One in a series of articles to discuss the merits of various proposals on the agenda for the 2008 ISU Congress.
There are several proposals in the Congress agenda that deal with the scoring of jump combinations.
The proposal on the left was submitted by Skate Canada. The two proposals on the right were submitted by the Singles & Pairs Technical Committee (SPTC).
CANADA,
Figure
Rule 353, paragraph 1) g) Amend as follows: Determination and Publication of results 1. Basic Principles of Calculation g) In Single and Pair Skating: i) Jump combinations are evaluated as one unit by multiplying the base value of the second (and third jump if executed) by a factor of 1.5 then adding the factored base values to the base value of the first jumps included and applying the GOE with the numerical value of the most difficult jump. The factored base value of the jump combination will be rounded to two decimal places; ii) Jump sequences are evaluated as one unit by adding the base values of the two highest value jumps, multiplying the result by 0.8 and after that applying the GOE with the numerical value of the most difficult jump. The factored base value of the jump sequence will be rounded to two decimal places; Reason: To better reflect mathematically the difficulty of performing jumps in combination or in sequence. To correct mathematical anomalies that occur when factoring sequences. Certain jumps done in sequence have a base value less than if done on their own Examples: 3A = 7.5 points 3A+2T+Seq = 7.04 points The greater the difference in base values between the two jumps, the more points are lost when factoring. At a certain point, a jump sequence will receive less base value than a solo jump. Logically this does not follow the basic principle of the ISU Judging System to reward each technical element with increased points. A jump performed as the second or third jump of a combination is more difficult than a jump done on its own. By factoring the second and third jump of a combination, this added difficulty is reflected in the scores. 
Single
& Pair Skating Technical Committee
Rule 353, subparagraph 1 g) i) Amend as follows: i) Jump combinations are evaluated as one unit by adding  the base value Reason: to give more credit to the difficulty of the second jump. Single & Pair Skating Technical Committee Rule 522, paragraph 1.c), Remarks Amend as follows: Jump combinations and sequences are evaluated as "one unit". Jump combination: the Base Value A jump sequence is evaluated as one unit. The Base Values of the two most difficult jumps included are added. The factor of 0.8 is applied for the sum. Following that the numerical value of GOE for result calculation is related to the one of the two jumps with the highest value. The factored base value of the jump combination/sequence will be rounded to two decimal places. Reason: to reflect the corresponding proposal of the S&PTC for Special Regulations and give credit do difficult second or third jumps in combinations and the guideline for calculation.

Having advocated for five years the idea that combinations and sequences are not scored correctly under IJS it's nice to see this issue will finally be taken up at the 2008 Congress. Unfortunately, neither of these proposals will deliver a realistic scoring of jump combinations and sequences as they are currently written, but at least it is a start.
The Canadian proposal would have the base values of the second and third jumps in a combination multiplied by a factor of 1.5 to reflect the greater difficulty of executing those jumps in a combination instead of as individual jumps. The SPTC proposals would have the base values of the second and third jumps in a combination multiplied by a factor of 1.1.
The reasons given for the SPTC proposals are clear, short and to the point. The goal is to increase the base value of the second and third jumps in jump combinations. Note that to make this change TWO proposals are required, since the numerical evaluation of jump combinations and sequences is described TWICE in the rules, once in rule 353 and again rule 522. This small detail is overlooked by the Canadian proposal. If left to itself, the Canadian proposal would make hash of the rules, with one requirement specified in rule 353 and a different requirement in rule 522.
Further, the reason for the Canadian proposal borders on gobbledygook. Let's parse the reason and afterwards perhaps someone can explain what I am missing.
Reason: To better reflect mathematically the difficulty of performing jumps in combination or in sequence.
OK. That seems clear. The purpose of the proposal is to change the value of jump combinations and sequences to better reflect their true difficulty.
To correct mathematical anomalies that occur when factoring sequences. Certain jumps done in sequence have a base value less than if done on their own
Examples: 3A = 7.5 points
3A+2T+Seq = 7.04 points
3F = 5.5 points 3F+2T+Seq = 5.44 points
3T = 4.0 points 3T+1A+Seq = 3.84 points
2A = 3.5 points
2A+1A+Seq = 3.44 points
I get that too. When you apply the 0.8 funny things can happen.
The greater the difference in base values between the two jumps, the more points are lost when factoring. At a certain point, a jump sequence will receive less base value than a solo jump. Logically this does not follow the basic principle of the ISU Judging System to reward each technical element with increased points.
Yes, logically the current approach for sequences does not make sense.
But what's the point? Nothing in this proposal changes the way sequences will be scored! The text of rule 353 1) g) ii) in this proposal is unchanged from what is in the current rulebook! All this proposal does is point out a problem, but it does not offer a solution.
A jump performed as the second or third jump of a combination is more difficult than a jump done on its own. By factoring the second and third jump of a combination, this added difficulty is reflected in the scores.
