Just a thought on Johnny

[Vodka Shot]

Mathman,

Aren't you a math professor? What do you make of what people are saying with regards to a rounding error affecting the outcome?

 

[Mathman]

^ I don't know what to think. GSRossano is the expert on this sort of thing. He posted a brief explanation on his website

http://www.iceskatingintnl.com/current/content/usnats08.htm

yesterday, but now I see that he has removed it to be included in a more comprehensive anaysis of the whole shebang.

As far as I can figure out, the argument is over the exact wording and intent of the judging system with respect to rounding. Not exactly a rounding error but a choice between two different rounding procedures. Dr. Rossano feels that the software that makes the calculations does not follow the letter of the ISU rules. I have not followed the debate on other boards.

Personally, I think it would have been beyond cool if USFS would have declared it a tie and made Johnny and Evan do a sudden death jump-off. Start off with a triple toe, then triple sal, etc., up to 3A and quad. First one to miss loses.

 

[Vodka Shot]

....And then run through an obstacle course and climb a rock wall while American gladiators try and pull them down!

Thanks for the info, seems to make more sense to me now.

 

[daisies]

They had better both be placing at Worlds. So hence even though they compete against eachother they work as a TEAM for the USFSA to make sure they both or someone else gets to Worlds next year.

This is getting to be silly. Are Evan and Johnny huddling together before their skates to go over a game plan?

Evan: "OK, I'll go for the quad-triple and you play it safe with no quad. That way we will be sure to place high enough to get three men to Worlds next year."
Johnny: "Got it. And you do that spazzy straight line step sequence that makes the crowd go wild, flailing your arms so much that you detract from what your feet are actually doing."
Evan: "Great! Go team!"
Both: "Ready? Break!"

Um, I don't think so.

 

[Medusa]

^ I don't know what to think. GSRossano is the expert on this sort of thing. He posted a brief explanation on his website

http://www.iceskatingintnl.com/current/content/usnats08.htm

yesterday, but now I see that he has removed it to be included in a more comprehensive anaysis of the whole shebang.

As far as I can figure out, the argument is over the exact wording and intent of the judging system with respect to rounding. Not exactly a rounding error but a choice between two different rounding procedures. Dr. Rossano feels that the software that makes the calculations does not follow the letter of the ISU rules. I have not followed the debate on other boards.

Personally, I think it would have been beyond cool if USFS would have declared it a tie and made Johnny and Evan do a sudden death jump-off. Start off with a triple toe, then triple sal, etc., up to 3A and quad. First one to miss loses.

Well, I did the math - and I can confirm the result of the website. It is actually a rather simple mistake or misunderstanding.
Ok, first the rulebook apparently (I didn't find the place of these calculations rules) says this:

"It also calls for calculating the single trimmed mean for each Program Component, multiplying by a factor (2.0 in the Men's Free Skate), and then rounding to two decimal places.The factored results are rounded to two (2) decimal places and added. The sum is the program component score."

Definitions
Single trimmed mean -- take the 9 single marks from the judges, delete the highest and the lowest, add the rest 7 marks and divide the sum with 7. The result is the single trimmed mean. Example from Evan's Skating Skills score:

7,5 8,0 7,75 8,0 7,75 7,75 7,75 7,75 7,75 -- you delete the 7,5 and one of the 8,0 -- you add the rest and the result is 109/2 -- divide with 7 -- 109/14 -- multiply with factor 2 -- 109/7 -- round -- 15,57

What the guys at the Nationals did is this:
They took the 109/14 -- round -- 7,79 -- multiply with factor 2 -- 15,58

So instead of 15,57 points, Evan got 15,58 points. But that actually happened three times with his PCS:

Skating Skills: 15,58 instead of 15,57
Transitions: 15 points at both calculations
Performance: 16,14 at both calculations
Choreography: 15,72 instead of 15,71
Interpretation: 16,28 instead of 16,29

So he got twice 0,01 too many points and once 0,01 less. So he got 78,72 instead of 78,71.

Well, that's it. I don't know whether it happened before, but this time it seems somehow significant.

But I am all in favour for MM's proposition. Sounds great - imagine the TV-Ratings after the spectacle on Sunday. And it is a very viewer-friendly way to elect the "real" champion!

 

[Mathman]

Thanks for the info, seems to make more sense to me now.

Oops, Medusa beat me to it. I'll leave my post anyway -- two heads are better than one, LOL.

The issue is when to do the rounding, before or after factoring.

For instance, the Program Compnent Scores in the men's LP is multiplied by a factor of 2. So if you rounded the average of, say, the Interpretation scores, then multiplied the answer by 2, that would double the "rounding error."

Example. Johnny Weir's score (trimmed mean) in Performance/Execution was 8.142857143...

That rounded to 8.14.

Multiply by 2, and this gave Johnny a total of 16.28 for that component.

Now do it the other way: Take the same actual score of 8.142857143..., and first multiply by 2.

That gives 16.28571429...

Round this to the nearest hundredth and you get 16.29.

Johnny gets an extra .01. Johnny wins!

(Who would have thought that a competition could ever come down to such a close margin?)

 

[Mathman]

BTW, if they didn't do it this way (round first), then on the protocols the five program component scores would not always add up to the total, so that would look pretty fishy, too.

 

[GoldMedalist]

They had better both be placing at Worlds. So hence even though they compete against eachother they work as a TEAM for the USFSA to make sure they both or someone else gets to Worlds next year.

You have problems.

You're looking at two separate apples and calling it an apple pie.

We might as well say every tax payer in the country is part of a "Team", since they all work and give their money to a shared beneficiary.

