Sochi Figure Skating Scandal: A (Mostly) Objective and (Somewhat) Mathematical Analysis of Why Kim Yuna Should Have Won the Gold Medal
• This guest post is contributed by Thomas Lai, my blog reader. • Right click on this blog but is forbidden. Whoever still needs this post in WORD format, please email me. • Read Related Articles: (2) Sochi Figure Skating Scandal: What's Next? A Possible Agenda To The Next Stage (3) Sochi Figure Skating Scandal: Worldwide Figure Skating Fans' Letter to International Sports Journalists and Figure Skating Insiders |
Thomas Lai's (Mostly) Objective and (Somewhat) Mathematical Analysis of
Why Kim Yuna Should Have Won the Gold Medal
There are many arguments floating around on the Internet supporting why South Korean Kim Yuna should have gotten the gold medal for women figure skating at the 2014 Sochi Winter Olympics. People claim that she’s underscored while the gold medalist, Russian Adelina Sotnikova, received inflated scores. Some of the evidence presented so far is very solid and easily quantifiable, while other is less so. Below, I have broken down the evidence into three categories (indisputable, strong, and circumstantial), and illustrate as mathematically as possible how each piece of evidence impacts or would have impacted the final results.
1. Free Skate: Wrong Edge on Adelina’s Triple Lutz + Triple Toe loop Combination
2. Free Skate: Under-Rotation on Adelina’s Triple Lutz + Triple Toe loop Combination
The Base Value is lowered due to the lower Base Value of the under-rotated Triple Toe loop, and the GOE is scaled according to the SOV. As you can see, had the errors been correctly denoted, Adelina’s Triple Lutz + Triple Toe loop combination would have gotten a score of 7.5 instead of 11.10. That’s a discrepancy of 3.6, just for this one combination.
3. Free Skate: Stepping Out of the Triple Flip + Double Toe loop + Double Loop Combination
The GOE should have been -1.40 instead of -0.90. The discrepancy is 0.50.
No, Kim Yuna would still have lost to Adelina, but only by a margin of 1.38 instead of 5.48. No matter whom you support, I hope that you can see from the illustration above that the judging was very poor at the 2014 Winter Olympics. Also, we have only looked at two elements above. If the judging was so poorly done for these two elements, would it not be reasonable to suspect the quality of judging for rest of the competition? We still have more evidence to consider below. It’s just that the rest of the evidence isn’t as objective or quantifiable, unfortunately.
4. The Technical Controller is also the Vice President of the Russian Skating Federation
The Technical Specialist, assisted by the Assistant Technical Specialist, identifies and calls the performed elements and the specific Levels of Difficulty of certain performed elements (e.g. spins, footwork,). He/She identifies illegal or additional elements, falls and adds if applicable, innovative elements.
To explain what the Technical Panel does in plain English, it’s the body which identifies each element performed by a skater and any mistakes committed by him/her. Remember the wrong edge and the missing “e” sign? Or the under-rotation and the missing “<” sign? The Technical Panel is the body responsible for these missing signs. And the Vice President of the Russian Skating Federation, being the Technical Controller, is the person who authorizes or corrects these mistakes on the score sheet!
5. In the four major competitions leading up to the Winter Olympics, Adelina made the same wrong edge mistake on her Triple Lutz in all four free skates
1. Unintentionally missed the mistake, or
2. Intentionally omitted it.
6. In the four major competitions leading up to the 2014 Winter Olympics, Adelina’s Layback Spin and Step Sequence in her free skate were never identified as Level 4, but they were at the 2014 Winter Olympics
Given the fact that the Technical Panel at the 2014 Winter Olympics either missed the wrong edge mistake unintentionally or omitted it intentionally, would it be unreasonable to question whether Adelina really deserved a Level 4 designation in both her Layback Spin and Step Sequence at the Winter Olympics?
How much impact do these elements have? The level of the Layback Spin and Step Sequence is directly related to the Base Value of the element. In addition, a Level 3 Step Sequence has a SOV of 0.5, whereas a Level 4 Step Sequence has a SOV of 0.7. In other words, a +1 GOE for a Level 3 Step Sequence results in +0.5 in actual score, whereas a +1 GOE for a Level 4 Step Sequence results in +0.7 in actual score. In light of this, how would Adelina’s score have been impacted if her Layback Spin and Step Sequence were Level 3, not 4? Assuming all the GOE’s stay the same:
So adding the Base Value and the GOE together, these elements at Level 3 would have received 7.98. At the 2014 Winter Olympics, Adelina received 9.37 for these elements since they were identified by the Technical Panel to be Level 4. The discrepancy is 1.39. In addition to the indisputable mistakes mentioned earlier, would this have been the difference between silver and gold for Kim Yuna?
