Ref:Very interesting mathamatical point, mathman. The problem would be the data entry, but ingnoring that for a minute, we have all seen competitions decided by a point or two and sometimes much less. So, what if a commentator had a real time mathamatical modeling computer that would say, "with these nine scores, and the final result for pairs being S/S having 212.26 and V/T having 212.18, the majority of random pics would have picked V/T as the winners, therefore the Germans better go buy lottery tickets...."
I believe the first version of the random draw was something like this: out of 14 judges eliminate 3 by a random draw, then throw out the two highest and the two lowest. I am not 100% sure if I remember the details exactly right, but in any case there are two mathematical issues. These were debated with great vigor at one time.
(1) Does the random draw turn the contest into a roll of the dice, or does it just seem that way. I am quite sure that it just seems that way. Here's why.
Suppose there are 50 countries in the judges' pool. Six months before the contest 14 countries are chosen at random to supply judges. At the time of the contest another random draw takes place in which 11 scoring judges are selected from among the 14.
Mathematically speaking the result is exactly the same as if the 11 were chose at random from the original pool of 50 in the first place. So, no, the two-stage random draw is no more of a crap shoot than is the one-stage random draw. Either way, each country has exactly 11 chances out of 50 of landing a spot on the scoring panel.
(This analysis is ever-so-slightly skewed in later versions of the procedure in which some judges were carried over from the short program to the long and others, chosen at random, were replaced.)
The ways in which the two methods (one random draw well before the event versus a two-stage random draw) differ are not mathematical but rather involve things like, once the 14 candidates have been chosen the lobbying starts -- the 14 get invited to cocktail parties, they receive birthday presents, etc. -- so in that sense the extra three are not treated the same as the 36 who were not chosen in the first round.
So, since there is no mathematical reason pro or con, what are the advantages of having a two-stage draw versus the traditional one-stage draw?
Disadvantages: The two-stage draw is stupid on its face, and makes everybody say...huh?
Advantages: The ISU offered some, but I will not list them here in order to save the ISU embarrassment.
Anyway, the bottom line is, any method of choosing judges is a crap-shoot. At 2002 worlds as soon as the panel of judges was announced it was clear that there were 6 Slutskaya judges and 3 Michelle Kwan judges on the panel. In the ABC broadcast, after Michelle had skated Peggy Fleming turned to Dick Button and asked, "Well, do you think that was enough to beat Slutskaya?" Button replied, "With this panel of judges, no."
Maybe no one cares anymore, but I thought the idea was to make the scoring more fair, not random.
Well, no one cares any more because there isn't any random draw any more, so these questions are now moot.
As to the motive behind the changes in judging procedures (anonymity, etc.), the intuition was not to make the judging more fair but to make it so hopelessly opaque that no one would be able to support complaints about the judging a la Salt Lake City.
Or you could ask Elene Gedevanishvili if SHE thinks the comm bloc is dead....
Well, Georgia
was part of the Soviet bloc.
Edited to add: Oops, I forgot mathematical point #2 -- the trimming of the mean. Suppose that we have a certain number of scoring judges, however determined. Should we throw out the highest and lowest before averaging? Should we throw out the two highest and the two lowest? (One version of the iSU judging procedure called for throwing out the two lowest and the one highest.) The extreme version of trimming would be to throw out all except the middle -- in there words, to use the median score instead of some sort of average.
The main question is, does it make any difference, or would the same person win almost all the time bio matter which system is used? (There are also questions about measures of variation, etc.) Unfortunately there are not any nice formulas to apply in determining the sampling distribution of the trimmed mean. (Formulas that have "sigma over the square root of n" don't work -- which throws out 90% of all statistical methods.
) Most studies of this kind involve boot-strapping methods where you try to get and approximation, then use that approximation to get a better one, etc.
In general, all of these methods -- the mean, the median, and the in-between idea of the trimmed mean -- turn out about the same in situations where the data is approximately symmetric about the mean. (It does not need to be normally distributed.)
Applied to figure skating scores, the most dramatic asymmetry occurs via keying error -- a judge intend to type 9.5 and hits 0.5 by mistake. The current method of minimal trimming (delete only one high and one low mark) catches that kind of error without throwing away any valuable data. So I think the current method is a good one and the best available.
:yes: I hate the anonymous judging!:disagree:
Sorry...Just kidding.....)
