[blml] Swiss Teams formats

[richard willey]

This post might be timely considering all the posts regarding scoring tables:

Girben Dirksen, Alex Ogan and I are doing some work studying different
formats for Swiss team type events.  Our end goal is trying to
determine how to make these events more "efficient".  For the purpose
of this discussion, we're assuming that efficient = accurate.  Our
only goal is to produce a system that is as accurate as possible in
rating the various teams that participate.

We're using a fairly simple methodology based on Monte Carlo
simulation.  We start by creating a set of virtual teams with known
strength.  (Team strength is assigned using a Gaussian distribution).
We then have the teams compete against one another.  At the end of the
tournament, we're able to compare the sample statistic (the result of
the tournament) with the population statistic (the known ranking of
the teams).  We can then vary the Conditions of Contest and see
whether this improves or degrades the accuracy of the sample
statistic.

For the moment, we're using a very basic measure of "accuracy":  (The
average (objective) rank of the winning team).  Long term we're
planning to adopt a more sophisticated metric based on the statistical
notion of the Coefficient of Determination (R^2).

We've already produced one quite interesting result.  We can
significantly improve the accuracy of a tournament by "rear loading"
the boards.  Assume for the moment that a Swiss Teams event will
consist of 72 boards distributed across 9 rounds.

Format A holds round constant.

Format B has

Round 1 = 4 boards
Round 2 = 5 boards
Round 3 = 6 boards
...
Round 9 = 12 boards

Format C =

Round 1 = 12 boards
Round 2 = 11 boards
Round 3 = 10 boards
...
Round 9 = 4 boards

>100000 Swiss team tournaments of 9 rounds, team 1 = strongest team,
team 2 = next
>strongest, etc. (from Gaussian distribution). Calculated AVERAGE TEAM NUMBER
>of the winner.

>8-board rounds: 2.86
>increasing round length (4 ... 12): 2.69
>decreasing round length (12 ... 4): 3.10

>Sounds like first-order proof that longer matches later on is a good idea.

>Finally I tried 16 rounds (8 board less!) of 4 boards and got: 3.93

>I didn't use a VP table yet but instead a match result was IMPs/board
* sqrt(boards) ,
>the formula on which the VP table is based.



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