Yes, it would have. Kim Yuna would have won the gold medal by a margin of 0.01.
7. Short Program: Both Yuna’s and Adeline’s short programs have two outliers in their Program Component Scores (PCS)
Because judging is anonymous, we don’t know which judge from which country gave a particular score at the 2014 Winter Olympics. However, we can see whether the scores from all the judges fall within a reasonable range. First, as always, let’s take a look at the score sheets:
Kim Yuna’s Short Program:
In addition to the two outliners mentioned above, notice that there is a Judge who gave Adelina a much lower PCS than the others. This is what the trimmed average is designed to protect against. The lowest and the highest score for each component are discarded, and the average of the remaining seven scores, i.e. the trimmed average, becomes the final score for that component. What the trimmed average doesn’t protect against is when you have more than one Judge simultaneously inflating the score of one skater and deflating the score of another. The trimmed average reduces the impact of this, but it can’t negate the impact.
2. The trimmed average of the remaining seven Judges excluding Judge #1 and Judge #7
Notice how for Yuna, her scores don’t change much between the average and the trimmed average. For Adelina, her trimmed average is appreciably higher than her average because the low outliner score seen in the graph above is mitigated by the trimmed average. Now the actual comparison chart:
So it’s reasonable to say that the discrepancy could have been somewhere in the 1.20 to 1.50 range. Would this have been the difference between gold and silver for Kim Yuna? Using only the indisputable evidence listed above, i.e. assuming Adelina’s Layback Spin and Step Sequence are worthy of the Level 4 designation, we get the following tables:
So, if we look at the average, Yuna would have beaten Adelina by 0.05. If we look at the trimmed average, Yuna would still have lost by 0.12.
8. Free Skate: The PCS for Adelina’s free skate have a high degree of variation
I won’t attempt to illustrate the impact here since there are too many variables. One could argue that the four scores at the top were too high, or that the four scores at the bottom were too low. We’ll never know for sure unless more official judges from ISU rate the performances. What we do know is that there is a much higher degree of variation in Adelina’s free skate score, but why? We may never know for sure without further evidence, but unfortunately, all remaining evidence is circumstantial. Nevertheless, it’s still worth a look.
9. Adelina’s PCS has grown tremendously in the three months leading up to the 2014 Winter Olympics
Earlier on we have looked at bits and pieces of Adelina’s performances in the four major competitions leading up to the 2014 Winter Olympics. These competitions occurred in the span of three months, from Nov 2013 to Jan 2014. Let’s take a look now at her actual scores:
Can you see any discernable differences in artistic value between her performances?
10. Adelina’s GOE has also grown tremendously in the three months leading up to the 2014 Winter Olympics
I won’t even bother with a chart this time, since the differences are very obvious.
11. Questionable choice in the selection of competition officials
Judges highlighted in yellow only participated in the short program. Judges highlighted in orange only participated in the free skate. Officials highlighted in red are from Russia.
Two of the four incoming judges for the free skate are also questionable. First, there is the Russian judge Alla Shekhovtseva, the wife of Valentin Piseev. Valentin Piseev is the ex-President of the Russian Skating Federation and its current General Director. Again, the potential for a conflict of interest to occur is undeniable. The second judge is the Ukrainian judge Yury Balkov, who was suspended for trying to fix the 1998 Nagano Winter Olympics. He was suspended for only a year after the 1998 incident. We have already demonstrated that just two Judges working together could also have a non-trivial impact on the PCS.
Without knowing how each judge scored, there is no way to prove one way or another whether the questionable appointments of these Judges had a biased impact on the results. However, unlike the previous two points, this one can be easily proven or disproven, if only ISU would release how the Judges scored.
2. A margin of 1.38 could easily have been manipulated by as few as two people. For example:
4. The selection of the competition officials is questionable with undeniable potential for conflict of interest.
2. Change the fundamentally flawed ISU Judging System to minimize judging bias.
2. Read this blog post and follow the suggestions to put pressure on ISU:
3. Join this Facebook group to connect with other people with the same goals:
Indisputable Evidence
In figure skating, which edge of the skate you take off on to start a jump matters a great deal. This is because the difficulty is different for different edges, and difficulty is what determines the Base Value (BV) of a jump. Think of the Base Value as the score a skater gets if he/she does an average job on the jump. If the execution is better than average, he/she gets a higher score, and vice versa.
