That's why I think it might have turned out different under IJS. Sato's strengths were in the difficult-to-measure-and-quantify skillls. The IJS would have given full value to Bonaly's TES advantage.

6.0 judging, besides being harsher on falls, also came down hard on two-footed landings, compared to the IJS. I remember Michael Weiss trying and trying and trying to get a quad Lutz ratified, but he never landed one without brusshing the ice with his free foot. Consequently he never got official credit for a quad Lutz at all.

On the other hand, .6.0 was pretty lenient when it came to flutzed takeoffs, especially in ladies,, compared to the IJS's specified penalties for wrong or unclear edges -- although it took many revisions of the IJS before the current details were agreed on.

I don't know about "too high or two low." My observation in starting this thread was more about the mathematical esthetics of the entire scale of values. It seems inharmonious to me. So I wondered what other (non-mathematical) factors might be in play. (I got an earful of responses, so I should be happy, right?)

a mathematical pattern does not have to be linear. It can be, for example, logarithmic. For a simple jump the athlete gets one point, but to get two points the jump must be 10 times more difficult.

I agree it doesn't. It also doesn't make more sense to compare the axel to the other jumps because it is very different from the other jumps.
I watch a bunch of other sports with coefficient of difficulty, or call it base value or degree of difficulty (gymnastics, diving, acrobatic skiing, snowboarding). None of these sports have directly proportional scoring methods. Should the quad axel be worth more points ? I still don't think it should for all the reasons I have mentioned. The simple maths I shared was to show that there is nothing logical in making these base values or else the quad axel would have an even lower value as it is not 4 times the rotation of a single axel but 3. I just wanted to point that out because I thought it was interesting to notice. That half turn is causing for a lot of troubles

In the end, my point is that what seems humanly impossible now will probably be more and more common. Just ten years ago, I never thought we would see so many quad lutzes, flips and loops in a skating world that had seen mostly salchows and toes for what? 20-30 years. And now, many skaters in the top ten in the world have an exotic quads and some, use two of them in their SP... If that trend continues, we may see more skaters do the quad axel, and as I wrote in my post, demystify that jump. I don't like the idea that one element should define a winner, so I am 100% fine with a relatively lower base value. Could it be1 point more? I wouldn't care.... but it shouldn't be 15 points or 20 points like some people hope for.

OK, I understand what you mean, even though I still think the BV of the 4A should be raised.

As for the "simple maths" you've pointed out, I think it would make sense to count prerotations as well. I mean, the 1T is actually just 180 degrees in the air, while the 2T is 540 degrees in the air, which is three times more! The 1A is around 450 degrees, while the 2A is 810 degrees, which is not even two times more.

Obviously, the more rotations we're dealing with, the less important the jump type is (from this viewpoint). I mean, with singles the relative difference between the 1A and the 1T is huge, there's 450/180=2.5 more revolutions on the axel. For quads it's just (4*360+90)/(4*360-180)~1.214.

But this is meant just for fun; as I stated earlier, these simple arithmetic observations don't say anything about the actual difficulty of specific jumps.

Well, the previous progression of Base Values depending on the number of rotations, was not linear either; and a 12.5 value for 4A isn't even linear...

