Normalization Clarification
 

When I mentioned normalizing based on number of regionals attended, this is what I had in mind:

N = number of regionals attended
P = total points awarded
F = normalization adjustment factor
Q = qualification score

Q = F * P / N (note that this is equivalent to Q = P/(N/F))

For Andy's formula, he has F = 1. I think F should be around 2.

The reason for this is so you don't discourage teams too much from attending more than one regional. In this manner, in the long run, you are more likely to qualify for nationals by attending more regionals, but you are not 4 times more likely to qualify by attending 4 regionals (if F = 2, you are twice as likely to qualify by going to four regionals).

My formula is similar to the SAT's. You lose one point for a blank answer, and 1.125 (or something like that) for a wrong guess. the point is to make sure that in the long run, you are better off to not guess. The above formula makes sure that, in the long run, you are still better off to attend more regionals, but it reduces the advantage somewhat.

-Chris

Re: Good start
 

I LIKE EQUATION :D However i suggest (as I think Chris suggested) adding a normalization for the number of teams you are competing against at each regional... This way teams are not discouraged from going to large regionals.

n = number of regionals a team attends
t = the sum of the team attendance at each of the regionals you attend
T = average number of teams at all regionals (a constant)
p = total "FIRST points" a team wins during all regionals it attends
Qp = qualification points a team gets

Qp = (p*t)/(n*T)
which also gives you a unit of points per event. Basically this means that a team who attends one small regional (eg 40 teams) competiton needs to earn 1.5 times as many points to go to nationals as a team who attends a single large regional (eg 60 teams). At the same time, a team who attends a single regional only needs half as many points as a team who attends two regionals of the same size.

Patrick