In Adelina’s free skate, she took off on the wrong edge for the Triple Lutz in her Triple Lutz + Triple Toe loop combination. A Lutz requires taking off on the outer edge of the skate, not the inner. This is indisputable because everyone can see this in a slow-motion video of the jump. You can find a link to an animated GIFF of the jump in question below:
Normally, wrong edge is called out by an “e” sign on the score sheet. However, in this case, the “e” sign is missing:
For each technical element such as a triple jump, each Judge gives a Grade of Execution (GOE) in the range of -3 to +3 to represent how well the element is performed. An average execution gives you a 0 GOE. A mistake gives you a negative GOE. Good execution gives you a positive GOE, while a perfectly executed element gives you the maximum bonus, a +3 GOE.
According to the Guidelines for Marking Grade of Execution from the International Skating Union (ISU) Communication 1790 dated April 26, 2013, a wrong edge gets a GOE between -1 to -3:
As you can see, even if the “e” sign is missing, a judge can still give a -1 GOE, which is exactly what one (and only one) judge did, as seen in the score sheet above. If the wrong edge were properly denoted by an “e” sign, the GOE should have been either -1 or -2. Let’s assume a minimum deduction of -1 here. What would that have done to the score?
Element | Base Value | GOE | Judges | ||||||||||
3Lz + 3T | 10.10 | -0.70 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
Note that a GOE of -1 given by the Judges doesn’t translate into a -1.00 in the actual score. That’s because each element has a Scale of Value (SOV). The SOV for a Triple Lutz is 0.7, hence a -1 GOE translates into -0.70 in the actual score.
Already, you can see that a simple missing “e” results in a difference of 1.70 in the score, from +1.00 GOE to -0.70 GOE.
What matters more than the take-off edge is the number of rotations in a jump. Needless to say, more rotations are more difficult, and hence a jump with more rotations has a higher Base Value. If a jump doesn’t meet the required number of rotations, it’s considered under-rotated. The automatic deduction for under-rotation depends on how severely under-rotated a jump is. If it’s under-rotated by less than a full rotation, the GOE is either -1 or -2. If it’s under-rotated by one or more full rotations, the GOE is -3.
Adelina’s Triple Toe loop in her Triple Lutz + Triple Toe loop Combination was under-rotated. Not only did she start to rotate before leaving the ground, but she also landed on her foot before it had completed the last rotation. This is clearly visible in the following animated GIFF (same as the one above). The jump in question is the second one in the combination:
Normally, under-rotation is called out by an “<” sign on the score sheet. However, in this case, the “<” sign is again missing:
According to the Guidelines for Marking GOE published by the ISU, under-rotation results in a GOE of either -1 or -2:
What makes under-rotation worse than wrong edge is that under-rotation also adjusts the Base Value of the element. A fully rotated Triple Toe loop has a Base Value of 4.1, while an under-rotated Triple Toe loop has a Base Value of 2.9, a reduction of 1.2.
If the under-rotation had been correctly denoted, what would have been the impact to the score? Again, assuming a minimum deduction of -1 for the under-rotation and a minimum deduction of -1 for the wrong edge:
Element | Base Value | GOE | Judges | ||||||||||
3Lz + 3T | 8.90 | -1.40 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 |
The Base Value is lowered due to the lower Base Value of the under-rotated Triple Toe loop, and the GOE is scaled according to the SOV. As you can see, had the errors been correctly denoted, Adelina’s Triple Lutz + Triple Toe loop combination would have gotten a score of 7.5 instead of 11.10. That’s a discrepancy of 3.6, just for this one combination.
When a skater lands a jump and has to step out of the landing in order to steady himself/herself, it carries a GOE of either -2 or -3. This was exactly what Adelina did in her Triple Flip + Double Toe loop + Double Loop combination. This is clearly visible in the animated GIFF below:
Instead of getting -2’s and -3’s, Adelina got three -2’s and six -1’s from the nine judges:
This is against ISU’s own guidelines:
Had the judges followed the proper guidelines, what would Adelina’s score have been for this element? Let’s again assume a minimum deduction of -2:
Element | Base Value | GOE | Judges | ||||||||||
3F + 2T + 2Lo | 9.24 | -1.40 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 |
The GOE should have been -1.40 instead of -0.90. The discrepancy is 0.50.