Agreed. But how much more difficult? Is it really 50% more difficult? And what of the third jump? Is not that even more difficult that the second jump? It would be nice to know why Skate Canada thinks the value should be 1.5 for both the second and third jump. It would also be nice to know why the SPTC thinks the second and third jumps are only 10% more difficult in combination than alone. Both numbers seem purely arbitrary.
Between these two proposals the SPTC proposals are the least offensive. They accomplish some good but they do not go far enough.
How can doing two or more jumps in sequence be less difficult (worth less points) than doing those jumps alone? Further, the second and subsequent jumps in a sequence must be somewhat more difficult than doing those jumps alone. In order to reflect the true difficulty of a sequence compared to executing the two jumps individually, it makes more sense to say the base value of a jump sequence should be equal to the base value of the first evaluated jump plus a factored base value of the second evaluated jump. Pulling numbers out of the air, the factor should perhaps be in the range 1.1 to 1.2 for the second of the two scored jumps. We leave it to experienced coaches to tell us what the exact value should be.
As for jump combinations, given that many skaters do not execute combinations with three jumps, we infer that including the third jump in a combination is more difficult than including just two jumps. That says that while the second and third jumps should be factored, the factor for the third jump should be more than the factor for the second jump. Again pulling numbers out of the air, the factor for the second jump should perhaps be in the range 1.2 to 1.4 and the factor for the second jump in the range 1.4 to 1.8. Experienced coaches should again be the ones to tell us what the exact values should be.
Finally, if the base values are specified to one decimal place (as they are) and the factors are specified to one decimal place (as they should be) then the factored base values would have exact values of no more than two decimal places and rounding is not required in this calculation.
The following examples illustrate how the values of some combinations and sequences would change under these proposals, and an alternate example for how they could be evaluated.
Element  Current (1)  Canada (2)  SPTC (3)  ISIO (4) 
3A+2T+Seq  7.04  7.04  7.04  8.63 
2A+2F+Seq  4.16  4.16  4.16  5.37 
2F+2S+Seq  2.4  2.4  2.4  3.13 
4T+3T  13.0  15.0  13.4  13.8 
4T+3T+2T  14.3  16.95  14.83  15.62 
3A+3T  11.5  13.5  11.9  12.3 
3Lo+3Lo  10.0  12.5  10.5  11.0 
3Lz+2T+2Lo  8.8  10.2  9.08  9.66 
2Lz+2T+2Lo  4.7  6.1  4.98  5.56 
Sequence  Combination  
(1) (2) (3) (4) 
0.8 * (BV1 + BV2) 0.8 * (BV1 + BV2) 0.8 * (BV1 + BV2) BV1 + 1.1 * BV2 
BV1 + BV2 + BV3 BV1 + 1.5 * BV2 + 1.5 * BV3 BV1 + 1.1 * BV2 + 1.1 * BV3 BV1 + 1.2 * BV2 + 1.4 * BV3 
In these examples, the Canadian proposal would give jump combinations a large increase in value. In the Men's Free Skate, the points for jumps would increase approx. 57 points for a skater with fully populated combinations and two tripletriple combinations, substantially increasing the importance of jumps in general, and tripletriple jumps in particular. The SPTC proposal would result in a small increase in points for jumps, typically 1 point or less. The ISIO example would increase points for jumps by about 23 points.
For the Ladies event, the most significant impact of these proposals would be to give the few ladies with tripletriples a boost compared to the majority of the ladies who execute combinations consisting of double toe loops and double loops. Under the Canadian formula, ladies with tripletriples could outscore their competition in jumps by an additional three points compared to the current point method.
All these example place a greater premium on jumps over other competition skills than is currently the case, with the Canadian proposal having the largest impact in that respect.
After posting the above discussion, we were reminded there are some coaches and skaters who propose that when evaluating a jump combination, no tripletriple combination should be worth more than a quadruple jump, the idea being that there are skaters who can execute tripletriple combinations but cannot execute an individual quad jump. Thus, a tripletriple must be less difficult than a quad, and should have a lower base value than a quad. As a basic concept this makes a lot of sense. It also points out a paradox in the evaluation of jumps.
Consider the following.
There are skaters who can execute an individual triple Axel and an individual triple toe loop who cannot execute a triple Axel  triple toe loop combination. And there are skaters who can execute the triple Axel  triple toe loop combination who cannot execute a quad toe loop.
That would say that the base value of a triple Axel  triple toe loop combination should be greater than the base value of the two jumps alone, but should also be less than the base value of a quad toe loop. Under the current SoV that says the value of the combination should be assigned a value greater than 11.5 and at the same time less than 9.0, which is obviously impossible! The same paradox exists for lower level skaters when comparing combinations such as double Axel  double toe loop to an individual triple toe loop. At Juvenile, for example, a double Axel  double toe loop combination should be greater than 4.8 points but less than 4.0 points.
The jump combination paradox would tend to say that the problem with determining the base value for jump elements extends beyond the formula for evaluating jump combinations and sequences, and indicates the entire SoV for jumps needs to be systematically reconsidered.
Copyright 2008 by George S. Rossano