Can you please show me a < call on his score sheets in Beijing? Then, can you please show me a Solo Quad or a Quad Combination that wouldn't be underrotated? (For your information, he's fully rotated most of his Quads in the two seasons between 2018 and 2020 but he used to underrotate before, and progressively lost the full rotation of his quads later, but was never called in spite of this fault being chronic.) Not speaking of the fact that he's always had stiff landings yet the GOE cap at 3 was never applied to him. Did he sit any of his sit spins? (I know that the Olympic video is the only one allowed, and that we don't see the lower part of his body, but he's doing it exactly as his usual sit spin which he never sits, being never called of course. You know, really sitting a sit spin is painful and drains energy, if he wants to jump five quads he "must" compensate.) Then why was his Short Program one been given any value, and why wasn't his Free Skating one been marked V? Did he make body moves challenging his balance on 1/3 of his Step Sequence? He just can't it seems. But he always get a Level 4.
On the so-called World Record of his Short Program, and just on the Technical score, we're already at about 8-point candy (overscoring) on the 4F<, 3 points on the 3A<, 8 points on the 4Lz (some say q) + 3T<, 4 points on the FSSp, 1 point on the StSq, probably some with the other spins' GOEs, we're above 24 points overscoring on the Technical Score alone, were down to 90, and there's the Components too...
What is insulting, is to call it a real World Record when one can see that it's not (I don't know if you can). It's insulting to Figure Skating and to all the Figure Skaters who deserved a better score, not to speak of the holder of the last (in fact, underscored) real World Record in a Short Program.
Sorry this is out of topic.
What's in topic is that at the moment, the 4A in competition is in reality underrotated too (just this jump, this skater is not a chronic underrotator on other jumps, for the little I saw of his skates), but apart from the fraudulent ratification that ensued (the first 4Lz was probably so too, and the first 4F was so), the fact of not calling this underrotation on an undervalued (in my opinion) jump, gives the skater a good reward for jumping it, although I don't know what GOEs should be given for it, apart for the Base Value. In fact, if we consider that an underrotated jump doesn't only get lower Base Value, but also low Grades of Execution, the present situation is more akin to a new jump in the Scale of Values, which has nearly four real rotations in the air (if you watch most of the current competitive skaters, this is not a small feat) and is to be landed about 100° under the usual rear landing of jumps... Amidst all the scoring unfairness in Figure Skating, this one isn't a big concern, it just has to be described.

Linearity does not play a role in the scale of values, but (leaving out quads) exponentiation does, sort of, and has since the beginning.

double = 3xsingle, triple = 9xsingle (approximtely). But quad does not = 27xsingle. This is the sense in which quads are "undervakued" compared to the scoring of other jumps.

There is, of course, the question of hpw to determine how much harder one jump is than another. As Alex Federov suggests above, maybe a logaritmic scale fills the bill. If 50,000,000 skaters world-wide can do a 1T, but only 50,000 can do a 2T, then the relative difficulty could be determined by

log (50,000,000/50,000) = log (1000) = 3. which would justify the factor of 3 in the scale of balues.

For the 4A, if 1000 skaters can do a 3A but only 1 can do a 4A. again a logaritmnic factor of 3.

OK, this is why mathematicians are not figure skaters. Strill, any long list of numbers invites one to search for coherent patterns, just for fun. I actually suspect the truth lies is that the ISU said to itself, "29 points for a quad Axel? No, that's too much, lets make it lower."

Linearity does not play a role in the scale of values, but (leaving out quads) exponentiation does, sort of, and has since the beginning.

double = 3xsingle, triple = 9xsingle (approximtely). But quad does not = 27xsingle. This is the sense in which quads are "undervakued" compared to the scoring of other jumps.

There is, of course, the question of hpw to determine how much harder one jump is than another. As Alex Federov suggests above, maybe a logaritmic scale fills the bill. If 50,000,000 skaters world-wide can do a 1T, but only 50,000 can do a 2T, then the relative difficulty could be determined by

log (50,000,000/50,000) = log (1000) = 3. which would justify the factor of 3 in the scale of balues.

For the 4A, if 1000 skaters can do a 3A but only 1 can do a 4A. again a logaritmnic factor of 3.

OK, this is why mathematicians are not figure skaters. Strill, any long list of numbers invites one to search for coherent patterns, just for fun. Where I actually suspect the truth lies is that the ISU said to itself, "29 points for a quad Axel? No, that's too much, lets make it lower."

FIgure skaters are already lucky the ISU is doing things the way they do. Take diving.
There is no base value but a coefficient (degree of difficulty) that is applied to the scoring aggregate of the judges (grade of execution)

Two things here :

1) the simpler jumps have a higher DD in versus the very intricate dives. They start much higher (look at the 3 meter as on the 1 meter springboard, some of the quads are not possible).

I like looking at diving because we can see that there are indeed "half turns" depending on the starting position and the arrival in the water.
Also, interesting that twisting dives have their own table of values.