Unfortunately, this is where the indisputable AND quantifiable evidence ends. So had these mistakes been appropriately accounted for, would Kim Yuna have been the gold medalist? Let’s take a look at the table below:
Short Program | Free Skate | Grand | |||||||
BV | GOE | PCS | Total | BV | GOE | PCS | Total | Total | |
Kim Yuna | 31.43 | 7.60 | 35.89 | 74.92 | 57.49 | 12.20 | 74.50 | 144.19 | 219.11 |
Adelina Sotnikova | 30.43 | 8.66 | 35.55 | 74.64 | 61.43 | 14.11 | 74.41 | 149.95 | 224.59 |
Adelina Sotnikova (wrong edge, under-rotation, stepping out accounted for appropriately) | 30.43 | 8.66 | 35.55 | 74.64 | 60.23 | 11.21 | 74.41 | 145.85 | 220.49 |
No, Kim Yuna would still have lost to Adelina, but only by a margin of 1.38 instead of 5.48. No matter whom you support, I hope that you can see from the illustration above that the judging was very poor at the 2014 Winter Olympics. Also, we have only looked at two elements above. If the judging was so poorly done for these two elements, would it not be reasonable to suspect the quality of judging for rest of the competition? We still have more evidence to consider below. It’s just that the rest of the evidence isn’t as objective or quantifiable, unfortunately.
If you are looking for the definition of “potential conflict of interest”, look no further than the above sentence. However, before we go on, an explanation is in order. Who is the Technical Controller at a figure skating competition? In ISU’s own words (LINK):
Technical Panel
The Technical Panel is composed of the Technical Controller, the Technical Specialist and the Assistant Technical Specialist, each one from different ISU Members (countries). A Data Operator assists them for recording purposes. An instantaneous slow-motion video replay system operated by a Replay Operator supports the Technical Panel in the identification of the performed elements.
The Technical Specialist, assisted by the Assistant Technical Specialist, identifies and calls the performed elements and the specific Levels of Difficulty of certain performed elements (e.g. spins, footwork,). He/She identifies illegal or additional elements, falls and adds if applicable, innovative elements.
The Technical Controller authorizes or corrects all calls, supervises the Data Operator and can propose corrections, if necessary.
In case of disagreement, the majority among the three Officials prevails.
To explain what the Technical Panel does in plain English, it’s the body which identifies each element performed by a skater and any mistakes committed by him/her. Remember the wrong edge and the missing “e” sign? Or the under-rotation and the missing “<” sign? The Technical Panel is the body responsible for these missing signs. And the Vice President of the Russian Skating Federation, being the Technical Controller, is the person who authorizes or corrects these mistakes on the score sheet!
One may say that the Technical Controller is just one person on the three-people Technical Panel. As stated above, “in case of disagreement, the majority among the three Officials prevails”. However, the indisputable evidence here is that there is an undeniable potential conflict of interest on the Technical Panel. Why does it matter? Because it creates a reasonable doubt that bias might have been present on the Technical Panel, and as illustrated above, the Technical Panel has a significant impact on the scores in a competition.
Strong Evidence
Every time Adelina attempted the Triple Lutz in the three months leading up to the 2014 Winter Olympics, she made the same wrong edge mistake. Here is the relevant portion of the score sheets for these competitions:
One may say this doesn’t mean anything since Adelina could have fixed the mistake. I’m no figure skating expert, so I don’t know how easy or difficult it is to fix such a mistake in such a short period of time, but that’s not the point here. We have already demonstrated that she DID have the wrong edge mistake. The point here is that the Technical Panel for all four of these competitions were able to correctly identify the wrong edge mistake. So the Technical Panel at the 2014 Winter Olympics, the highest level figure skating competition in the world, either:
2. Intentionally omitted it.
First, let’s take a look at the score sheets:
So, in summary:
Layback Spin Level | Step Sequence Level | ||
Nov 2013 | Cup of China 2013 | 3 | 2 |
Nov 2013 | Trophee Eric Bompard 2013 | 3 | 3 |
Dec 2013 | Grand Prix Final 2013 - 2014 | 3 | 3 |
Jan 2014 | European Championships 2014 | 3 | 3 |
Feb 2014 | Winter Olympics | 4 | 4 |
Given the fact that the Technical Panel at the 2014 Winter Olympics either missed the wrong edge mistake unintentionally or omitted it intentionally, would it be unreasonable to question whether Adelina really deserved a Level 4 designation in both her Layback Spin and Step Sequence at the Winter Olympics?
