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Nope. It was a really lovely program, choreographed by Jeff Buttle.

I liked it too

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Originally Posted by chuckm
skaters would become really cautious and attempt only those jumps they routinely land.
Is that good or bad? Should every skater attempt a quad even if he/she has a zero success rate for landing? How about a 25% success rate? I would like to know what the minimum required success rate should be, so we can come up with a scoring proposal accordingly--A system that a skater can yield a "profitable expected value" on that element as long as his/her jump can meet the minimum required success rate. By "profitable expected value", I mean: Expected value of performing a difficult jump (e.g., 3A) - Opportunity Cost > 0. Opportunity cost is the expected value of performing an easier jump of the same type (e.g., 2A). That is to say, the deduction system should be designed as such so that: E(difficult jump with the minimum required success rate) ≥ base mark of the easier jump (i.e., E (easier jump with a 100% success rate)).

We know the base marks for 3A = 8.50, 2A =3.30 , 4T = 10.30 , 3T = 4.10, and the total deduction for a fully rotated but fallen jump is 4 (maximum GOE deduction 3 + fall deduction 1), so what is the expected minimum success rate for landing the jump right now? The answer is 0%. 0% × 8.50 + 100% (8.50 - 4) = 4.5 ≥ 3.30 (the opportunity cost for 3A), or 0% × 10.30 + 100% (10.30 - 4) = 6.4 ≥ 4.10 (the opportunity cost for 4T)
What is the expected minimum success rate for rotation right now? Let R = the rate of fully rotating the jump, and (1 -R) = the rate of being downgrated. To isolate the rotation factor, we assume that everything else is successful, and so there is no mandatory deduction for a fall.
R × 8.50 + (1 - R) (3.30 - 3) ≥ 3.30 ==> 8.5R + 0.3 + 0.3R ≥ 3.30 ==> 8.8R ≥ 3 ==> R ≥ 34% for 3A
or R × 10.30 + (1 - R) (4.10 - 3) ≥ 4.10 ==> 10.3R + 1.1 + 1.1R ≥ 4.1 ==> 11.4R ≥ 3 ==> R ≥ 26% for 4T.

In conclusion, the COP is a funny system that demands a minimum of 26% success rate for rotation but 0% for its landing.

What should be the total deduction for a fully rotated fallen jump in order to maintain a minimum of 25% success rate for landing?

Let Xn+1 = base mark of the difficult jump, Xn = base mark of the easier jump. Y = deduction for a fall.
So we have: 25% Xn+1 + 75% (Xn+1 -Y) = Xn
thus, 1/4 × 8.50 + 3/4 (8.50 - Y) = 3.30 ==> 8.5 - 3Y/4 = 3.30 ==> 5.2 = 3Y/4 ==> Y = 6.93 for 3A
And 1/4 × 10.30 + 3/4 (10.30 - Y) = 4.10 ==> 10.3 - 3Y/4 = 4.10 ==> Y = 8.27 for 4T

And therefore I recommend a total deduction (GOEs and mandatory deduction or whatever) of 7 points for a fall in a difficult jump (i.e., 3A or quads).

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Originally Posted by chloepoco
Mathman for President of ISU!!
I would vote for Mathman should he decide to run for president of the United States.
Originally Posted by Spun Silver
Mathman, look at it this way. One day in the not too far distant future, the outcry and the dwindling audience caused by certain competition outcomes will lead to a change in the IJS, perhaps (hopefully) along the lines you just proposed. Then it will be "your" system that the experts here are patiently explicating.
Maybe "educating the ISU and the judges" is more urgent than "educating the public" in today's figure skating.

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Originally Posted by skatinginbc
And therefore I recommend a total deduction (GOEs and mandatory deduction or whatever) of 7 points for a fall in a difficult jump (i.e., 3A or quads).
We don't want to raise the fall deduction remains at 1.0 per fall (regardless of what the skater is doing when s/he falls), because already falling on lower-valued elements and falling on nothing result in negative points).

So you would recommend that the GOE increments for the high-rotation jumps (≥3.5 revolutions) be 2.0 instead of 1.0, so that -3 across the board means 6.0 points off the base mark. Combined with the 1.0 fall deduction, that would give your 7.0.

