Skaters/Judging experts on GS - Question

Mathman said:

A "median with gray area" is very similar in spirit and effect to the trimmed mean.

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What I tried to say is that if a "true score" (the error-free value of a skater's performance) falls on the boundary of the rating levels, the measurement error places a significant role in the grade that the skater will receive.
Observed Score = True Score + Measurement Error
If the grade is in increments of 1 but the true value of a skater's performance is 0.5, the observed grade (either 0 or 1) will contain a high proportion of measurement error (0 = 0.5 - 0.5)(1 = 0.5 + 0.5)(Measurement Error = |0.5|).
If some scoring categories have a big minimum gradation than other categories (e.g., 1.00 in GOE of difficult jumps vs 0.25 in PCS), we can say that the impact of measurement errors is not randomly distributed. Luck or judge's subtle boost can play a more significant role in some elements.

Mathman said:

This discussion has been going on so long that now I have forgotten exactly what perceived flaw in the CoP it is that we are trying to fix.

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I thought our discussion is to convince ourselves that the COP is good, better than 6.0 or any preferential voting system. Even if it is not good enough, maybe we can tweak a bit here (e.g., using the median), or tweak a bit there (e.g., changing the formula) and still be able to keep the spirit of COP (i.e., specified criteria). The major flaw of CoP, in my opinion, concerns judges’ focus on parts so much so that it is difficult for them to evaluate the performance as a whole at the same time. And its algorithm is basically adding up different body parts in hope of making a living thing out of them.

Mathman said:

^ Do you really mean to multiply the D and E scores? Couldn't the E score be negative?

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Don't laugh at me, but I do mean "multiply". The minimum score is 0 and maximum 10 for all four categories, with a perfect score of 200 (= 10 x 10 + 10 x 10). ∑(DxE), the sum of multiplication between difficulty and execution, is the formula used in diving for years and it hasn't caused an Olympic scandal yet. My algorithm can be seen as ∑(Parts x Whole) (i.e., skating is a product of the parts and the whole) or ∑(Difficulty x Performance) (i.e., skating is a product of the difficulty levels and the performance) or ∑(Cop x 6.0) (i.e., the judging method is a product of the CoP and the 6.0), or Elements (50%) + Presentation (50%) (i.e., first mark + second mark).
Two panels of adjudicators are required: One (i.e., technical specialists) decides the type or level of each element (4T vs 3T) and assesses the skating skill levels based on prescribed criteria. The D-score is the combined base mark total of all elements (base mark is the fixed scale for each element, just like the current system except that we need to tweak the numbers). The S-score (Skating skill) is the combined score total of all subcategories (e.g., speed, edges, footwork, transition, etc.) that are rated separately on a scale. The other panel (i.e., judges) assessed the execution (E-score) and presentation (P-score) holistically as if assigning the 6.0 first mark and second mark. So, there is a panel watching for parts and another for the whole. It solves the criticism that it is impossible for the judges to focus on parts and evaluate the whole at the same time. I think all categories will be in increments of 0.1 (instead of my original 0.25) so as to accommodate the fine gradation in element base marks. And most importantly, the medians will be used to determine all ratings (level, score).

I like medians.

^ I understood that part. (Although I believe that the "measurement error" or "sampling error" for medians is not so well understood as it is for means.)

My point was that if the true value of a skater's performance is .5, and you are allowed to give only a 0 or a 1, then the trimmed mean is a way to get around that while still retaining some of the desirable properties of the median.

On the other hand, in sports there is actually an advantage to allowing a judge's score to have a magnified effect on the final outcome. If you jump 7.9999 feet in the high jump instead of 8 feet, that .0001 is magnified into total failure when the bar falls.

If the difference between V&M and D&W is in fact only 0.02 points, that will be completely lost in the statistical noise taken over all components and elements. Yet if one is better than the other, by however small an amount, that difference deserves to be taken into account in the final result.

Mathman said:

Do you think that this aspect of the scoring system could have an adverse effect on originality and expression? Maybe Virtue and Moir (and their choreographer) felt that a certain kind of linking step is more Fred and Ginger, but they had to change it to get more CoP points?

