The famous pie rule is that when two
people are to share a pie, one person cuts
the piece and the other gets to pick which
piece to take. That is to guarantee a fair
cut.

Suppose you have ten teams that are to
select 100 players, i.e., 10 per team. Give
each team a pick in each round
to put a
player from the pool into one of ten
buckets. However, no team will know at
this stage to which team any given bucket
will go. Any bucket that has ten players
may not be added to.

When all players have been selected, allow
the teams to choose which of the ten
buckets to take.

Some one may say that this is no good
because all teams don't have the same
needs, e.g., team 1 has a great goalie and
not even one good center forward, team 2,
on the other hand, really could use a
better goalie. That's fine. It is just one
more criteria in making sure that the
buckets are evenly balanced.

Alternative 1: allow the teams to know a
priori the order they get to pick the
buckets

Alternative 2: make the order of picking
buckets random

Alternative 2b: only announce which team
has the next pick

Alternative 3: completely randomly assign
the buckets to teams

Alternative 4: add a rule on trades. e.g.,
no trades allowed for a certain number of
games.

Alternative 5: allow teams to make
intermediate picks of buckets (e.g., after x
number of rounds), and then be stuck with
what comes next in that bucket.

Alternative 6: through a voting mechanism
or caucusing, rank all the players. Then
assign them in order (bucket of player i = i
mod 10).

Alternative 7 (the true pie rule): if there
are n teams that have not yet picked a
bucket and i is the next team to pick, let
teams i+1 through n distribute the
remaining players over n buckets and let
team i pick any of the n buckets. Repeat.

(Alternative 7 came to me as I was writing
this. Now I like it best!)