UPA College Rankings Algorithm

The UPA College Top 25 is an algorithm-based ranking system created by Sholom Simon. The rankings are calculated weekly, starting in March, by Sholom and are published by the UPA on its website.

The Top 25 algorithm becomes more accurate as more valid scores are provided by college tournament directors and teams. Scores should be entered through the Score Reporting tool on the UPA website. Scores for any team in the ranking system can be checked through the Score Checker tool on the UPA website.

The most basic explanation of the 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(.66,(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).

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+4)/7).4))            (3)

Suppose games were played on four consecutive Saturdays. Since the ratings are done on Mondays, 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. Finally, it is hoped that the winner of Nationals will come out as number one in the rankings. Luckily this has always happenned, although one year a team that lost in the semifinals almost finished first.

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. On Monday, 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 20 times (this is why a computer is indispensable). Eventually (usually after only about 8 interations) the ratings reach some sort of equilibrium. It's kind of a neat process to watch. 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.

The biggest problem with the system is that in some areas of the country not everyone is calling in scores. Let me give a classic example of how an entire region can be adversely effected by this.

Suppose the best team in Region X always calls in their games (and, in fact, more winners than losers call games in). So, suppose this team "State U." calls in 13 games of theirs, all victories. None of the other teams had called in any scores. This team beat, say, team B in the finals of two other tournaments. Obviously, team B must've been pretty good to make it to the finals, but to the computer, team B was simply 0-2. In fact, to the computer, it looked like the 13-0 team was playing a really wimpy schedule because every team that had played was winless! So what happens? State U doesn't get a very high ranking. Now, weeks later, the other scores are called in. It's too late, State U is already ranked lower than they should be, and all these other schools are, correctly, ranked lower than State U is. So, the whole region gets ranked lower than they should be.