How much impact do these elements have? The level of the Layback Spin and Step Sequence is directly related to the Base Value of the element. In addition, a Level 3 Step Sequence has a SOV of 0.5, whereas a Level 4 Step Sequence has a SOV of 0.7. In other words, a +1 GOE for a Level 3 Step Sequence results in +0.5 in actual score, whereas a +1 GOE for a Level 4 Step Sequence results in +0.7 in actual score. In light of this, how would Adelina’s score have been impacted if her Layback Spin and Step Sequence were Level 3, not 4? Assuming all the GOE’s stay the same:
Element | Base Value | GOE | Judges | ||||||||||
LSp3 | 2.40 | 1.07 | 2 | 2 | 2 | 3 | 2 | 2 | 3 | 2 | 2 | ||
StSq3 | 3.30 | 1.21 | 2 | 3 | 1 | 2 | 3 | 3 | 3 | 2 | 2 |
So adding the Base Value and the GOE together, these elements at Level 3 would have received 7.98. At the 2014 Winter Olympics, Adelina received 9.37 for these elements since they were identified by the Technical Panel to be Level 4. The discrepancy is 1.39. In addition to the indisputable mistakes mentioned earlier, would this have been the difference between silver and gold for Kim Yuna?
Short Program | Free Skate | Grand | |||||||
BV | GOE | PCS | Total | BV | GOE | PCS | Total | Total | |
Kim Yuna | 31.43 | 7.60 | 35.89 | 74.92 | 57.49 | 12.20 | 74.50 | 144.19 | 219.11 |
Adelina Sotnikova | 30.43 | 8.66 | 35.55 | 74.64 | 61.43 | 14.11 | 74.41 | 149.95 | 224.59 |
Adelina Sotnikova (wrong edge, under-rotation, stepping out accounted for appropriately) | 30.43 | 8.66 | 35.55 | 74.64 | 60.23 | 11.21 | 74.41 | 145.85 | 220.49 |
Adelina Sotnikova (wrong edge, under-rotation, stepping out accounted for appropriately; Level 3 Layback Spin and Step Sequence) | 30.43 | 8.66 | 35.55 | 74.64 | 59.33 | 10.72 | 74.41 | 144.46 | 219.10 |
Yes, it would have. Kim Yuna would have won the gold medal by a margin of 0.01.
So far we have mostly focused on the Technical Panel, whose job is as objective as you can get in judging figure skating. The only problem with the Judges we have looked at so far are the GOE’s for stepping out of a landing. However, even though the Judges’ job is more subjective, there are clear objective guidelines for scoring mistakes. Now let’s take a look at the subjective side of figure skating judging.
7. Short Program: Both Yuna’s and Adeline’s short programs have two outliers in their Program Component Scores (PCS)
Because judging is anonymous, we don’t know which judge from which country gave a particular score at the 2014 Winter Olympics. However, we can see whether the scores from all the judges fall within a reasonable range. First, as always, let’s take a look at the score sheets:
Kim Yuna’s Short Program:
Notice how Judge #1 and Judge #7 gave significantly lower scores than the other Judges.
Adelina Sotnikova’s Short Program:
Notice how Judge #1 and Judge #7 gave significantly higher scores than the other Judges.
Perhaps it’s easier to spot the outliners if we plot the average PCS given by each Judge for the five components:
Kim Yuna | |||||||||
Skating Skills | 8.25 | 9.00 | 9.50 | 9.25 | 9.00 | 9.00 | 8.50 | 9.25 | 9.25 |
Transitions / Linking Footwork / Movement | 8.00 | 9.00 | 9.25 | 8.75 | 9.00 | 8.25 | 7.75 | 8.50 | 8.75 |
Performance / Execution | 8.00 | 9.50 | 9.75 | 9.00 | 9.25 | 9.25 | 8.50 | 9.25 | 9.00 |
Choreography / Composition | 7.75 | 9.25 | 9.75 | 9.00 | 9.00 | 8.50 | 8.00 | 9.25 | 9.25 |
Interpretation | 8.50 | 9.75 | 9.75 | 9.25 | 9.25 | 9.50 | 8.25 | 9.00 | 9.25 |
Average | 8.10 | 9.30 | 9.60 | 9.05 | 9.10 | 8.90 | 8.20 | 9.05 | 9.10 |
Adelina Sotnikova | |||||||||
Skating Skills | 9.50 | 8.50 | 9.00 | 8.75 | 8.75 | 8.75 | 9.25 | 8.00 | 8.75 |
Transitions / Linking Footwork / Movement | 9.25 | 8.25 | 8.50 | 8.50 | 8.50 | 8.50 | 9.00 | 7.50 | 8.75 |
Performance / Execution | 9.75 | 8.50 | 9.25 | 9.25 | 9.00 | 9.50 | 9.75 | 8.50 | 8.50 |
Choreography / Composition | 9.50 | 8.75 | 9.25 | 8.75 | 8.75 | 9.00 | 9.25 | 8.25 | 8.50 |
Interpretation | 9.75 | 8.75 | 9.00 | 9.00 | 9.00 | 9.00 | 9.50 | 8.50 | 9.00 |
Average | 9.55 | 8.55 | 9.00 | 8.85 | 8.80 | 8.95 | 9.35 | 8.15 | 8.70 |
In addition to the two outliners mentioned above, notice that there is a Judge who gave Adelina a much lower PCS than the others. This is what the trimmed average is designed to protect against. The lowest and the highest score for each component are discarded, and the average of the remaining seven scores, i.e. the trimmed average, becomes the final score for that component. What the trimmed average doesn’t protect against is when you have more than one Judge simultaneously inflating the score of one skater and deflating the score of another. The trimmed average reduces the impact of this, but it can’t negate the impact.