2) do not forget that a missed dive can get a 0 or a very low score from the judges. I don' t think I need to tell you what multiplying by 0 does So no matter the difficulty of the dive, if the dive is not successful, the points for that dive will be very low.
In figure skating, the base value cannot be that high because the lowest score a skater can get with a failed dive is not zero. I am not talking about a pop... nor a downgrade but a jump that is rotated but with a fall, let's say a triple axel, 8 minus 5 goe = 4 points - 1 point deduction is still 3 points, which is close to the double axel base value at 3.3.... In that sense a fall on a quad axel 12.5 minus 5 goe = 6.25 - 1 point deduction is still a whopping 5.25 points which is higher than a successful triple toe, triple salchow, triple loop and almost the same as the base value of a triple flip.

So the base values should not be made too high because then, failed attempts become more rewarding than successful attemts from the category under (triples).

^ The diving information is very interesting. I always thought that it was the other way around, that the degree of difficuly was established first mainly by how many twists and sometsaults, and then the "GOE" was applied by the judges as a percentage of the value of the jump, reflecting quality.

I do think that there is a point to be made regarding the once-every-four-years casual TV viewer. If the diver doesn't send up a big splash on entry, it was a good dive. If a gymnast doesn't fall off the balance beam and sticks the landing, that's about all I am capable of observing.

^ The diving information is very interesting. I always thought that it was the other way around, that the degree of difficuly was established first mainly by how many twists and sometsaults, and then the "GOE" was applied by the judges as a percentage of the value of the jump, reflecting quality.

I do think that there is a point to be made regarding the once-every-four-years casual TV viewer. If the diver doesn't send up a big splash on entry, it was a good dive. If a gymnast doesn't fall off the balance beam and sticks the landing, that's about all I am capable of observing.

The degree of the difficulty is a multiplier. It is established first because the divers need to submit their dive list and the DD is listed of course.
But then the judges mark the dive out of 10 with the two lowest and highest scores tossed. Then the remaining scores are added together and then multiplied by the DD. So not a percentage but a mutliplication here.

If a diver falls, so doesn't reach a vertical entry (not talking about splash) the dive scores 0. If there is a "pop" the dive scores zero. That diver will not advance nor medal. Imagine if if were the same for skaters ? You fall, you score 0, at least for that one jump. Perhaps that's why i don't like high base values when a fall on a quad still ends up scoring more points than a triple.

About the suggestion that the increse of base value should be tied to the % increase in number of rotations, that might theoretically be a viable approach, but I do not see anything in the actual numbers that leads me to think that the iSU is thinking along those lines.

1T to 2T: Increse of 100% in rotation. Increase of 225% in point value.

2T to 3T: Increase of 50% in rotation. Increase of 223% in point value.

If thre ISU were to follow this line of thought, then the values of quads are not too bad, but the valuses of triples should all be lowered (except the triple Axel).

That is an interesting distinction. Let's say the judges award a score of 8 out of 10 to the dive. Then the formula is

DD x 8.

Or, it seems like we could say,

80% of DD times ten.

Let's say you do a forward 3 1/2 somersault with Degree of Difficulty 3.1 (I got this number from the scale of values that you linked above ). You get 8 style poins out of 10. So you get dredit for 80% of the DD, rather than the full 3.1 for a perfect dive.

Now multiply everybody's score by ten.

Except for the part about multiplying every competito'rs score by ten, this seems a lot like GOEs in figure skating as a percentage of the base value.

On the question of whether a skater should get any credit at all for a failed jump, that was actually debated in the early days of the IJS. Dick Button, for one, was very vocal with the opinion that if you leap into the air and come down on your butt, then you have not done any figure skating element at all. (Falling on a jiump was right up there with having an unattractive free leg position on your layback spin in the catalogue of unforgivable figure skatijng sins.)

This view, however, did not prevail. The ISU brain trust felt the need to ditinguish between bad falls, not so bad falls, half-way falls, hand down supporting wieght, hand down not supporting significant weight, fall but a ggod take-off and satisfactory air position, fall after complete rotations versus a fall caused by not getting the blade all the way around., etc. The current idea that a jump with a fall is not a complete zero is quite in harmony with the view of figure skating as a broad variety of skills, with each aspect of each element deserving its due amont of points regardless of other flaws.

