Points for Jumps

[CarneAsada]

With all the people complaining about how jumps don't matter, Asada 2 clean triples, Kostner 8 doubles, pathetic pageantry, sport is dying etc., I thought it might be interesting to stop lurking and post a hypothetical system to gauge people's reactions.

Now, I propose keeping all the base values for jumps up to 2A the same. Here are the proposed values for triples up to 3A:

Triple	BV
Toe Loop	4.0
Salchow	4.2
Loop	5.5
Flip	5.8
Lutz	7.0
Axel	10.0

As all the talk about degeneration and setting the sport back by 20 years only refers to ladies, I will not suggest values for quads (in any case pretty much no one has done anything higher than 4S). Underrotated jumps (<) will receive 70% of the BV as before. GoE for a jump is worth 15% of the BV.

Bonuses can be had for late jumps and for combinations. Halfway bonus is still 10%. For combinations:
1. A 3-2T with the first jump being Loop, Flip, Lutz or Axel will receive a 5% bump to the BV of the first jump.
2. A 3-2L with the first jump being Loop, Flip, Lutz or Axel will receive the same bump as above in addition to the 2Lo having its BV boosted by 0.5.
3. For 3[anything]-3T, the first jump will receive a bonus of 0.001*[BV of first jump]². The 3T will receive a bonus of 0.5.
4. For 3[anything]-3Lo, the first jump will receive a bonus of 0.0015*[BV of first jump]². The 3Lo will receive a bonus of 1.5.
5. A 3S on the end of a combination will receive a bonus of 1.5.

This system of bonus stacking will of course lead to very high values for jumps, so increases to the BV of the non-jump technical elements like spins and steps may be in order.

Additionally, many people are calling for a return to 6.0. SO, I propose at the end of all this number crunching, the TES is multiplied by 4.5 while the PCS is multiplied by 5 (theoretical maximum of 400) and we take the natural logarithm of each number to bring the values somewhere near 6. At the end we have:

TES = ln(4.5) + ln(Raw TES)
PCS = ln(5) + ln(Raw PCS)

Thoughts?

[Mathman]

Thank you for this post! Welcome to Golden Skate!

OK, I was with you down to the natural logarithm. I'll need some time to digest this. But any system of figure skating scoring that relies on the transcendental number "e" is cool with me.

[Kunstrijdster]

CoP is based on irrational numbers, anyway. I'd say we give it a try.

[Reginald]

I would support this, but with the ISU, it isn't going to happen.

[Mathman]

A couple of comments about the logarithm part.

First, at the end of the day the 4.5 and 5.0 multipliers have no effect. Every skater just gets an automatic 3.1 added on to her score, regardless of whether she skated or not. (ln(4.5) = 1.5, ln(5) = 1.6.)

The other problem is that applying the logarithm essentially cancels the exponential increase in jump values per revolution -- IMHO the right formula is to triple the base value for each extra revolution.

Single toe = 0.5
Double toe = 1.5
Triple toe = 4.5
Quad toe = 13.5

If we took logarithms for each jump separately, that would exactly undo that geometric progression. The same is true of the squaring feature in the calculation of bonuses for combinations.

On the other hand, taking the log of the sum[ of all elements – do you have some examples of a complete program worked out to see what happens?

The other thing that caught my eye was this. If we make such a big gap between a triple flip and a triple Lutz, then we need to have a stricter penalty for wrong-edge take-offs.

The 15% GOE means 15% per GOE point, right? So a +3 GOE would be 45% of base value. I like that feature.

[CarneAsada]

A couple of comments about the logarithm part.

First, at the end of the day the 4.5 and 5.0 multipliers have no effect. Every skater just gets an automatic 3.1 added on to her score, regardless of whether she skated or not. (ln(4.5) = 1.5, ln(5) = 1.6.)

The other problem is that applying the logarithm essentially cancels the exponential increase in jump values per revolution -- IMHO the right formula is to triple the base value for each extra revolution.