Of course, no one knows what the score would have been had Judge #1 and Judge #7 scored in a way more aligned with the rest of the Judges. However, we could illustrate the impact of these outliner scores by looking at:
1. The average of the remaining seven Judges excluding Judge #1 and Judge #72. The trimmed average of the remaining seven Judges excluding Judge #1 and Judge #7
Kim Yuna | Factor | Avg | Trimmed Average | |||||||
Skating Skills | 0.80 | 9.00 | 9.50 | 9.25 | 9.00 | 9.00 | 9.25 | 9.25 | 9.18 | 9.15 |
Transitions / Linking Footwork / Movement | 0.80 | 9.00 | 9.25 | 8.75 | 9.00 | 8.25 | 8.50 | 8.75 | 8.79 | 8.80 |
Performance / Execution | 0.80 | 9.50 | 9.75 | 9.00 | 9.25 | 9.25 | 9.25 | 9.00 | 9.29 | 9.25 |
Choreography / Composition | 0.80 | 9.25 | 9.75 | 9.00 | 9.00 | 8.50 | 9.25 | 9.25 | 9.14 | 9.15 |
Interpretation | 0.80 | 9.75 | 9.75 | 9.25 | 9.25 | 9.50 | 9.00 | 9.25 | 9.39 | 9.40 |
36.63 | 36.60 |
Adelina Sotnikova | Factor | Avg | Trimmed Average | |||||||
Skating Skills | 0.80 | 8.50 | 9.00 | 8.75 | 8.75 | 8.75 | 8.00 | 8.75 | 8.64 | 8.70 |
Transitions / Linking Footwork / Movement | 0.80 | 8.25 | 8.50 | 8.50 | 8.50 | 8.50 | 7.50 | 8.75 | 8.36 | 8.45 |
Performance / Execution | 0.80 | 8.50 | 9.25 | 9.25 | 9.00 | 9.50 | 8.50 | 8.50 | 8.93 | 8.90 |
Choreography / Composition | 0.80 | 8.75 | 9.25 | 8.75 | 8.75 | 9.00 | 8.25 | 8.50 | 8.75 | 8.75 |
Interpretation | 0.80 | 8.75 | 9.00 | 9.00 | 9.00 | 9.00 | 8.50 | 9.00 | 8.89 | 8.95 |
34.86 | 35.00 |
Notice how for Yuna, her scores don’t change much between the average and the trimmed average. For Adelina, her trimmed average is appreciably higher than her average because the low outliner score seen in the graph above is mitigated by the trimmed average. Now the actual comparison chart:
Kim Yuna | Adelina Sotnikova | Difference | Discrepancy | |
Actual | 35.89 | 35.54 | 0.35 | |
Average | 36.63 | 34.86 | 1.77 | 1.77 – 0.35 = 1.42 |
Trimmed Average | 36.60 | 35.00 | 1.60 | 1.60 – 0.35 = 1.25 |
So it’s reasonable to say that the discrepancy could have been somewhere in the 1.20 to 1.50 range. Would this have been the difference between gold and silver for Kim Yuna? Using only the indisputable evidence listed above, i.e. assuming Adelina’s Layback Spin and Step Sequence are worthy of the Level 4 designation, we get the following tables:
Copy of the Original Table
Short Program | Free Skate | Grand | |||||||
BV | GOE | PCS | Total | BV | GOE | PCS | Total | Total | |
Kim Yuna | 31.43 | 7.60 | 35.89 | 74.92 | 57.49 | 12.20 | 74.50 | 144.19 | 219.11 |
Adelina Sotnikova | 30.43 | 8.66 | 35.55 | 74.64 | 61.43 | 14.11 | 74.41 | 149.95 | 224.59 |
Adelina Sotnikova (wrong edge, under-rotation, stepping out accounted for appropriately) | 30.43 | 8.66 | 35.55 | 74.64 | 60.23 | 11.21 | 74.41 | 145.85 | 220.49 |
Average Ignoring the Scores from Judge #1 and #7
Short Program | Free Skate | Grand | |||||||
BV | GOE | PCS | Total | BV | GOE | PCS | Total | Total | |
Kim Yuna | 31.43 | 7.60 | 36.63 | 75.66 | 57.49 | 12.20 | 74.50 | 144.19 | 219.85 |
