# Thread: Men's PCS at Worlds.

1. Originally Posted by Mathman
This can't be determined from the data. The ISU makes sure of this. The judges almost surely did not match up from lowest to highest as in your table.
This is exactly what the data shows, however they are lined up. I arranged the scores in order only to make it easier to see the spread and what scores were thrown out. If the fact that Hanyu received more higher scores than Joubert does not determine that more judges favored him, you can't support the opposite as proclaimed from the same data either.

But in the aggregate, if the mean is larger than the median (the data is skewed to the right), this means that there is a tendency, however small in this example, for a few extra large scores have a greater effect on the mean than the few extra small ones.
But the data show also there are larger number of higher scores for Hanyu so his aggregate does not come entirely from a few extra large scores. He has more larger scores, especially after the high and low were discarded, which is why the the tendency is small.

That's kind of a red herring. It is true but does not address the question of which skater was favored by the majority of the judges.

Anyway, the point is that it can, and does, happen in the CoP, that one skater is favored by a majority of judges but the other gets more CoP points, whatever the averaging procedure.
But you can't prove that this is the case as announced.

I guess that's OK. That's how an add-up-the-points system works. It's different from 6.0, though. In 6.0, if you win the majority of first place ordinals, you win, period.
In this case Hanyu did win more higher ordinals than Joubert, seemingly even in just the PCS, which is why I debate your statement which can't be proven:

Thus the CoP. A majority of judges think that skater A was better, but skater B gets higher scores.
BTW, I was the one who complied the SSX10 vs PCS data per your suggestion.

2. Originally Posted by SkateFiguring
It's not true majority of judges thought Joubert's presentation was slightly better. Joubert received 11 higher scores than Hanyu who received 14 higher scores than Joubert.
I was talking about Presentation (PE + CH + IN). You mixed the SS and TR data in and came up with a different result, which has nothing to do with what I was talking about, and which like the design of CoP is capable of confusing the casual viewers. My conclusion had a scope (i.e., PE + CH + IN) and context (i.e, median as an estimate of majority opinions). You took it beyond its scope and out of context.
Originally Posted by SkateFiguring
eta I realized the original numbers and conclusions were drawn on 3 components of PE, CH, and IN. But the facts remained, Joubert had 6 higher scores while Hanyu had 7 higher scores bestowed by the judges and Joubert had 1.25 X 2 more points thrown out within these categories.
Interestingly, by using your "logic" of rearranging the data and combining "votes" across categories, I combined the data in all three categories and found Joubert actually had a higher mean (8.37) than Hanyu's (8.36) and, of course, a higher median (8.50) than Hanyu's (8.25). Both measures of central tendency supported my hypothesis that Joubert won the majority vote . Seriously, we cannot simply rearrange the data into pairs that did not come from the same judge and then compare who beat whom. Since the ISU hides the judges and scrambles the order of scores, the best we can estimate the majority ranking/vote is through the use of median.

3. Originally Posted by Bluebonnet
So I think we got the pattern.
Indeed, from your data I see the pattern: Besides a small number of incidents where the difference between SS and IN scores is greater than the minimal increment, the scores in these two categories were almost identical (i.e., no greater than the minimal gradation). This is the pattern (Correlation coefficient between SS and IN):
Men's SP: 0.9647
Men's LP: 0.9795

Cup of China
Men's SP: 0.9693
Men's LP: 0.9641

NHK:
Men's SP: 0.9859
Men's LP: 0.9813

The observed correlation between SS and IN is too high (ranging from 0.9641 to 0.9859). It strongly casts doubt about the judges' capacity to treat SS and IN as distinct categories and about whether those few cases where skaters showed discrepancy between SS and IN should have had an even greater difference in their scores if the judges did not have the tendency of scoring them in the same range.