So the base values should not be made too high because then, failed attempts become more rewarding than successful attemts from the category under (triples).

I probably agree that a failed attempt (let's say fully rotated but with a fall) of the 4A should not be more rewarding than the BV of the 3A. On the other hand, I don't think it should be substantially less rewarding than the 3A either. Currently a fully rotated 4A with a fall gives you (12.5/2)–1=5.25 points, which is less than the BV of the 3F. Not to mention that falls do have a negative impact on PCS too.

I probably agree that a failed attempt (let's say fully rotated but with a fall) of the 4A should not be more rewarding than the BV of the 3A. On the other hand, I don't think it should be substantially less rewarding than the 3A either. Currently a fully rotated 4A with a fall gives you (12.5/2)–1=5.25 points, which is less than the BV of the 3F. Not to mention that falls do have a negative impact on PCS too.

I am more hardcore. I am thinking that any failed attempt (fall) on a quad should not be worth more than any triple jump not just the one below It should be just about a landed double

On the question of whether a skater should get any credit at all for a failed jump, that was actually debated in the early days of the IJS. Dick Button, for one, was very vocal with the opinion that if you leap into the air and come down on your butt, then you have not done any figure skating element at all. (Falling on a jiump was right up there with having an unattractive free leg position on your layback spin in the catalogue of unforgivable figure skatijng sins.)

This view, however, did not prevail. The ISU brain trust felt the need to ditinguish between bad falls, not so bad falls, half-way falls, hand down supporting wieght, hand down not supporting significant weight, fall but a ggod take-off and satisfactory air position, fall after complete rotations versus a fall caused by not getting the blade all the way around., etc. The current idea that a jump with a fall is not a complete zero is quite in harmony with the view of figure skating as a broad variety of skills, with each aspect of each element deserving its due amont of points regardless of other flaws.

That is an interesting distinction. Let's say the judges award a score of 8 out of 10 to the dive. Then the formula is

DD x 8.

Or, it seems like we could say,

80% of DD times ten.

Let's say you do a forward 3 1/2 somersault with Degree of Difficulty 3.1 (I got this number from the scale of values that you linked above ). You get 8 style poins out of 10. So you get dredit for 80% of the DD, rather than the full 3.1 for a perfect dive.

Now multiply everybody's score by ten.

Except for the part about multiplying every competito'rs score by ten, this seems a lot like GOEs in figure skating as a percentage of the base value.

Not quite because the top two scores and the bottom two scores are discarded; the remaining three scores are added together and multiplied by the dive's difficulty rating, known as the degree of difficulty. So it's 3 scores of 8 is 24 times the D.D so a 3.0 at 8.0 average equals a 72 score. It's not the same as figure skating because the BV value can change depending on the quality of the jump... It's also not the same as there are NO mandatory minus 5 for instance. It's also not the same when you consider that 3 out of 7 scores are kept only... and often, most of the judges agree. I think this way of judging leads to less wuzrobbed moments

That's why I think it might have turned out different under IJS. Sato's strengths were in the difficult-to-measure-and-quantify skillls. The IJS would have given full value to Bonaly's TES advantage.

6.0 judging, besides being harsher on falls, also came down hard on two-footed landings, compared to the IJS. I remember Michael Weiss trying and trying and trying to get a quad Lutz ratified, but he never landed one without brusshing the ice with his free foot. Consequently he never got official credit for a quad Lutz at all.

On the other hand, .6.0 was pretty lenient when it came to flutzed takeoffs, especially in ladies,, compared to the IJS's specified penalties for wrong or unclear edges -- although it took many revisions of the IJS before the current details were agreed on.

At the same time, Bonaly wasn't consistent with jump rotation, and her skating skills would have been seriously dinged, like something that couldn't have been ignored (even if they respected her presentation which actually was really nice if you ignored what her feet & knees were doing).

I do find it interesting how 2002 olympics would have changed with IJS. Given plushenkos sp fall, I don't think he'd have made the BV difference to challenge Timothy goebels 3 quad program (and Timothy wouldn't have been penalised as much for 2 foot landing on 3A). Goebels would definitely have beaten plushenko I think then.