For a couple of years the increments used to be 1.5, meaning the reduction from base mark was 4.5 for severe/multiple errors. For purposes of negotiating with the reward-risk proponents, that might be a compromise from which to start. Then if there are still too many instances of skaters falling on rotated 3As and quads racking up more jump points than skaters who play it safer and deliver all their content, it might be time to propose the 2.0 negative increments for those big jumps. Or other ways to reward clean programs if the falls on big jumps aren't the primary problem.

Of course there's no move that has a 100% success rate because ice is slippery -- or sometimes not slippery enough if skate suddenly encountgers a foreign object/substance or a hole/rut. So you might have a skater who lands three great jumps from the 3A/quad category and then falls on a double axel or a crossover.

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I prefer seeing a range increase in GOEs for all jumps, for instance, ranging from -5 to +5 (-5 for a butt-on-the-ice fall, -3 to -4 for a butt-off-the-ice "fall", etc.). So here we have a 5-point deduction for a high-risk jump. And I would like to get rid of the -1 mandatory deduction for a fall and have it reflected in where it should belong, namely, PCSs. Say, if we combine PE, CH, and IN into one category "Presentation", the deduction for a fall is 0.5 to 1.00 point depending on the degree of disruption. After factoring 2 for PCSs in LP, we get another maximum 2 points for the fall. So 5 + 2 = 7. Bingo!!! The advantage is that someone like Chan who can recover from a fall really fast will not be punished fully. And it should be rightfully so.
With the GOEs ranging from -5 to +5, we are basically using a 10-point scale, and thus proposals like Mathman's in the previous page can be incorporated easily if we desire to.

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Originally Posted by skatinginbc
I prefer seeing a range increase in GOEs for all jumps, for instance, ranging from -5 to +5 (-5 for a butt-on-the-ice fall, -3 to -4 for a butt-off-the-ice "fall", etc.). So here we have a 5-point deduction for a high-risk jump. And I would like to get rid of the -1 mandatory deduction for a fall and have it reflected in where it should belong, namely, PCSs. Say, if we combine PE, CH, and IN into one category "Presentation", the deduction for a fall is 0.5 to 1.00 point depending on the degree of disruption. After factoring 2 for PCSs in LP, we get another maximum 2 points for the fall. So 5 + 2 = 7. Bingo!!! The advantage is that someone like Chan who can recover from a fall will not be punished fully. And it should be rightfully so.
With the GOEs range from -5 to +5, we are basically using a 10-point scale, and thus proposals like Mathman's in the previous page can be incorporated easily if we desire to.
+5 to -5 works for me if we get rid of levels. Which would probably mean dividing up the panels differently.

Then technical judges could reward extra difficulty in the positive GOEs but balance that against minuses for weaknesses and errors.

Otherwise I don't see the need for five positive grades.

What would you use them for on jumps, in any case?

Or would it be something like fully rotated, cleanly landed jumps start with +1 or +2, and 0 would be reserved for jumps landed upright but with no speed, scratchy or brief wrong edge landings, slight underrotations, OR slight touchdowns (i.e., the kind of jumps that would get -1 in the +3/-3 scale)?

Say, if we combine PE, CH, and IN into one category "Presentation", the deduction for a fall is 0.5 to 1.00 point depending on the degree of disruption. After factoring 2 for PCSs in LP, we get another maximum 2 points for the fall. So 5 + 2 = 7. Bingo!!!
I think the factor would have to be a lot larger than 1.0/0.8 for short programs and 2.0/1.6 for long if you combine those three components into one.
Otherwise together they would only contribute a maximum of 20.0 points for top programs that earn over 100 for elements plus skating skills.

And remember, the fall deduction also applies to bad skaters who are falling on underrotated double jumps and starting with PCS in the 2s. You don't want a system that will cause them to end up with negative total scores on a bad day.

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Originally Posted by skatinginbc
0% × 10.30 + 100% (10.30 - 4) = 6.4 ≥ 4.10 (the opportunity cost for 4T)

R × 10.30 + (1 - R) (4.10 - 3) ≥ 4.10 ==> 10.3R + 1.1 + 1.1R ≥ 4.1 ==> 11.4R ≥ 3 ==> R ≥ 26% for 4T.
For quads, it is even more stark because you probably cannot do a 3T as an alternative to the 4T. (See Oda, when he tripled his quad, then lost credit for a 3A+3T combination later because of it.)

