Wednesday, August 29, 2012

Climbing on and Off Olympus: Big Swiss Cheese

The way large team tournaments operate in Swiss format fascinates me.  Its kind of like a gigantic fractal, and for me quite honestly and vividly and literally is a kind of mini-model of, if not the cosmos, complex systems [1], whereby things grow, collapse, achieve stability, migrate, or disappear.  My oft repeated phrase, the refrain 'I thought this was supposed to be about chess?'  Well, I am just getting to that.

What is so beautiful and elegant is how very rapidity with which a set of complex elements, ranked according to values, gets shuffled and sorted then assigned values according to an evaluation.  The accuracy in the first and second passes necessarily has limitations, but again, in large team tournaments, this is very fast, and becomes very, very highly articulated.

This is how it works.  One hundred-fifty six teams were seeded, of which, one hundred and fifty actually started.  Of those, forty-five scored 4.0, and eighteen scored 3.5.  Due to top seeds playing very weak teams to start, whether a team scored 4.0 or 3.5 cannot be especially statistically significant, since while the board by board teams are highly assymetric, but may contain top boards less disparate than the other boards.  That is to say, 'stands a fighting chance', as we say in English.

For example, Russia scored 3.5 and we can from that hardly say that they are more accurately assigned forty-sixth place after round one.  To continue here: in an individual competition, after round one, you would have a lot of +1.0's, some 1/2-1/2's, and of course 0.0's.  But here we start out with 4.0, 3.5. 3.0, etc, all the way down to 0.5 and 0.0, seven sets.  This is not where the magic starts.  But after round two, you can have a full FIFTEEN sets.

It gets much tougher, very fast as you go, so that now at the end of the second round, you have five teams at the top:  one with 8.0 (Slovakia, if I view this right), and five with 7.5, and five with 7.0.  Things happen pretty fast.  Of course, if you take a closer look, linked here, and here, and here, things are not so simple, but whatever it is, to me this is very fascinating.  Not sure if this is the term, in mathematics, relates to what is called a run-away analysis [2].  See you all soon. 

[1] Notably biologic, chemical, physical, social, cultural, artifactual, heuristic.  Shall I go on?  Lets see,lets do one or two more: spiritual, governmental, sexual.  Do these go together or just the luck of the draw. 

Double click image to enlarge

[2] This term is not right, but I am close.  For example, see 'Jeff Sagarin's Computer Rankings', for sports at USA Today.  Don't be thrown off by the popular rag [3] part, this smart F'r is a mere MIT graduate, smarter than sh_t.  He not only ranks opponents, but the opponents opponents, etc.  You get the idea.  The permutations are infinite.

[3] Popular rag:  colloqueal for cheap newspaper,.


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