Single toe = 0.5
Double toe = 1.5
Triple toe = 4.5
Quad toe = 13.5

If we took logarithms for each jump separately, that would exactly undo that geometric progression. The same is true of the squaring feature in the calculation of bonuses for combinations.

On the other hand, taking the log of the sum[ of all elements – do you have some examples of a complete program worked out to see what happens?

The other thing that caught my eye was this. If we make such a big gap between a triple flip and a triple Lutz, then we need to have a stricter penalty for wrong-edge take-offs.

The 15% GOE means 15% per GOE point, right? So a +3 GOE would be 45% of base value. I like that feature.

You are right of course about the logarithm canceling out exponential increases in BV if done per element. However, this would be done on the sum as you noted later.

Regarding wrong-edge takeoffs, I think something resembling the penalty in the 2008-2009 season would be good. An "e" would be a -2 GoE deduction added on after everything else is considered and a "!" would be -1.

I do not have examples of programs worked out to see what happens. However, here are two hypothetical jump layouts, let's call the hypothetical ladies doing them Superwoman and Lazy Superwoman, and the idealized jump layouts of a few more realistic programs of the CoP era (note that all the programs planned by the real ladies were remarkable both for their difficulty and for the fact that they never once pulled them off as shown below):

Superwoman	Lazy Superwoman	Yu-Na Kim 08-09	Mao Asada 07-08	Mao Asada 08-09	Miki Ando 08-09
2A	3A	3F-3T	3A	3A-2T	4S
3F	3A-2T	3Lo	3F-3T	3A	3F
3A(x)	3Lz-3T	3Lz-2T-2Lo	3Lz	3F-2Lo-2Lo	2A-3T
3Lz(x)	2A-1/2Lo-3S	2A-3T	3Lo	3S	3Lz-3Lo-2Lo
3A-3T-3Lo(x)	3Lz	3Lz	3F-3Lo	3F-3Lo	3Lz
2(1ft)A-3S(x)	3Lo(x)	3S	2A-2Lo-2Lo	3T	3Lo
3Lz-2Lo(x)	3F(x)	2A	2A	2A	2A

Now add in 3 Lvl 4 spins and Lvl 4 steps. It would be easy to calculate the difference between the layouts in the current system, then compare it to the difference in raw points under the proposed system. While the BV of the vastly-more-difficult 1st layout is still a bit higher in the current system, my proposed bonuses will stack up very quickly.

To illustrate, we can take a 3Lz-3Lo-2Lo (7+5.5+1.8 points without bonus) done after the halfway mark.
Under the current system, it would be 1.1*(6+5.1+1.8) = 14.19 points.
If the system merely counted the halfway bonus, it would be 15.73 points.
With everything counted, BV = 1.1*[7.0*(1+0.0015*7.0²)+(5.5+1.5)*(1.05)+(1.8+0.5)] = 1.1*(7.0*1.0735+7.0*1.05+2.3) = 18.88 points.

This kind of compounding is why I suggested a logarithmic scale in the end. Telling the audience that the Superwoman scored something crazy like 200 points and 30% above Lazy Superwoman when they both did 8 triples and repeated 3A and 3Lz would certainly leave a bad taste in people's mouths. If I was really committed to forcing it to be out of 6.0, then I might have to calculate the theoretical ceiling for the TES of a program composed of nothing more than a 3A, divide it by e⁶ (approximately 403), take the reciprocal, and have that be the multiplying factor. 80 PCS * 5 is about 400 so that works out in the end.

[Krislite]

This is all well and good, and I do like the principle behind this scoring scheme. However, just imagine explaining this to a layperson or casual fan. First, you tell her there are dozens of different base values, depending on the element, the levels, etc. There are five or so components, each with a half a dozen consideration that go into them. Then the base values get bonuses, GOE's or base value increases depending on the combination thereof, and then the sum of all these figures is adjusted via the natural log (the WHAT???). And that's how a score is derived.

How are we going to save figure skating and draw a bigger fan base?