Here is another way to look at it. Suppose you always, every time out, both under-rotate your quad and fall (but you can get three-and-a-half revolutions to avoid downgrade).

4T<(fall) 6.30
3A
3A+2T
3Lz
3Lz+3T
3F+3T
3Lo+2T+2Lo
3S

Alternative program (if you get tired of falling every time):

Substitute 2A (3.3) for your 4T<(fall) (6.3)., giving up 4 points in base value in every performance.

But wait. Maybe you are so bad at the quad that the only question is do you get 4T< (fall) ofr4T<< (fall). Let's say its 50-50 between those two possibilities.

Expected value = .5x6.30 + .5x1.00 = 3.65. This is bigger than 2A = 3.3.

So it you can at least avoid a downgrade half the time (and fall all the time), going strictly by the points you still come out ahead with the quad attempt. (If you know you are going to fall every time you can practice getting right up and back into the flow of the program so that you don't take a hit in program components.)

I don't think that any skater would actually do this, but the scoring system does allow and encourage it.

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Originally Posted by skateflower
Even if you are a dictator, you still can't change the fact most people don't give a **** about his skating. You can't 'educate' audience to like his skating because it isn't really 'likeable' . Lame, safe, and forgetable choreography and performance year over year.
Not necessarily limited to a certain skater....

If regular people (i.e. non-skating fans) find performances boring, they won't bother spending their time for learning the rules. Music fans would get sick of hearing the same music over and over and over again. Dance lovers would roll their eyes to the COP definition of "good choreography". They will just switch the channel while eating popcorn. If the skating community doesn't listen to the public, saying like "you know nothing about COP, fools", the public has no obligation to learn from the skating fans, either.

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Double post.

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Mathman, your comments that an under-rotation on a jump gets 70% of base value and full rotation with a fall gets full base value, completely ignores the -3 GoE for the fall, so in fact, the rotated jump with the fall also gets no more than 70% of base (quads), and in the case of the lesser triples, like Salchows or toe loops, substantially about 30% of base. Falls on footwork generally result in a loss of levels and the -3 GoE.

It annoys me no end that commentators always talk about a -1.00 for a fall, when in fact, the point loss on a fall is substantially more than 1.00 if the fall comes on any element.

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Mathman, your comments that an under-rotation on a jump gets 70% of base value and full rotation with a fall gets full base value, completely ignores the -3 GoE for the fall, so in fact, the rotated jump with the fall also gets no more than 70% of base (quads), and in the case of the lesser triples, like Salchows or toe loops, substantially about 30% of base.

Oh, that's right. Sorry.

OK. I will try again. Let's say that nine out of ten tries you get 4T<(fall) and one time out of ten you get 4T, no under-rotation, no fall.

If you attempt the quad, on the average over all trials, you will get .9x3.2 +.1x10.3 = 3.91.

This is better than the alternative, 2A = 3.3. (You might get positive GOE on the 2A, but you might get positive GOE on the one successful 4T as well, so that's a wash.)

So in this situation it pays you to go for the quad even if your success rate is only one in ten.

I think that is out of balance. Even in the scenario where you get both a UR and a fall every single time you jump, you still lose only a tenth of a point (3.2 versus 3.3). The risk seems to be virtually non-esistent, and the reward huge in the case of a rare success.

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However, if you want to play the percentages game, it might help to research what kinds of percentages the quad guys actually have in practice and in competition.

I suspect that the ones who fall most of the time also underrotate most of the time. (It's very hard to cheat a quad and stay up on one foot because of the massive rotational force needed even for 3.5 revolutions.)

And the ones who fall on rotated quads have much better percentages of staying upright, even landing cleanly.

There are probably also some who often stay upright without fully rotating or landing on one foot -- which traditionally, long before IJS, has been considered a worse failure than rotating and falling.