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Actually, I really like this part of IJS. IMO, skating is about skating, not about posing. It's possible to give the impression of Fred & Ginger while skating. In fact, V & M are more than capable of doing that trick.

skatinginbc said:

Don't laugh at me, but I do mean "multiply". The minimum score is 0 and maximum 10 for all four categories, with a perfect score of 200 (= 10 x 10 + 10 x 10). ∑DxE, the sum of multiplication between difficulty and execution, is the formula used in diving for years and it hasn't caused an Olympic scandal yet. My algorithm can be seen as ∑Parts x Whole (i.e., skating is a product of the parts and the whole) or ∑Difficulty x Performance (i.e., skating is a product of the difficulty levels and the performance) or ∑Cop x 6.0 (i.e., the judging method is a product of the CoP and the 6.0), or Elements (50%) + Presentation (50%) (i.e., first mark + second mark).

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Is the formula ∑DxE, are you saying (∑D)xE, or ∑(DxE). In diving, each individual dive gets its own E score, right?

To me, this way of "tweaking" the CoP seems a lot like junking the CoP and going back to 6.0. You get an overall technical score for all of your elements combined, then you get an artistic score for all of your elements combined.

Then you get a technical score for all of your program components combined, then an artistic score for all of your program components combined. Couldn't we just call this the 12.0 method (the 6.0 method done twice)?

skatinginbc said:

I thought our discussion is to convince ourselves that the COP is good, better than 6.0 or any preferential voting system.

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I still think that the purpose of judging a figure skating contest is to determine a winner. Who skated best, who second best, etc.

I believe that any CoP-type numbers should be our servants, not our masters, in carrying out this task.

I like medians.

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I do, too. But think about just what it is that we like when we say we like medians rather than means.

The median is the score given by the typical judge. If the contest is clear-cut, it is the score given by the majority of the judges. Can't get any more 6.0-ish than that!

No adding, averaging, or processing of data needed. No need to split hairs about the exact distance between the first and second place skaters or the exact increments of scoring.

Mathman said:

If the difference between V&M and D&W is in fact only 0.02 points, that will be completely lost in the statistical noise taken over all components and elements. Yet if one is better than the other, by however small an amount, that difference deserves to be taken into account in the final result.

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Interestingly, the medians amplified their tiny difference in both GPF Interpretation and 4CC Linking Footwork, whereas the trimmed means showed no difference or little difference (0.04).

Mathman said:

Is the formula ∑DxE, are you saying (∑D)xE, or ∑(DxE).

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∑(DxE)

Mathman said:

In diving, each individual dive gets its own E score, right?

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Right. But in skating, a program with various elements is performed as an integrated whole. There is no official break in between elements. And the elements are not totally independent of each other. Screwing up on one element may have an impact on the next (shortened spin due to time limit, popping a jump, etc.).

Mathman said:

Couldn't we just call this the 12.0 method (the 6.0 method done twice)?

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6.0 means three things: (1) holistic assessment, (2) norm-referenced (judging against other competitors), and (3) a Condorcet method (One-by-One system)
CoP means three things: (1) analytical assessment (a performance is divided into parts; each part is judged separately), (2) criterion-referenced (judging against specified standards), (3) a point system (the total points earned deciding the placement)
My proposal is largely COP because it is a criterion-referenced point system although both holistic and analytical assessments are utilized.

Here is an interesting interview with Alexander Lakernik from Vislaia Pete's site, linked by SkateFiguring in the Chan fan fest thread. It mentions the early work on a CoP-type scoring system by famous Russian pairs coach Stanislav Zhuk. (Zhuk coached Rodnina and Zaitsev and Gordeeva and Grinkov.)

http://kwantifiable.xanga.com/75902...-ijs-going-into-details-we-have-gone-too-far/

My proposal: Total score = (Element Difficulty Score x Element Execution score) + (Skating Skill x Presentation)

Say, Chan's Free Program scores at 2011 GPF:
Element D = 9.0
Element E = 7.0
Skating skill = 9.0
Presentation = 8.5
Total score = 9.0 x 7.0 + 9.0 x 8.5 = 63.0 + 76.5 = 139.5

Dai's Free Program scores at 2011 GPF:
Element D = 8.0
Element E = 8.5
Skating Skill = 8.5
Presentation = 8.5
Total score = 8.0 x 8.5 + 8.5 x 8.5 = 68.0 + 72.25 = 140.25

Dai would have won the free.