Adelina Sotnikova | 30.43 | 8.66 | 34.86 | 73.95 | 61.43 | 14.11 | 74.41 | 149.95 | 223.90 |
Adelina Sotnikova (wrong edge, under-rotation, stepping out accounted for appropriately) | 30.43 | 8.66 | 34.86 | 73.95 | 60.23 | 11.21 | 74.41 | 145.85 | 219.80 |
Trimmed Average Ignoring the Scores from Judge #1 and #7
Short Program | Free Skate | Grand | |||||||
Trimmed Avg Ignoring Judge #1 & #7 | BV | GOE | PCS | Total | BV | GOE | PCS | Total | Total |
Kim Yuna | 31.43 | 7.60 | 36.60 | 75.63 | 57.49 | 12.20 | 74.50 | 144.19 | 219.82 |
Adelina Sotnikova | 30.43 | 8.66 | 35.00 | 74.09 | 61.43 | 14.11 | 74.41 | 149.95 | 224.04 |
Adelina Sotnikova (wrong edge, under-rotation, stepping out accounted for appropriately) | 30.43 | 8.66 | 35.00 | 74.09 | 60.23 | 11.21 | 74.41 | 145.85 | 219.94 |
So, if we look at the average, Yuna would have beaten Adelina by 0.05. If we look at the trimmed average, Yuna would still have lost by 0.12.
If nothing else, I hope this illustration shows you that using a trimmed average is NOT the Holy Grail against dubious scoring.
If we repeat the above exercise for the PCS of the free skate, what do we see?
Kim Yuna | |||||||||
Skating Skills | 9.00 | 8.50 | 9.50 | 9.00 | 9.50 | 9.25 | 9.25 | 9.00 | 9.75 |
Transitions / Linking Footwork / Movement | 8.75 | 7.75 | 9.50 | 8.75 | 9.25 | 9.00 | 9.00 | 8.75 | 9.25 |
Performance / Execution | 9.25 | 8.75 | 9.75 | 9.25 | 9.25 | 10.00 | 9.50 | 9.50 | 9.50 |
Choreography / Composition | 9.50 | 8.25 | 10.00 | 9.00 | 9.50 | 9.50 | 9.25 | 9.25 | 9.75 |
Interpretation | 9.25 | 8.75 | 10.00 | 9.25 | 9.50 | 10.00 | 9.75 | 9.50 | 9.75 |
Average | 9.15 | 8.40 | 9.75 | 9.05 | 9.40 | 9.55 | 9.35 | 9.20 | 9.60 |
Adelina Sotnikova | |||||||||
Skating Skills | 9.50 | 9.50 | 9.25 | 8.75 | 9.50 | 9.00 | 9.50 | 8.75 | 8.50 |
Transitions / Linking Footwork / Movement | 9.25 | 9.25 | 8.75 | 8.50 | 9.25 | 9.00 | 9.50 | 8.75 | 8.50 |
Performance / Execution | 9.75 | 9.50 | 9.25 | 9.00 | 9.75 | 9.50 | 9.75 | 9.00 | 9.25 |
Choreography / Composition | 9.75 | 9.75 | 9.25 | 8.75 | 9.50 | 9.75 | 9.75 | 9.00 | 9.50 |
Interpretation | 9.75 | 9.75 | 9.00 | 9.25 | 9.75 | 9.25 | 9.75 | 8.75 | 9.25 |
Average | 9.60 | 9.55 | 9.10 | 8.85 | 9.55 | 9.30 | 9.65 | 8.85 | 9.00 |
Yuna’s chart doesn’t tell us much, except that one Judge really, really didn’t like her performance. On the other hand, Adelina’s chart is really interesting. You can see that there are basically two groups of scores, with a group of four significantly higher than another group of four. It’s as if the Judges were watching two different performances.
I won’t attempt to illustrate the impact here since there are too many variables. One could argue that the four scores at the top were too high, or that the four scores at the bottom were too low. We’ll never know for sure unless more official judges from ISU rate the performances. What we do know is that there is a much higher degree of variation in Adelina’s free skate score, but why? We may never know for sure without further evidence, but unfortunately, all remaining evidence is circumstantial. Nevertheless, it’s still worth a look.
