this analysis, despite New England winning the "strength of opponents" tiebreaker for the division title (but we're better anyway)! These ratings also show the huge differential between the top half and the bottom half of the Eastern division, as well as drives home what a monumental task Carolina faces next week. In the other division, the depth of which Dallas and St. Louis really dominated the field is clear here, as Seattle is really the only team that managed to post a rating anywhere near the two; also, the same top half vs. bottom half stratification is felt.

Of course, this analysis has its issues (most notably, team strength varies significantly from week-to-week), and it's not much more than a fun diversion from the upcoming action, but it provides some measure of quasi-objectivity and -- more importantly -- allows us to make some quasi-accurate playoff predictions (coming soon...)!