Why was Chan's Element E score (= 7.0) so low while Da's (= 8.5) so high? Well, if you look at the GPF protocol, Chan's base mark total was 83.75 and GOE total was +3.84 (= 87.59 - 83.75), whereas Dai's base mark total was 78.79 and GOE total was +8.26 (= 87.05 - 78.79). Dai's execution (GOE) was obviously better than Chan's that day.

This is how I came up with my estimates:
Using 5 as the average and then plus half of the GOE total:
Chan's execution score = 5 + 3.84/2 = 5 + 1.92 ≈ 7.0
Dai's execution score = 5 + 8.26/2 = 5 + 4.13 > 8.5 (lower estimate just to be conservative)

See my point? My proposal equally rewards difficulty and quality. A difficult program plagued with multiple flaws may not always win under my system.

How do you arrive at those D and E scores?

Would you care to take some skaters you've never heard of before, watch their programs, and with no prior bias figure out what their scores would be, to give us an idea of what that figuring out process consists of?

Or should judges and tech panels keep doing what they're currently doing and then the accounting program converts the IJS scores to D and E scores between 0 and 10 (i.e., as much as the averaging and rounding process already loses precision, this extra conversion step would lose even more)?

skatinginbc said:

Why was Chan's Element E score (= 7.0) so low while Da's (= 8.5) so high? Well, if you look at the GPF protocol, Chan's base mark total was 83.75 and GOE total was +3.84 (= 87.59 - 83.75), whereas Dai's base mark total was 78.79 and GOE total was +8.26 (= 87.05 - 78.79). Dai's execution (GOE) was obviously better than Chan's that day.

This is how I came up with my estimates:
Using 5 as the average and then plus half of the GOE total:
Chan's execution score = 5 + 3.84/2 = 5 + 1.92 ≈ 7.0
Dai's execution score = 5 + 8.26/2 = 5 + 4.13 > 8.5 (lower estimate just to be conservative)

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I don't understand your logic. Where did you get the average of 5? 5 of what? Also, where did you get the Element D 9.0 and 8.0?

You have totally, completely changed the ratio of BV and GOE of the original CoP scores, and grossly emphasized execution and presentation.

I like it!

Joesitz used to argue in favor if such a system, based on the model of diving. But he never gave enough detail for me to understand how it might work.

For the D and E scores, presumably the judges would have to keep score of each element separately, making note of its difficulty and quality. I think this would not be too much different from the Base Value/GOE idea in the current system.

Bluebonnet said:

You have totally, completely changed the ratio of BV and GOE of the original CoP scores, and grossly emphasized execution and presentation.

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Not so much as it might seem. For a triple Lutz, for instance, the base value is 6.0 points and the possible swing in GOE, from -2.1 to +2.1, is 4.2. That's a pretty big chunk of base value.

For a triple toe, the base value is 4.0 and the possible swing in GOE is still 4.2. So for this element, the current judging system actually puts slightly more emphasis on the GOE than on the base value.

If you look at the original CoP, the swing in GOE was 6 points, making the GOE more important than the base value (slightly) for all jumps below a triple Lutz. Even for a quad, I don't remember what the original base value was -- I think 9.0? And you could earn a 6 point swing, from -3 to +3 on GOE.

So this is not far off from the present balance. And in fact it has the advantage that there is not a fixed number of GOE points for all elements, but rather a proportional scale. After multiplying, a big GOE on a triple Axelwould get you more absolute points than a big GOE on a triple flip, proportionally.

Bluebonnet said:

I don't understand your logic. Where did you get the average of 5? 5 of what? Also, where did you get the Element D 9.0 and 8.0? You have totally, completely changed the ratio of BV and GOE of the original CoP scores, and grossly emphasized execution and presentation.

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Both D score and E score range from 0 to 10 (the middle point is 5). The E score is rated based on a plus-and-minus system. Everyone starts with 5. Visible errors, edge calls and so on are minuses. Good executions (good height, good running edge, etc) that meet a "bullet" are pluses. I am no skating expert, so I used the GOEs of the past results to do the rough estimates and show roughly how the system will look like.

Each element will have a base mark (of course, different from the current one). A standard podium-hopeful competitive program (4T, two 3As and all that) is set at around 8 points. Chan had two quads, so I gave him 9 points just for the sake of it. It was just a rough estimate. The main purpose is to demonstrate what the system will look like.