Circumstantial Evidence
Earlier on we have looked at bits and pieces of Adelina’s performances in the four major competitions leading up to the 2014 Winter Olympics. These competitions occurred in the span of three months, from Nov 2013 to Jan 2014. Let’s take a look now at her actual scores:
Short | Free | Grand | ||||||||
BV | GOE | PCS | Total | BV | GOE | PCS | Total | Total | ||
Nov-13 | Cup of China | 31.83 | 4.03 | 30.17 | 66.03 | 47.32 | 3.04 | 60.31 | 108.67 | 174.70 |
Nov-13 | Trophee Eric Bompard | 26.71 | 2.53 | 30.77 | 60.01 | 55.75 | 9.40 | 64.65 | 129.80 | 189.81 |
Dec-13 | Grand Prix Final | 30.43 | 7.10 | 30.85 | 68.38 | 48.85 | -2.40 | 60.47 | 104.92 | 173.30 |
Jan-14 | European Championships | 29.33 | 7.82 | 33.58 | 70.73 | 54.86 | 7.17 | 69.60 | 131.63 | 202.36 |
Feb-14 | Winter Olympics | 30.43 | 8.66 | 35.55 | 74.64 | 61.43 | 14.11 | 74.41 | 149.95 | 224.59 |
If we chart her PCS growth in the last three months, what do we see?
One may ask what the point of this illustration is. After all, couldn’t she have improved so much legitimately in three months? Again, I’m no skating expert, but keep in mind that the PCS has nothing to do with what jumps you perform, how you perform those jumps, etc. Instead, it’s basically an artistic measure of the program, and it is composed of five components:
- Skating Skills
- Transitions / Linking Footwork / Movement
- Performance / Execution
- Choreography / Composition
- Interpretation
As you can see, some components such as choreography are related to the program itself, not the skater. In any case, you can see a side-by-side comparison of Adelina’s performance at the European Championship in Jan 2014 and her performance at the 2014 Winter Olympics in Feb 2014 by following the link below:
Can you see any discernable differences in artistic value between her performances?
Another way to put Adelina’s drastic PCS growth in perspective is by comparing her growth to that of other skaters. Below is a screenshot from a video onyoutube:
Again, one may ask what this proves. After all, even if 99.9% of all skaters don’t exhibit growth like this, it still doesn’t mean Adelina couldn’t have done so legitimately. This is a point I have to concede, and this is why I consider this piece of evidence circumstantial.
10. Adelina’s GOE has also grown tremendously in the three months leading up to the 2014 Winter Olympics
So far we have looked at the Base Value of the technical elements, which is determined by the Technical Panel. We have also looked at the Program Component Score given by the Judges. What we haven’t looked at in details is the Grade of Execution of each of the technical elements. To recap, for each technical element such as a triple jump, each Judge gives a GOE in the range of -3 to +3 to represent how well the element is performed. An average execution gives you a 0 GOE. A mistake gives you a negative GOE. Good execution gives you a positive GOE, while a perfectly executed element gives you the maximum, a +3 GOE.
How many perfect elements are there in Adelina’s recent performances? First, let’s take a look at the score sheet for her free skate at the 2014 Winter Olympics:
Notice that Judge #2 and Judge #7 were both extremely happy with Adelina’s execution. Judge #7 in particular thought that Adelina was perfect in almost every single one of her elements. Now let’s look at how many +3 GOE’s Adelina received in her recent competitions:
Short | Free | Total | ||
11/01/2013 | Cup of China | 3 | 1 | 4 |
11/25/2013 | Trophee Eric Bompard | 4 | 5 | 9 |
12/05/2013 | Grand Prix Final | 3 | 6 | 9 |
01/13/2014 | European Championships | 6 | 20 | 26 |
02/07/2014 | Winter Olympics | 14 | 33 | 47 |
I won’t even bother with a chart this time, since the differences are very obvious.
Again, I have to concede that this doesn’t prove anything. You could say that Adelina’s growth is legitimate, as evident by her performance at the European Championships. On the other hand, you could say that she received a generous number of +3 GOE’s even at the European Championships. I’ll just leave you with one question:
- If Adelina is really such a skater of once-in-a-century caliber, why did Russia not pick her for either event in the team competition at the 2014 Winter Olympics?
11. Questionable choice in the selection of competition officials
This table shows the nationality of all the competition officials for the 2014 Winter Olympics.
Technical Panel | Short Program | Free Skate | ||
Technical Controller | Alexander Lakernik | Russia | Alexander Lakernik | Russia |
Technical Specialist | Vanessa Gusmeroli | France | Vanessa Gusmeroli | France |
Assistant Technical Specialist | Olga Baranova | Finland | Olga Baranova | Finland |
Judges | ||||
Judge | Robert Rosenbluth | USA | Yury Balkov | Ukraine |
Judge | Karen Howard | Canada | