0
I made no such claim.
However, that would be an interesting study. Maybe we can cajole Vanshilar into undertaking it. Take all possible permutations of judges' scores (9 factorial divided by k factorial whenever there are k scores the same), and see what percentage of the time it comes up one way rather than another.
As for what is intuitively more likely, well … in this argument some people think it is more likely that some judges are stingier across the board, while others think it is more likely that some of the judges were biased. I do not have an opinion about which of these is more likely. We do know that in figure skating judging both happen. My only point is that we cannot decide by looking at the protocols, thanks to randomized anonymous judging.
I can't fathom the cognitive dissonance of someone who can put these two sentences side-by-side.
It's easy enough to write code to iterate through different possibilities, but I'm not sure what the study is exactly supposed to be. Is it trying to figure out that assuming each permutation were equally likely, what were the rankings for each skater from each judge? How many skaters would be compared (and which)?
I don't know, either, what such a study would show. An earlier poster gave the opinion that matching high scores with high scores and low scores with low scores is inherently more likely than matching high scores with low scores and low scores with high scores. I just wondered how many of the latter kind of matchings would result in a situation where a minority of the panel dominated the ordinal majority. Maybe some sort of Bayesian analysis could then say something about the relative likelihood of (a) three judges conspiring to fix the results and (b) some judges were stingy and some generous across the board.
I don't think so. though. In this instance (as in almost all applications of statistics to figure skating judging) non-statistical considerations swamp anything we are trying to study. That is to say, judges' scores are not a sample drawn at random from a nicely distributed population -- certainly they are not if someone is playing sample demon by deliberately cheating or responding to national bias.
I meant I didn't know what I was supposed to do -- if it was just trying out each permutation of say skater X's judge 1 with any of skater Y's judge 1-9, then skater X's judge 2 with any of skater Y's remaining 8 judges, etc., and compare how often skater X was ranked higher than skater Y by the judges or something like that. In which case, at a first glance it seems like it's just a matter of iterating through the 9! = 362880 possible permutations, which seems easy enough. I guess adding a third skater would make it a lot more difficult since there'd be (9!)^2 ~ 1.3 e11 permutations which would take a lot longer, so it's probably better to just do pair-wise comparisons between different skaters depending on how efficiently I feel like coding it up.
But what exactly would I be comparing? Is it the sum of the PCS scores from each judge? Is it the sum of the GOEs? If I do something like the total score that each judge gave, then the technical calls and base values (which are based partially on the technical calls) could affect the rankings, but some of those are themselves under dispute. Yet if I only look at the sum of the PCS scores, for example, then it would only show how the judges would've ranked the skaters' overall impressions (artistry, etc.) and not consider the overall performance such as technical elements, which could change the judge's overall rankings. That would be true of any subset of the scores such as GOE's as well. So basically it could be done, but the implications are somewhat limited.
If we're looking to determine if there were any judging irregularities, whether high scores matched with high scores or high scores matched with low scores would be exactly the type of statistical analysis that would be performed, except that anonymous judging specifically removes this as an option. For example, "fair" scoring might look like (just making up numbers so they're not realistic):
Skater X: 10 9 8 7 6 5 4 3 2
Skater Y: 9 8 7 6 5 4 3 2 1
While judging with a few biased judges might look like:
Skater X: 8 7 6 5 4 3 2 10 9
Skater Y: 9 8 7 6 5 4 3 2 1
In the first case, of course, every judge felt skater X did better, while in the second case, every judge felt skater Y did better except the last two who threw the scores so that skater X would have a higher average. If the judges were known, it would be easy enough to do an X-Y plot (i.e. matching the scores from each judge) to determine this. Under anonymous judging, the scores shown in either case would be the same -- removing the ability to do this kind of analysis and to detect such biased judging. I'm not sure how you would construct a Bayesian analysis to determine how likely it is that you had some judges conspiring to fix the scoring, given that your beliefs on the number of conspiring judges would be the prior in the first place if I were to do the permutations -- so the results depend very much on your beliefs, which is, of course, different for different people and under disagreement in this thread.
of course qwertyskates is going to react from mathman's post..took it personally and now making an accusation w/ the poster.. how predictable.. and every poster who defended sot's ogm..
that 31 goes+ for sotnikova if it's indeed true is insane.. and it looks like someone who's in payroll..
ISU should reveal the scores!! there's nothing to hide.. besides russia and the US advocates to get rid of anonymous judging.. why not try to make an example of this?? after all it was a legit win.. right??
They should release the judge's marks but also the technical caller's marks. See if the Russians Lakernik and Baranova worked together against Gusmeroli.
Of course the ISU won't do this though because they have something to hide.
Just as a purely mathematical puzzle, I would be interested to know the following. I do not know what conclusion I could draw from the answer -- probably none.
Here are the total PCS for each of the nine judges for Sotnikova and Kim. (These are slightly different from what I posted earlier. I think these are right. I have a visual handicap that makes adding up lists of numbers difficult.)
SOT 48.25, 48.00, 48.00, 47.75, 46.50, 45.50 45.00 44.25, 44.25
KIM 48.75, 48.00, 47.75, 47.00, 46.75, 46.00, 46.00 45.25, 42.00
Fix Sotnikova's order and for each of the 300,000 possible ordering of Kim's, record the number x of judges that favored Sotnikova (half a point for a tie). What is the frequency distribution of x?
At the moment I cannot think of any reason why anyone would want to know this. But I think it might point my mind in the right direction to worry about it some more. I have a feeling that questions of this sort have already been extensively studied, and the result would be the same if we used the numbers 1, 2, 3, …, 9 instead. But the interesting thing would be, how does the distribution change as a function of the difference in the means? (In this example the means for the two skaters are about the same.)
Eh okay but the numbers that I'll be using are:
SOT 48.25, 48.00, 47.75, 47.75, 46.50, 45.50 45.00 44.25, 44.25
KIM 48.75, 48.00, 47.75, 47.00, 46.75, 46.00, 45.75, 45.25, 42.00
I guess basically I'll tally up how often I had x = 0 to 9 in increments of 0.5.
While I'm working on it, does anyone want to speculate on what would it mean if I find that the distribution was generally above x = 4.5 (indicating more judges favored Sotnikova), or if I find that the distribution was generally below x = 4.5 (indicating more judges favored Kim)?
I think it's fairly obvious from the context that Ven is talking about the levels, URs, wrong edges, etc., regardless of if they're called marks, calls, indicators, or whatever.
It's this kind of ignorant comment that makes me angry and also proves that this is just Yuna hater who just cannot see Yuna being in the right way, but in the end, it's pretty obvious there was manipulative and biased judging that caused this controversy. Flutz and UR not being called on Adelina was a dead giveaway. And if you cannot see( or purposely refuse to ) that, well sorry my friend, you need new set of eyes. Perhaps Yuna fans are just trying to make this sport more fair by setting her as an example and prove that she's a victim of this corrupted sport.
Plus you failed to understand what Ven was saying
Bookmarks