 

[skatergirl45]

Isn't this supposed to be skating not math???? lol

Anyways, I think that this shows the problem of the new judging system. All my (non skating) friends were like, "how come the guy with the heart on his costume came in second?"

All I could say was because the other guy had harder footwork and spins and they were like, HUH????

 

[GoldMedalist]

Isn't this supposed to be skating not math???? lol

Hurray, you've just pointed out the #1 reason why the casual fan has been pushed away from the sport.

 

[gsrossano]

BTW, if they didn't do it this way (round first), then on the protocols the five program component scores would not always add up to the total, so that would look pretty fishy, too.

And my guess is that is why they added an extra rounding step that is not called for in the rules -- so the protocol printout would look pretty. But the rules are quite clear about the order of operation -- average, factor, round (rule 3435 (2) (n, o, and p)).

Of course the obvious way to make the protocols not look fishy would be to print the factored PC scores in the far right column instead of the unfactored average. Then the five numbers at lower right would actualy add up to the PCS total at the bottom right.

Medusa's numbers are exactly right. If you do the same exercise for Weir you find two PCs go up by 0.01 and two go down by .01 and the total stays the same.

This effect also does not show up in the Junior and Senior Men's SP since the factor is 1.00. The effect comes into play for any segment where the factor is not exactly one.

I would also add, that for every event where the factor is not exactly one, every PC score has a 50:50 chance for rounding incorrectly. That means with 5 PCs, there is a chance all five could round incorrectly introducing a 0.05 error in the total for one skater.

In principle, one skater could go up by 0.05 points and another down by 0.05 creating an artificial difference of 0.10 points, and if it happened in both programs, that would be an artificial difference of 0.20 points. But the chances of that are about 1 in a million -- equivalent to one nationals every 3,000 years!

But for a total of only 0.01 point, that happens about 1% of the time (very roughly).

 

[daisies]

So, should we be outraged? I kinda am. I think they should award two gold medals. Then again, I don't know if this is simply a part of IJS that we are supposed to accept.

 

[Mathman]

Hurray, you've just pointed out the #1 reason why the casual fan has been pushed away from the sport.

Reluctantly (what is more beautiful than a differential equation? ), I agree. Although it was the intention of the ISU to reward a "balanced program," I do think that the math has pushed the artistic element into the background.

I am going to interpret Haydn's violin concerto opus 76 #4 on ice. Here is my interpretation. I will do 4T, 3A+2T, 3Lz, 3A, 3F+2T*, 3S*, 3Lo*, 2A*, and then I will do FCosp4 (three changes of position and two changes of edge), and three more, and then my strtaighline footwork sequence and my other straightline sequence. That's Haydn.

Now I will interpret Bach's Toccata and Fugue in D minor. I'll do 4T, 3A+2T,...

 

[gsrossano]

So, should we be outraged? I kinda am. I think they should award two gold medals. Then again, I don't know if this is simply a part of IJS that we are supposed to accept.

As a minimum, this is a bug in the program that MUST be fixed, since it affects all results for all skaters worldwide where the program is used.

If USFSA agrees with my analysis and my reading of the rules then Johnny outscored Evan, and the question is what can/will they do about it? (Not my call, of course, I will be watching along with everybody else.)

 

[Mathman]

So, should we be outraged? I kinda am. I think they should award two gold medals. Then again, I don't know if this is simply a part of IJS that we are supposed to accept.

I would have said, nah, no reason to be outraged. A tie determined by rounding conventions? In an actual competition that could never happen. :frown2:

Anyway, there are many people who would rather put up with an ocassional statistical anomaly than to leave everything up to the whim of the judges to do whatever they wanted, as in ordinal judging.

 

[Vodka Shot]

Thanks for the explanation everyone. I just did the math and I got the same numbers as Medusua.

And this is only in Evan's LP, I pulled up a random ladies protocol and the anomaly wasn't there. So, the question is, was this done on purpose so as gsrossano says, "to make the protocol print out pretty?" was it a computer glitch, or was there something more sinister going down....?

*puts on Sherlock hat*

 

[Mathman]

If USFSA agrees with my analysis and my reading of the rules then Johnny outscored Evan, and the question is what can/will they do about it? (Not my call, of course, I will be watching along with everybody else.)

Does the ISU do it the same way? Have they always done it this way, since CoP judging began?

I very much doubt that USFS will go back in time and adjust the results of past competitions. I think they will say, this is the accepted interpretation of how to implement the rules that we have always used. It is "fair" in the sense that the same method is used for every skater.

The reason that it should be corrected for the future is not because Johnny was robbed but because the method allows an element of chance to creep in -- we want championships decided by the performances, not by the vagaries of the method of calculating the scores. (Then, too, it might be another hundred years before the problem comes up again.)

 

[Hsuhs]

If USFSA agrees with my analysis and my reading of the rules then Johnny outscored Evan

:chorus: Yeah right. They'll do exactly that.

But, seriously, who can blame people for wanting to protect their investment.

this is a bug in the program that MUST be fixed

I think they'll fix it if it happens again. One day in the coming 250 years(c).

 

[Mathman]

.And this is only in Evan's LP, I pulled up a random ladies protocol and the anomaly wasn't there. So, the question is, was this done on purpose so as gsrossano says, "to make the protocol print out pretty?" was it a computer glitch, or was there something more sinister going down....?

*puts on Sherlock hat*

For the ladies LP the factor is only 1.6 instead of 2, so this problem will happen less frequently.

It will still happen, though. Look in ladies LP for a component score that ends in .14 and you will see an example.

Now I am going to look at Caroline Zhang's score and see if I can squeeze an extra hundredth out.

 

[Vodka Shot]

See if you can get a bit more for Ashley while you're at it.