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Originally Posted by gkelly
there's no move that has a 100% success rate because ice is slippery
I was aware of it. To be conservative in proving my point that skaters would not "become really cautious and attempt only those jumps they routinely land", I purposely gave a liberal estimate for the opportunity cost of a difficult jump. It was like to prove A > C, I proved that A > B given that B > C, where B is the expected value of a jump with a 100% success rate and C the expected value of a jump with a less than perfect success rate.
Originally Posted by Mathman
For quads, it is even more stark because you probably cannot do a 3T as an alternative to the 4T.
To have a scoring system that applies to every skater, we cannot say that 3S is one of Mao's weaker jumps and so 3S should worth more points for her whenever she lands it. No, the base value of 3S should be the same for every skater no matter how hard or easy it is for certain individuals. By the same token, to estimate the opportunity cost of a jump for the purpose of designing a scoring system, the estimate should be fixed despite the fact that it varies from one person to another or one time to another. Take Patrick Chan as an example, this is his layout without a quad: 3A, 3F+3T, 3Lz, 3A + 3T, 3S, 3Lo, 3Lz +2T+2Lo,2A. And this is his layout with one quad: 4T, 3A+3T, 3Lz, 3A, 3Lz+1Lo+3S, 3F+3T, 3Lo, 2A. And this is his layout with two quads: 4T, 4T+3T, 3A, 3Lz+1Lo+3S, 3Lo, 3F+3T, 3Lz, 2A. The opportunity cost for including the first quad is barely 2T+2Lo (1.4 + 1.8 = 3.2 < 4.1 = 3T) but his including the second quad is a huge 3A (50% × 8.50 + 50% × (8.50 - 4) = 6.5 > 4.1 = 3T). Note: I use a 50% success rate for Chan's 3A because he would have planned a two quads + two 3As program had he had a high success rate for 3A. This season his 3A success rate has improved, so he might have another 3A back next season, and if he does so, the opportunity cost for his second quad will be significantly reduced.
Indeed, as Mathman pointed out, my use of 3T value as an estimate of the opportunity cost for 4T is liberal in most cases and violates the Zayak Rule. But for the sake of simplicity in scoring design, I like it this way: All estimates of the opportunity costs for jumps are the base values of the jumps with one less rotation--Plain and easy and consistent in design. It is based on the assumption that a skater will attempt one more rotation only after they can perform that jump with high consistency and ease.
Originally Posted by gkelly
+5 to -5 works for me if we get rid of levels.
Why only if we get rid of levels? I like levels. How many bullets does the COP have for each element? 6 or more? One bullet = +1, two bullets = +2, and there are still enough bullets left to make it up to +5. +5 for a 3T does not contribute the same as +5 for a 4T to the final score. The GOEs are still proportioned according to the base mark of each element.
Originally Posted by gkelly
I think the factor would have to be a lot larger than 1.0/0.8 for short programs and 2.0/1.6 for long if you combine those three components into one. Otherwise together they would only contribute a maximum of 20.0 points for top programs that earn over 100 for elements plus skating skills.
And remember, the fall deduction also applies to bad skaters who are falling on underrotated double jumps and starting with PCS in the 2s. You don't want a system that will cause them to end up with negative total scores on a bad day.
If we combine three categories (each worth 10 points) into one, then we have a big category (Presentation) worth 30 points. A skater with PCS in the 2s will get 6 to 9 in Presentation. Even if he falls on all 8 jumping passes, the skater will receive a total deduction of 4 to 8 points (0.5 to 1.00 for each fall) and probably still have a few scores left. In my proposal, the minimum score for a category is 0--No negative score.
BTW, the lowest presentation score (PE + CH + IN) in this year's Junior Worlds preliminary round is 8.5 points. The greatest number of falls is 3.

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Take Patrick Chan as an example, this is his layout without a quad: 3A, 3F+3T, 3Lz, 3A + 3T, 3S, 3Lo, 3Lz +2T+2Lo,2A. And this is his layout with one quad: 4T, 3A+3T, 3Lz, 3A, 3Lz+1Lo+3S, 3F+3T, 3Lo, 2A. And this is his layout with two quads: 4T, 4T+3T, 3A, 3Lz+1Lo+3S, 3Lo, 3F+3T, 3Lz, 2A.
Well, I don't think any of those three jump layouts is legal (all have 3 different jumps repeated). So I am not sure if "I like it that way" should take precedence in our calculations over jump layouts that skaters can, and do, actually plan.

