2004 WORLD TEAM TANTRIX CHAMPIONSHIP

 

HOW THE DRAW WILL WORK

 

This page is subject to change if anyone spots a flaw in the logic before the draw!

 

The seeding bands have now been published at http://tournaments.tantrix.co.uk/2004wttc/seedings.htm and the draw will take place in the www.tantrix.com game lobby - probably in a game/chat room – look for the one that’s full of people!

 

Triple control:

 

As usual, three people will be involved – this time it will be Zoltán Németh (“Zormac”) from Hungary drawing the tiles without knowing which teams or groups they represent (so that you will know that he cannot draw them to benefit HUN) and me, i.e. Steven Trezise (“steven2”) from the UK, knowing which tile numbers correspond to which teams or groups but having sent the list to Dave Dyer (“ddyer”) from the USA before the draw so that you will know that I cannot change them to benefit GBR during or after the draw.

 

Keeping teams from the same country apart:

 

The need to achieve dual objectives, i.e.

 

a)      to ensure that one team from each seeding band ends up in each group

b)      to ensure that no more than one team from each country is in any one group in order to keep the tournament feeling very international for everyone

 

… means that the draw will be more complex than usual. As a result, it may look like we are making the draw up as we go along but in reality it has been planned in advance!

 

It should be clear to everyone watching the draw which team is ending up in which group, even if they have not read what follows, but to prove that there is a system behind the draw and to give those of you who like to understand these things in more detail a chance of following what is going on, here is a description of how the draw will work and why.

 

N.B. this is also the ‘instruction manual’ will use to try and avoid me having to do too much thinking during the draw itself and to ensure consistency from year to year … and while it may sound very complicated, it isn't really … and it gets simpler as we find out which groups the higher teams are in and many of the possibilities described below do not materialize! J

 

Zoltán will always be drawing from tiles 1-4 or a subset thereof.

 

All of the randomisations mentioned below will be emailed to Dave Dyer (see above for the reason why) in advance of the draw.

 

Seeding Band 1:

 

The no. 1 and 2 seeds HUN A and NZL A will automatically be placed in into Groups A and D respectively.

 

Zoltán will then draw from tiles 1 and 2 to find out which team goes into Group B - one will be GBR A and the other GBR B, at random, as assigned by Steven and sent to Dave before the draw.

 

Seeding Band 2:

 

What we won’t do and why …

 

Moving onto seeding band 2, if we started with four tiles in the bag, drew for the second team in Groups A to D in that order (as would be normal in an individual tournament) and said that GBR C would go into the group they were drawn in if it did not include another GBR team and into the next free group otherwise, it should not be too hard to see that this would give Group D three times as much chance of getting GBR C in it as Group A!

 

What we will do …

 

Zoltán will first draw from tiles 1 to 2 to find out, according to SB2 randomisation no. 1, which group GBR C goes into (i.e. A or D) with each tile representing a different group (randomised) and then he will put tiles 1 to 3 back in the bag and draw from them again with each tile representing a different team (SB 2 randomisation no. 2) to find out which of FRA A, GER A and USA A goes into the other three groups. He will do this in group letter order, i.e. B, C, D if GBR C has ended up in Group A … or A, B, C otherwise.

 

The remaining seeding bands – general rules (this bit is for mathematicians only!):

 

We will continue to apply this kind of logic to the rest of the seeding bands, i.e. we will first draw to find out which group/s any B or lower team/s will be in and then draw from the A teams to find out which one goes in which of the remaining groups in group order.

 

In cases where two or more B or lower teams from different countries are in the same seeding band, we will first draw to find out which group for the lower team is in, e.g. C before B. This is because there will be less groups that the lower team can go in - i.e. the more higher teams from that country there are, the more groups will already be off-limits.

 

For the particularly committed mathematicians amongst you who are trying to follow (and possibly test) my logic, if (for example) the three higher teams (1A from country 1, 2A and 2B from country 2) have been drawn into different groups, then:

 

a)       if we drew the group for the 1B team first (with each of the three groups without 1A in it having a 0.33 probability of getting 1B in it), the pre-draw probability of the group with 1A in it getting 2C would be 0.67, i.e. very high

b)       if we drew the group for the 2C team first (with each of the two groups without 2A or 2B in it having a 0.50 probability of getting 2C in it), the highest pre-draw probability for any one group of getting the 1B team would be 0.42.

 

Thus, drawing the group for 2C first will minimise the ‘worst’ probability if anyone group getting any one team in it, which (to my mind, anyway) keeps the draw as random as possible and this is also consistent with the fact that when we get to a D team, that will have to be placed first, in the only group left open to it. N.B. If in a future year, more than one country has a D team in the main draw and they are in the same seeding band, we will need an extra safeguard built into the higher seeding bands to ensure that we cannot be left with both D teams having to go in the same group.

