This is more of a mathematical question than a FileMaker one, but I
thought maybe someone in this group might have come across it in their
programming:

I have an FM11 database designed to distribute ranked items to four
participants using random assignment in rounds of four. I want to be
able to grade how well each player did in getting to pick first,
second, third and fourth when all the rounds are completed.

Specifically, there are 100 items, each of which constitutes a
record. There are four players interested in the items, so there are
four number fields in each record -- one for each of player. Each
player uses his number field to rank his interest in an item from 1 to
100. Taken as a whole, players will rank the items differently and
there may be some items for which no rank is given if the player isn't
interested at all. Each round, the database randomly decides who gets
to pick first, second, third and fourth, then assigns the top ranked
item in that player's list to them, removing the item from contention.

I'd like to build some tolerances into the system so that if the
random distribution ends up favoring one player too much -- say with a
lot of first-choice picks -- or another player too little -- say with
a lot of last-choice picks, the players can decide ahead of time that
the distribution should be done over. However, in order to grade how
well each player did in an overall distribution, I have to be able to
weight how much each position is worth relative to the others in the
round. For example, here are two sample distributions:

Sample A
Pick Number: 1 2 3 4
Sam 4 8 5 8
Raphael 8 5 6 6
Peter 5 5 9 6
Herb 8 7 5 5

Sample B
Pick Number: 1 2 3 4
Sam 4 7 7 7
Raphael 9 5 9 2
Peter 7 6 5 7
Herb 5 7 4 9

In Sample A, Sam only gets 4 first-choice picks, which isn't that
great compared to Raphael's 8, but he gets 8 second-choice picks,
which is better than Raphael's 5. Taking into account their third-
and fourth-place picks, what would the overall grade be for how well
they did in the lineup? Is Sam's result in Sample B -- 4 first, 7
second, 7 third and 7 fourth -- better than Herb's, since Herb got one
more first-place pick but 3 fewer third-place picks?

How would I score this? There must be a standard statistical model
that's been developed over the years so that I wouldn't have to make
something up that wasn't accurate. And further complicating the issue
is that not everyone participates in every round, since not everyone
is interested in all 100 items. So it wouldn't be a matter of just
saying how many first-place picks to each player get relative to each
other: a player that participates in every round is much more likely
to get more first-place picks than a player that's only interested in
half the items.

Makes sense? What do you think.

Thanks for your help,
-J.