2012 Club Season Rankings
2012 marks the first season in which there is a formalized regular season of sanctioned events which impact the Club Series. The Club Rankings are used to help determine strength wildcard bid allocation throughout the series. The results that count are games between official regular season club teams at USA Ultimate sanctioned club events during the 2012 Club Season. The threshold for inclusion in the rankings starts at 5 games, but is raised to 10 games prior to the end of season rankings.
Below is a description of the rankings algorithm that is being used for the 2012 Club Season. Please note that the agorithm in use for the 2012 Club Season is a modification of the College Rankings algorithm that was used during the 2012 College Season. For complete game results go to the Score Reporter.
The modification to the algorithm removes the possibility that a team rated more than 600 points higher than its opponent will drop in rating when beating that team by a large enough point differential. The game is preserved to serve as a connection between teams but does not impact the actual rating of the respective teams involved. USA Ultimate continues to look to improve its ranking algorithm through consultation with Rodney Jacobson, Sholom Simon and other volunteers.
USA Ultimate Club Rankings Algorithm
The USA Ultimate Club Top 25 is a modification of the algorithm-based ranking system created by Sholom Simon and used in the College Series. The rankings are calculated weekly starting in early August and are published by USA Ultimate on its website.
The Modified Top 25 algorithm becomes more accurate later in the season as more valid scores are provided by club tournament directors and teams. Scores should be entered through the Score Reporting tool on the USA Ultimate website.
The most basic explanation of this Modified Top 25 rating system is this: for each game a team plays, the team gets rating points. These rating points are then averaged.
The next level of complexity is how to compute the points for a given game, and how to average them. The points for a given game is given by this formula:
pts = opp_rate + (400 / x) (1)
where opp_rate is the rating of the opponent, and x is a factor that depends upon the score. (Note: we subtact the amount of (400/x) in the case of a loss.) The formula for x is:
x = max(2/3,(2.5*(losing score/winning score)^2)) (2)
Rather than explain it, let me give an example. Suppose team A beats team B 15-11. According to the formula, take the fraction 11/15, square it, and multiply by 2.5. This gives us 1.34. Suppose, further, that team B has a rating of 1000. According to formula (1), we simply compute 1000 + 400/1.34 and get 1298. The "max" that's used for formula (2) makes it so that the smallest that x can equal is .66, which means that the best (or worst) a team can do in a specific game is to perform at 600 points better (or worse) than their opponent. (A score of 13-5 will get you 600 points).
One exception to the above are games where the higher ranked team wins the game by a large enough point differential to get X=2/3 from formula (1). Such results are given a negligible weight (10^-9), so that the connection remains without having that result impact the ranking of those two teams.
So, suppose team A has played in 4 games, and each individual game rating is 1298, 913, 1410, and 1103. Well, we simply average them together, and team A has a rating of (1298+913+1410+1103)/4 which is 1181. But, actually, the averaging isn't quite that simple, either. We actually take a weighted average. In the above example, each game had a weight of 1, in actuality, the weight depends upon how recently the game was played. This formula is:
wt = min(1,1/(((today-gamedate+3)/7)^.4)) (3)
Suppose games were played on four consecutive Saturdays. If the ratings were done on a Monday, this would mean that the games were played 2, 9, 16, and 23 days ago. Well, by formula (3), any game played within 3 days of the rating gets a weight of 1. Games played the week before, or 9 days ago, get a weight of 1/((9/7)^.4) which is about .9. The games 16 days ago are weighted at about .72, etc. This is called a decay function, and, basically, it means that the more recent the game is, the more heavily it is weighted.
Finally, whatever the weight it, it is doubled for games at Regionals, and tripled for games at Nationals. After all, teams are usually at full strength during those tourneys, and the games are more important.
But that's not all! Suppose the ratings of the teams you play change. An underated team you lost to in the first round ends up winning the tournament. Should your rating reflect that teams' victories, in other words trying to take into account that the other team was a really good team. Of course it should. Suppose your team's rating went up during the course of the tourney, too; shouldn't other teams, in turn, get the benefit of that?
This is done in an interative process. Each week, every team gets re-rated. That is, we recompute every individual game rating, based on the previous week's ratings, and the new date. Then, each team gets a new rating for the current week. Then, we re-rate every team again, using this week's ratings, to get a new set of ratings. We do this thousands of times until the rankings stabilize and reach equilibrium. If some team does really well, and the rating goes up 250 points, then, on the second iteration, all teams that have played the first team goes up by a smaller amount, and on the third iteration, all the teams that have played the teams that played the first team will go up by a small amount, and so on.