Tournament formatting and other nerd stuff

Random certainly isn't fair.

Elaborate? I cant think of a more fair method.

Drawing names out of a hat for a standard or serpentine pick seems less fair.

Being first of the captains for the 2nd pick might be a lot more valuable than being the first of the captains for the 5th pick.

Random certainly isn't fair.

Was having a chat about this at the weekend (more for the next league rather than this Bench). Our conclusion was that random was unfair - but equally unfair to everyone.

I'm confused as to how equally unfair doesn't equal fair?

No need for confusion. It does equal fair.

Random gives everyone an equally fair chance, but if you are after a fair distribution, for instance in distributing draft picks, then you need a system.

That's the point though, random is not equally unfair. It's better for some than for others, it's only "fair" in the sense that anyone has the chance to get the more advantageous spots, but once they are assigned it's no longer fair.

As Lebowski says, to make it as fair as possible you need a system which tries to balance the advantage as much as possible between all the teams.

Serpentine is probably the best way of doing this, given the set of players. No method will be perfect, as these are real people, not a simulation, and you can't just say that A & D, equals B & C. There are so many more factors like form, familiarity, captain's opinion or knowledge of a certain player etc.

But serpentine doesn't give an even distribution, it gives bunched distribution.

How so?

Also, suggest a better system. I'm happy to have a maths geeks out on why a system is better than another.

Can we mod a separate thread for fair draft systems, this chat is killing the tourney buzz in here. And it seems the chan tags have stopped, which is a shame.

Agree, will move out, and create a tournament nerds thread.

Ok the systems that are fairest depend on the number of teams and number of picks.

If the number of teams and players is the same then I'd suggest the following method:

1 2 3 4 5
2 3 4 5 1
3 4 5 1 2
4 5 1 2 3
5 1 2 3 4

If that makes sense?

For the Bristol as there are 8 teams but only 7 rounds I'd do the above method but missing out the last round (which is still a much fairer than serpentine, where the first pick team will get the first pick in 4 of the 7 rounds!)...

When the disparity between number of teams and picks gets much bigger, I'd double the jumps, say 8 teams with 4 picks:
1 2 3 4 5 6 7 8
3 4 5 6 7 8 1 2
5 6 7 8 1 2 3 4
7 8 1 2 3 4 5 6

For some pick/ team ratios the fairest system is a bit more complicated... But I'll leave those possibilities for later. (Can't leave it, in the above example it might be slightly fairer to swap the pairs in alternating rounds)

So in your first example, team 3 will have a much better top 3 than team 5, for example.

Serpentine assumes that all players can have their value expressed in points whereby the ideal first pick is worth 56 points and the last person to be picked is only worth 1 point.

Polo players and the roles they play within an ad-hoc team on court vary, so their value depends on the strategies employed by the captains and how they're deployed.

Assuming the 56 - 1 point value just for the purpose of argument, Serpentine is unfair when you have an odd number of picks.

which is still a much fairer than serpentine, where the first pick team will get the first pick in 4 of the 7 rounds!)

What's wrong with that? After all, they get the last pick in 3 of the 7 rounds.

The first pick in a round is only relative, after all it's a less good pick than any of the picks in the round before.

Assuming the 56 - 1 point value just for the purpose of argument, Serpentine is unfair when you have an odd number of picks.

Well, in theory yes, but you need to look at the relative value of that last round.

Would you agree (in the theoretical example where each pick is worth 1 point worse than the one before), that with 6 rounds of picks, Serpentine is fine (every team has the same value).

Where that theoretical example falls down is that by the time you get to round 7, the difference between the "value" of players is tiny, and also at that point captains will be choosing for many different reasons (players they know, players that pair well with other players etc). I don't think it really matters which way round that round is.

I think the value distribution is s-shaped, not inverse-square, so considering we have 100ish entrants for 56 places, the difference between the upper quartile (3 picks-worth) of players is relatively small and down to style and taste; We might also assume that the lower quartile might all be equally useless when playing against an upper-quartile trio, so seeds 26 - 75 have a greater difference in value per seed position than the upper and lower quartiles.

Well, but the last pick in any team is likely to have the least impact simply because they are going to be played least.

You are right, I just don't think it really matters, and I can't come up with an alternative for the last round which I can justify mathematically.

Seed the players into even ability groups, have X groups = X captains. Assign the groups to the captains and ask them to pick a player (usually the best player) from their group. Then have the captains pass the groups of players (to the highest multiple of the number of captains) to their right (or left, or right-to-left alternating) and ask each captain to then again make a second pick from their assigned group. Repeat this process X captains times (there may be some leftover players, this is fine, they haven't been picked) until all the captains have selected their players. Then have each captain crouch (on all fours) on top of each other in pyramid form with the largest captains forming the bottom row and the smallest captains forming the upper rows. Each captain (starting with the captain on top) then passes their list of players rotationally (clockwise) to the next captain that forms a mini-triangle with themselves within the pyramid. Once the pyramid has been disassembled the process is complete.

Sounds like a conspiracy.

lol

thats not as silly as it seems.

Assuming the 56 - 1 point value just for the purpose of argument, Serpentine is unfair when you have an odd number of picks.

Can you suggest a system that would be fair when assigning those points with an odd number of picks?

#hasbeendoingthemaths

It gets worse, 7 is a prime number.

There would have been one other system I would have been tempted to use, it's an auction draft.

Basically, every captain has a set budget. Each captain takes it in turn to nominate a player they want, and bid on them. If no-one else beats that bid, they get the player. If another captain bids higher then they can bid even higher, etc, until there are no more bids.

What it means is that any captain has the chance to get any player they want.

The downside is that I think everyone would have to practice it a few times, to get an idea of a good strategy to make a team. I think a lot of people would blow their budget to get 2 or three 3 good players, and end up with a really unbalanced team.

It's great in theory, and great for fantasy football nerds, not so sure if it works in real life, where having a fun and fair tournament is more important than having a perfect draft system.