My proposal raises the ratio of Skating Skills (skating skill + transition under the current CoP) to be equal with the Presentation (choreography + performance + interpretation).

gkelly said:

Or should judges and tech panels keep doing what they're currently doing and then the accounting program converts the IJS scores to D and E scores between 0 and 10 (i.e., as much as the averaging and rounding process already loses precision, this extra conversion step would lose even more)?

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Not that stage yet. What I did was just rough estimates. As I said, the purpose of my post was to demonstrate what the system will look like. Unless skating experts like you agree with the logic behind my system, it will not fly.
My logic:
(1) Difficulty and Execution are equally important. What we want is well-executed difficult elements. No one should automatically win by default of the high base marks alone. With my system, we will see less painfully contorted slow spins we are getting used to.
(2) I see all elements as an integrated whole. They are not totally independent. If a skater includes a quad to raise the difficulty level but fails, he may still earn a good E-score as long as he keeps the rest of the program unaffected.
(3) Both artistry and skating skills are intrinsic, inseparable parts of figure skating. Good dancing/posing/acting without skating means zero in my system. Good skating without presentation (e.g, choreography) means zero as well.

Mathman said:

For the D and E scores, presumably the judges would have to keep score of each element separately, making note of its difficulty and quality. I think this would not be too much different from the Base Value/GOE idea in the current system.

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Yes. Skaters and fans would like to receive formative feedback regarding each element. Not much change except we have to design a new set of base marks and all that.

Mathman said:

Even for a quad, I don't remember what the original base value was -- I think 9.0? And you could earn a 6 point swing, from -3 to +3 on GOE.

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4T = 10.3

Math, I don't think the swing matters much because in the end, a skater earns either total +GOE or total -GOE which is half of that swing. And this number, such as +3 or -3, will be applied into the total. Chan's BV = 83.75, GOE = 3.84, Total TES = 87.59. GOE was less than 5% in the total TES earned. Takahashi's GOE was a little over 10% of the total TES.

Bluebonnet said:

Chan's BV = 83.75, GOE = 3.84, Total TES = 87.59. GOE was less than 5% in the total TES earned. Takahashi's GOE was a little over 10% of the total TES.

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This is my question as a casual fan: Should quality value about 10% of the TES or should it value as much as the difficulty score? Of course, it is a question up to the skating experts to decide.

skatinginbc said:

Both D score and E score range from 0 to 10 (the middle point is 5). The E score is rated based on a plus-and-minus system. Everyone starts with 5. Visible errors, edge calls and so on are minuses. Good executions (good height, good running edge, etc) that meet a "bullet" are pluses. I am no skating expert, so I used the GOEs of the past results to do the rough estimates and show roughly how the system will look like.

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This makes sense for the E score -- essentially the same as GOE ranging from -5 (0) to +5 (10) with your 5 the equivalent of the current 0/base GOE. I don't understand how you propose to combine to arrive at a single score based on all the elements -- averages? Would those be averages of the actual point values of the GOEs under something like the current scale of values, or percentages of the base values of their respective elements, or averages of grades regardless of point value?
E.g., if a skater gets maximum +GOEs on three level 1 spins and maximum minuses on two failed quads, and everything else straight base value, would the positives or the negatives prevail?
Would there be extra penalties or bonuses for presence or absence of certain kinds of disruptive errors?

Each element will have a base mark (of course, different from the current one). A standard podium-hopeful competitive program (4T, two 3As and all that) is set at around 8 points. Chan had two quads, so I gave him 9 points just for the sake of it. It was just a rough estimate. The main purpose is to demonstrate what the system will look like.

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I think it's too rough and will defeat the purpose.
E.g., in a single competition the top base value of the elements under the current scale of values might be 81.54 and the bottom base value might be 48.87. How would that translate into your D score? How many decimal places would you take? 8.2 vs. 4.9? 8.15 vs. 48.9?
Would the maximum possible value be 10.0, or would it be open ended?

What happens at lower level events, where you might have 20 skaters with base values ranging from a high of 23.39 to a low of 18.10?

Does the system have enough flexibility to address both wide and narrow ranges of scores in large fields?

I'm interested in how this can work for all levels of skating -- at least all that use IJS -- not just the senior championship medal contenders.

My proposal raises the ratio of Skating Skills (skating skill + transition under the current CoP) to be equal with the Presentation (choreography + performance + interpretation).