4. Originally Posted by gkelly
The averages of the whole panel are going to flatten out the differences between highest and lowest components -- some judges will give wider ranges. In this event, as unfortunately in many events, the widest range is rarely over 0.75 for a given skater. I would expect something like 0.75 or 1.0 to be the average difference (i.e., larger than 0.36). But I would expect differences on the order of 1.5 or 2.0 or more to be exceptions
I largely agreed. I expect the discrepancy between judges' scores to be smaller in a more objective category (e.g., no greater than 1.0 in Skating Skills) and slightly greater in a more subjective category (e.g., no greater than 1.5 in Interpretation). Anything greater than 1.5 is likely a rogue score. And my instinct told me that a normal standard deviation among judges' scores in IN is probably somewhere between 0.35 to 0.65, such as Chan's first showing last season (i.e., Skate Canada) = 0.42, Chan's first almost-clean skate (i.e., 4CC) = 0.46, Yuzuru's first showing (i.e., Cup of China) = 0.40, Yuzuru's first almost-clean skate (Worlds) = 0.61, an unfamiliar face at Worlds (e.g., Harry Hau Yin LEE) = 0.59, and another unfamiliar face at Worlds (e.g., Taras RAJEC) = 0.45.

The standard deviation for Dai's LP at Worlds was 0.16, so small, almost like the judges already made their decision before he even skated. His first showing at Skate Canada had a standard deviation of 0.58.

5. Originally Posted by SkateFiguring
This is exactly what the data shows, however they are lined up.
SS:
Hanyu. 7.50--7.50--7.75--8.00--8.25--8.50--8.50--8.75--9.00 - 8.39
Joubert 8.00--8.00--8.00--8.00--8.25--8.25--8.50--8.75--8.75 - 8.21

Joubert wins 3 judges to 2, with 4 ties.

Match up the judges differently:

Hanyu. 7.50--7.50--7.75--8.00--8.25--8.50--8.50--8.75--9.00 - 8.39
Joubert 8.75--8.50--8.25--8.25--8.00--8.00--8.00--8.00--8.75 - 8.21

Hanyu wins, 5 judges to 4, no ties.

Hanyu. 8.50--7.50--7.75--8.00--8.25--7.50--8.50--8.75--9.00 - 8.39
Joubert 8.75--8.50--8.25--8.25--8.00--8.00--8.00--8.00--8.75 - 8.21

Joubert wins, 5 judges to 4, no ties.

6. Originally Posted by skatinginbc
I expect the discrepancy between judges' scores to be smaller in a more objective category (e.g., no greater than 1.0 in Skating Skills) and slightly greater in a more subjective category (e.g., no greater than 1.5 in Interpretation).
But there might be a little concern here. Greater discrepancy on the more subjective categories would mean that sometimes in some cases the placement of the skaters could be decided by these subjective categories. Will you say "Be it. I'll accept it"?

7. Originally Posted by Bluebonnet
But there might be a little concern here. Greater discrepancy on the more subjective categories would mean that sometimes in some cases the placement of the skaters could be decided by these subjective categories. Will you say "Be it. I'll accept it"?
As I stated in Post #229, I expect the normal standard deviation for a subjective category to be somewhere between 0.35 to 0.65. Of course, I will happily accept such subjectivity because that is the way it should be. I'm happy that Yuzuru's PE scores at Worlds showed a great variance among judges (standard deviation = 0.51). It made so much sense to me: Some judges liked his musicality very much while the others disliked his postures. The scores looked REAL. And don't forget we use the mean (or maybe median one day, like the International Tchaikovsky Competition http://www.tchaikovsky-competition.c.../voting_system) to find the middle point of the judges opinions. If you ask me whether I would take the subjective opinions of nine people who observe an elephant (i.e., the "true" or "right" score of a skater) from various perspectives, or I would take the objective opinions of nine people who measures the elephant's ear (i.e., skating skills) and the ear only with a ruler, I would say the former approach is a better way of finding out the whole elephant.

8. Originally Posted by skatinginbc
I'm happy that Yuzuru's IN scores at Worlds showed a great variance among judges. It made so much sense to me: Some judges liked his musicality very much while the others disliked his postures. The scores looked REAL.
Well, the posture shouldn't be reflected in the interpretation category. That's one reason why I don't like the idea of combining those three (or all five) components.

9. Originally Posted by skatinginbc
As I stated in Post #229, I expect the normal standard deviation for a subjective category to be somewhere between 0.35 to 0.65. Of course, I will happily accept such subjectivity because that is the way it should be. I'm happy that Yuzuru's IN scores at Worlds showed a great variance among judges. It made so much sense to me: Some judges liked his musicality very much while the others disliked his postures. The scores looked REAL. And don't forget we use the mean (or maybe median one day, like the International Tchaikovsky Competition http://www.tchaikovsky-competition.c.../voting_system) to find the middle point of the judges opinions. If you ask me whether I would take the subjective opinions of nine people who observe an elephant (i.e., the "true" or "right" score of a skater) from various perspectives, or I would take the objective opinions of nine people who measures the elephant's ear (i.e., skating skills) and the ear only with a ruler, I would say the former approach is a better way of finding out the whole elephant.
But if you did as you said you will, there wouldn't have been 16 pages in this thread which were largely generated by your outrage on Patrick Chan.

