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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!)
Wikipedia: Pie Rule
http://en.wikipedia.org/wiki/Pie_rule
Application of "divide and choose" (which the poster means by "Pie rule") to strategy games? [jutta, Apr 26 2007]
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Annotation:
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Never heard of a pie rule. Unless it is some sort of government based on fruit filled pastry. I think you are referring to cake cutting algorithms. |
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Edit: Interesting link Jutta, I had never heard divide and choose applied to pie, always cake. And I like pie, but not really cake. |
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I only remember doing this with items weighing 1/8th of an ounce. |
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//put a player from the pool into one of
ten buckets// - so you play the darts
underwater, but you have to hide in a
bucket until it's your turn - sounds like
fun. |
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One of the goals of the existing draft system seems to be to balance out team strength - giving slightly better players to slightly worse teams. |
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In order to allow for the pie rule with this side condition, you'd have to make the existing team part of what's being redistributed. I think that would confuse fans. |
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[jutta] I did think of the problem you
mentioned. Over time, I think team
strength should smooth out. |
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If the bucket choosing order were known in advance, it would make sense for all teams except the last chooser to load one bucket with the weakest players. |
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It has always amazed me that in the great US of A, spritual home to free enterprise, that sports are such a cartel/closed shop. The system seems frighteningly socialist to me. Why not bid for the best players and pay them what you think they're worth? Then you could stop agonizing over things like drafts. |
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I think we should consider introducing a
Heisenberg's Bucket to this proposal...
retreats into shadows.... |
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"Alternative 6" yields buckets of varying desirableness. |
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For example, 20 players (of rank 20 down to 1) going into 10 buckets:
bucket 0 : 20,10
bucket 1 : 11,1
bucket 2: 12,2
bucket 3: 13,3
bucket 4: 14,4
bucket 5: 15,5
bucket 6: 16,6
bucket 7: 17,7
bucket 8: 18,8
bucket 9: 19,9
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If you're looking to make the buckets completely even, then an improvement is to reverse the order of every other column. Of course that isn't perfect unless the desirableness of the players is proportional to their rank. If you're assigning more than two players to each bucket, additionally staggering the columns would improve matters slightly. |
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