I think the quadster would have to have a relatively meager jump layout without the quad in order to have a real choice. For instance if a skater is committed (for some weird reason) to using one of his jumping passes on a double Axel no matter what, he could do

3Lz+3T, 3A, 3F, 3A+2T, 3Lo, 2A, with one pass left. (This is Lysacek, 2010 Olympics)

Now he has a choice of 4T (10.3) or 3Lz (6.0) for his last pass.

But this is an artificial example. He would do 3Lz with his seventh pass instead of 2A anyway, and then the choice would be between 4T (10.3) and 2a (3.3).

It is hard to find a realistic example where the trade-off would be any closer than that, 10.3 versus 3.3.

Or for a quad with a fall, 6.3 versus 3.3.

Or for an under-rotated quad, 7.2 versus 3.3.

Or for an under-rotated quad with a fall, 3.2 versus 3.3.

Edited to add. So, for a skater whose success rate on quads is 0%, he only loses one tenth of a point. He can easily make this up because the judges will give him higher scores in interpretation, etc., if he shows his stuff by taking a shot at the quad.

Example: Takahashi tried a quad flip several times. Landed 0 of them. Received no particular penalties from the judges and mucho cheers from the fans for his valiant efforts. Little if any risk, great potential reward.

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Originally Posted by Mathman
Well, I don't think any of those three jump layouts is legal (all have 3 different jumps repeated).
Oops. it should have been:
layout without a quad: 3A, 3F+3T, 3Lz, 3A+2T, 3S, 3Lo, 3Lz +2T+2Lo,2A.
layout with one quad: 4T, 3A+3T, 3Lz, 3A, 3Lz+1Lo+3S, 3F+2T, 3Lo, 2A.
layout with two quads: 4T, 4T+3T, 3A, 3Lz+1Lo+3S, 3Lo, 3F+2T, 3Lz, 2A.
The mistakes do not affect the rest of my analysis.

I agree with you and I am very aware that my estimate of the opportunity costs for quads was on the high side. My purpose was to come up with a conservative recommendation: The quad fall deduction should be 7 points, which is conservative given that I assumed an opportunity cost higher than it is in most cases. And hence even with the 7-point deduction, skaters will not "become really cautious and attempt only those jumps they routinely land".

Originally Posted by gkelly
I suspect that the ones who fall most of the time also underrotate most of the time. (It's very hard to cheat a quad and stay up on one foot because of the massive rotational force needed even for 3.5 revolutions.) And the ones who fall on rotated quads have much better percentages of staying upright, even landing cleanly. There are probably also some who often stay upright without fully rotating or landing on one foot -- which traditionally, long before IJS, has been considered a worse failure than rotating and falling.
The 2011-2012 season data show the following frequencies:
Full rotation without fall ==> 61 (64.21%)
Full rotation with fall ==> 10 (10.53%)
Underrotation without fall ==> 3 (3.15%)
Underrotation with fall ==> 13 (13.68%)
Downgrade without fall ==> 4 (4.21%)
Downgrade with fall ==> 4 (4.21%)

The data show that 74.74% of the attempted quads during the 2011-2012 season were fully rotated, 16.84% underrotated, and 8.42% downgraded. With those percentages in mind, what should be the total deduction for a quad fall in order to ensure that a skater would attempt quads only if he could maintain a minimum of a 25% success rate for landing?

Let Y = total deduction for a fall, and assume that the average GOE deduction for an underrotated quad without fall is -2 and for a downgraded quad without fall is -2.5.
(74.74% x 25% x 10.30) + (74.74% x 75% x (10.30 - Y)) + (16.84% x 25% x (7.20 - 2) + (16.84% x 75% x (7.20 -Y)) + (8.42% x 25% x (4.1 - 2.5 x 0.7)) + (8.25% x 75% x (4.1 - 0.7Y)) = 4.1
1.9236 + 5.7737 -0.5606Y + 0.2189 + 0.9094 - 0.1262Y + 0.0505 + 0.2537 - 0.0433Y = 4.1 (Again I use the value of 3T, a liberal estimate for the opportunity cost)
5.0298 = 0.7301Y
Y = 6.8892 (a conservative estimate), close to my recommendation of 7 point deduction.

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