 

If two B or lower teams in a seeding band have the same letter, we will draw to find out which group the higher seeded of those teams is in first, on the basis that this is the team that all the teams already drawn from the higher seeding bands are more likely to want to avoid, so the more random the draw for that team, the fairer it is to all of the higher seeded teams above them.

 

What all this means in practice is that what I will do for the remaining seeding bands is to send Dave as many different randomisations of the 4 teams / groups as we could possibly need for that seeding band, and then use them in strict sequence.

 

Seeding Band 3:

 

For seeding band 3, I will first ask Zoltán to discard the tile that represents FRA A’s group in SB3 randomisation no. 1 and then I will ask him to draw from the remaining three tiles to find out which group FRA B goes into.

 

I will then ask Zoltán to discard the tile that represents HUN A’s group and the tile that represents FRA B’s group in SB3 randomisation no. 2 and I will ask him to draw from the remaining two tiles (or three if FRA B happens to have been drawn into HUN A’s group) to find out which group HUN B goes into.

 

I will then ask Zoltán to draw from tiles 1 and 2 in SB3 randomisation no. 3 to determine which of AUS A and SWE A will be in the first of the two remaining groups in group letter order, with the team not drawn filling the space in the other remaining group.

 

Seeding Band 4:

 

For seeding band 4, I will first ask Zoltán to discard the tiles that represent HUN A and HUN B’s groups in SB4 randomisation no. 1 and I will then ask him to draw from the remaining two tiles to find out which group HUN C goes into.

 

I will then ask Zoltán to discard the tile that represents AUS A’s group and the tile that represents HUN C’s group in SB4 randomisation no. 2 and I will ask him to draw from the remaining two tiles (or three if HUN C happens to have been drawn into AUS A’s group) to find out which group AUS B goes into.

 

If one of the two remaining slots is in GER A’s group, GER B will automatically go into the other remaining slot and NED A will go into GER A’s group, but in the (more likely, if you work through the probability tree) event that GER A’s group has already been filled, I will then ask Zoltán to draw from tiles 1 and 2 in SB4 randomisation no. 3 to determine which of GER B and NED A will be in the first of the two remaining groups in group letter order, with the team not drawn filling the space in the other remaining group.

 

N.B. It may look like the choice of group for NED A is being squeezed by this method, but if you work through the possible permutations for this seeding band, you will find that NED A can actually end up in any of the four groups and they have a reasonably similar probability of ending up in each one.

 

Seeding Band 5:

 

Like seeding band 4, this seeding band has A, B, B and C teams in it, so it will work in the same way. So, what follows is a copy of the last section with the team names changed:

 

For seeding band 5, I will first ask Zoltán to discard the tiles that represent FRA A and FRA B’s groups in SB5 randomisation no. 1 and then I will ask him to draw from the remaining two tiles to find out which group FRA C goes into.

 

I will then ask Zoltán to discard the tile that represents NZL A’s group and the tile that represents FRA C’s group in SB5 randomisation no. 2 and I will ask him to draw from the remaining two tiles (or three if FRA C happens to have been drawn into NZL A’s group) to find out which group NZL B goes into.

 

If one of the two remaining slots is in USA A’s group, USA B will automatically go into the other remaining slot and RoW A will go into USA A’s group, but in the (more likely, if you work through the probability tree) event that USA A’s group has already been filled, I will then ask Zoltán to draw from tiles 1 and 2 in SB5 randomisation no. 3 to determine which of USA B and RoW A will be in the first of the two remaining groups in group letter order, with the team not drawn filling the space in the other remaining group.

 

N.B. It may look like the choice of group for RoW A is being squeezed by this method, but if you work through the possible permutations for this seeding band, you will find that RoW A can actually end up in any of the four groups and they have a reasonably similar probability of ending up in each one.

 

Seeding Band 6:

 

Suddenly it gets a lot simpler because HUN D has to go into the only group without a Hungarian team already in it.

 

I will then ask Zoltán to draw from tiles 1-3 in SB6 randomisation no. 1 to determine which of POL A, RoE A and ISR A will be in each of the three remaining groups in group letter order.

 

As I said above, this all sounds very complicated, but it isn't really - I just have to be careful to get the sequence of the draws within each seeding band right and Zoltán just has to pick from whatever subset of tiles 1, 2, 3 & 4 I ask him to draw from each time.

 

KO draw:

 

As is usual when no new teams are added between phases, there will not be a separate draw for the KO phase – it will be defined by the group phase draw instead.

 

To avoid any ambiguity, the QF pairings will be A1 v C2, B1 v D2 (the two winners to play in one SF), C1 v A2 and D1 v B2 (the two winners to play in the other SF) with the SF winners meeting in the Final and the SF losers meeting in the 3/4 playoff. A1 means the team that finished 1st in Group A, etc.