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Probably a good choice.

Not that stage yet. What I did was just rough estimates. As I said, the purpose of my post was to demonstrate what the system will look like. Unless skating experts like you agree with the logic behind my system, it will not fly.
My logic:
(1) Difficulty and Execution are equally important. What we want is well-executed difficult elements. No one should automatically win by default of the high base marks alone. With my system, we will see less painfully contorted slow spins we are getting used to.
(2) I see all elements as an integrated whole. They are not totally independent. If a skater includes a quad to raise the difficulty level but fails, he may still earn a good E-score as long as he keeps the rest of the program unaffected.

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OK. But by combining all the difficulty points into a single score and all the execution points into a single score, we lose the details of what was executed well and what was flawed or failed. Maybe a difficult move executed very well can make up for multiple flaws on easier elements, or maybe many easier elements executed well can make up for a failure on the biggest trick. Which could be true under any scoring system, depending how well executed or how much more difficult. The biggest advantage of the current method of breaking down scores is that we can see exactly where each skater gained and lost points. Are you proposing to hide that information by mushing all the difficulty points into one number and all the execution points into one number? Or will the detailed protocols still be available after the fact for those who want to know, and you're only proposing different calculations for dealing with the totals of each kind of score?

[](3) Both artistry and skating skills are intrinsic, inseparable parts of figure skating. Good dancing/posing/acting without skating means zero in my system. Good skating without presentation (e.g, choreography) means zero as well.[/QUOTE]

Well, good skating without presentation is still good skating. Since it's a skating contest, that can't literally mean zero. You have to at least give credit for the skating -- just no extra credit for presenting it well.

As an extreme, you could have a beautiful dancer come out and stand in one place on the ice and execute a beautiful dance above the waist, or with a few toepick steps, with not a single stroke actual skating.

And you could have a technically strong skater whose posture and extension are naturally weak and who hasn't made an effort to improve them, and who is shy and looks down all the time and ignores the music, come out and robotically execute a performance of difficult skating skills.

The general audience would probably enjoy the former performance better. But since there was zero skating content, it could legitimately earn 0 total points. (Of course there would also be no technical elements either.)

The latter performance had zero artistry, but it was a skating performance and deserves points for its skating content, even if 0 is appropriate for the presentation. So I don't think multiplying those two scores is appropriate.

Bluebonnet said:

4T = 10.3

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I'm sorry, I thought by "original base value" you meant the base value for a quad toe in the original version of the CoP from 2004. I think it was 9.0 back then.

Skatinginbc, if you give fixed D values for each element, then skaters of the future would not have a firm cap of 100 points of summation DxE. This might be OK, but it would be like gymnnastics, where the value keeps creeping up well past 10.0.

E.g., if a skater gets maximum +GOEs on three level 1 spins and maximum minuses on two failed quads, and everything else straight base value, would the positives or the negatives prevail?

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I think the proposal would go something like this.

FCCoSp4 base D level 4.5 points. E score .8 (corresponds to +3 GOE out of +5).

Contribution to total score for this element: 4.5x.8 = 3.6 points.

4T base D value 15. E score .2 (corresponding to -3 GOE out of 5)

Comtribution to total score: 15x.2 =3.0

This skater has 3.6 + 3.0 cummulative DxE points for his first two elements.

Note that in this example an outstnding combination spin is worth a little bit more than a fall on a quad.

One advantage to this scheme is that there would be no need for edge calls, underrotation calls, etc. They would just be bundled in with the E score.

skatinginbc said:

My proposal: Total score = (Element Difficulty Score x Element Execution score) + (Skating Skill x Presentation)

Say, Chan's Free Program scores at 2011 GPF:
Element D = 9.0
Element E = 7.0
Skating skill = 9.0
Presentation = 8.5
Total score = 9.0 x 7.0 + 9.0 x 8.5 = 63.0 + 76.5 = 139.5

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Wait a minute, now I'm confused again. Don't you want o multiply DxE for each element individually, then add the products? (post 165.)

gkelly said:

E.g., in a single competition the top base value of the elements under the current scale of values might be 81.54 and the bottom base value might be 48.87. How would that translate into your D score? What happens at lower level events, where you might have 20 skaters with base values ranging from a high of 23.39 to a low of 18.10?