10. Originally Posted by gkelly
Well, the posture shouldn't be reflected in the interpretation category. That's one reason why I don't like the idea of combining those three (or all five) components.
Sorry, I meant PE (standard deviation = 0.51) and I will edit my Post #232 accordingly. Hanyu's emotional involvement in the music was excellent (very convincing, honest), but his carriage was, eh, still much to be desired.

Originally Posted by Bluebonnet
But if you did as you said you will, there won't be 16 pages in this thread which were largely generated by your outrage on Patrick Chan.
Come on. My outrage concerns the lack of variance in his scores. It doesn't look real. And it doesn't make sense.

11. Data entry mistakes?
Originally Posted by Mathman
SS:
Hanyu. 7.50--7.50--7.75--8.00--8.25--8.50--8.50--8.75--9.00 - 8.39
Joubert 8.00--8.00--8.00--8.00--8.25--8.25--8.50--8.75--8.75 - 8.21

Joubert wins 3 judges to 2, with 4 ties.
In ascending order, the SS scores should’ve been:
Hanyu. 7.50--7.75--8.00--8.25--8.50--8.50--8.75--9.00--9.00 - 8.39
Joubert 8.00--8.00--8.00--8.00--8.25--8.25--8.50--8.50--8.75 - 8.21

So Hanyu wins 6 judges to 2, with 1 tie.
Match up the judges differently:

Hanyu. 7.50--7.50--7.75--8.00--8.25--8.50--8.50--8.75--9.00 - 8.39
Joubert 8.75--8.50--8.25--8.25--8.00--8.00--8.00--8.00--8.75 - 8.21

Hanyu wins, 5 judges to 4, no ties.
With the correct data substituted, I matched up the judges in the same way as you did:

Hanyu. 7.50--9.00--7.75--8.00--8.25--8.50--8.50--8.75--9.00 - 8.39
Joubert 8.75--8.50--8.25--8.25--8.00--8.00--8.00--8.00--8.50 - 8.21

Hanyu wins, 6 judges to 3, no ties.
Hanyu. 8.50--7.50--7.75--8.00--8.25--7.50--8.50--8.75--9.00 - 8.39
Joubert 8.75--8.50--8.25--8.25--8.00--8.00--8.00--8.00--8.75 - 8.21

Joubert wins, 5 judges to 4, no ties.
Hanyu. 8.50--7.50--7.75--8.00--8.25--9.00--8.50--8.75--9.00 - 8.39
Joubert 8.75--8.50--8.25--8.25--8.00--8.00--8.00--8.00--8.50 - 8.21

Hanyu wins, 5 judges to 4, no ties.

12. Originally Posted by skatinginbc
Come on. My outrage concerns the lack of variance in his scores. It doesn't look real. And it doesn't make sense.
This has gone back to the original argument. Who decides what looked "real" and what looked "unreal"? Who decides what made sense and what didn't make sense? YOU?! To use your subjective views against the judges' subjective views, who is "right"? You have no reason to dismiss that there might be sometimes that the judges have all been charmed by some skaters' performances in the same ways and gave very close scores. Tell me that there is no such possibility.

13. Originally Posted by Bluebonnet
Who decides what looked "real" and what looked "unreal"? Who decides what made sense and what didn't make sense? YOU?! To use your subjective views against the judges' subjective views, who is "right"?
The audience. A.k.a a paying customer. And he expressed his opinion in Nice.

14. Originally Posted by let`s talk
The audience. A.k.a a paying customer. And he expressed his opinion in Nice.
After we've gone through this thread for 16 pages, it seems that opinion in Nice from the audience wasn't correct after all.

15. Originally Posted by Bluebonnet
After we've gone through this thread for 16 pages, it seems that opinion in Nice wasn't correct after all.
That is exactly why popularity of FS is declining rapidly- a paying customer is told his opinion is not right after all. So he goes to watch something else.

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