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A lazy method is simply dividing the current base mark by 10, so we have 1.8 (18.10/10) to 8.2 (81.54/10). Ideally, we need to redesign the base marks so that they range from 1.0 (for the lowest level) to 9.0 (like Chan) and anything below or above is for the once-in-a-blue-moon occasion.
For instance,
Wayne Wing Yin CHUNG's 2012 Junior Preliminary Free Skate: Total Base Marks = 26.21, GOE = -2.47, Skating skills = (3.32 + 2.79)/2 = 3.06, Presentation = (3.00 + 3.21 + 3.00)/3 = 3.07, Total score = 54.38
Bernhard PAULI 2012 Junior Preliminary Free Skate: Total Base Marks = 28.99, GOE = -2.2, Skating Skills = (2.82 + 2.36)/2 = 2.59, Presentation = (2.82 + 2.89 + 2.79)/3 = 2.83, Total score = 54.15
Chung's estimated E score = 5 - 2.47/2 = 3.8, and total score under my system = (2.6 x 3.8 + 3.1 x 3.1) = 9.88 + 9.61 = 19.49
Pauli's estimated E score = 5 - 2.2/2 = 3.9, and total score under my system = (2.9 x 3.9 + 2.6 x 2.8) = 11.31 + 7.28 = 18.59
Their rankings are consistent under both systems.

gkelly said:

OK. But by combining all the difficulty points into a single score and all the execution points into a single score, we lose the details of what was executed well and what was flawed or failed. Maybe a difficult move executed very well can make up for multiple flaws on easier elements, or maybe many easier elements executed well can make up for a failure on the biggest trick. Which could be true under any scoring system, depending how well executed or how much more difficult. The biggest advantage of the current method of breaking down scores is that we can see exactly where each skater gained and lost points. Are you proposing to hide that information by mushing all the difficulty points into one number and all the execution points into one number? Or will the detailed protocols still be available after the fact for those who want to know, and you're only proposing different calculations for dealing with the totals of each kind of score?

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The feedback is good but not mandatory. 6.0 did not give feedback about every element, and lacking feedback was not the main reason that a new judging system was pushed into existence. Nevertheless, detailed protocols are still available if we have to have them. Just imagine the judging method remains roughly the same except that there is a total GOE score reported and used to calculate the total segment score.

gkelly said:

And you could have a technically strong skater whose posture and extension are naturally weak and who hasn't made an effort to improve them, and who is shy and looks down all the time and ignores the music, come out and robotically execute a performance of difficult skating skills...Since it's a skating contest, that can't literally mean zero. You have to at least give credit for the skating

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Sounds like he still skates to a "program" regardless how painful it is to watch. In that case, he won't receive a zero. Zero is reserved for blatant violations of the requirement--No program at all, in which jumps and spins and tracing of elaborate designs on the ice are all performed impromptu and separated by blatant breaks in between. If we want to reward those kind of skating skills, we might as well have a Special figures competition or a footwork competition or a jumping competition, WITHOUT music. If we like our current competition format, we are saying that it is essential for the skaters to integrate those individual elements or skills into a "program" (something prearranged in a meaningful way).

gkelly said:

I don't understand how you propose to combine to arrive at a single score based on all the elements -- averages?

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Simply add them up. No element is performed ==> receiving zero. All elements (e.g, all 8 jumping passes) are performed ==> automatic 5 points. And then add the Total GOEs (a plus-and-minus system) to the 5 points. Skipping one element ==> deduct 0.5 point from the base value ==> 4.5 points...

gkelly said:

Would those be averages of the actual point values of the GOEs under something like the current scale of values, or percentages of the base values of their respective elements, or averages of grades regardless of point value?
E.g., if a skater gets maximum +GOEs on three level 1 spins and maximum minuses on two failed quads, and everything else straight base value, would the positives or the negatives prevail?

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I propose using percentages of the base values of their respective elements just like the current method. Say, if a skater gets maximum +GOEs on three level 1 spins (I guess +0.3 x 3 = +0.9) and maximum minuses on two failed quads (+0.75 x 2 = +1.5), the negatives would prevail in this case. But if the spin levels are higher (4 or 3), the story might be different.

gkelly said:

Would there be extra penalties or bonuses for presence or absence of certain kinds of disruptive errors?

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No. There will be a deduction category however, only for time and costume violations and so on.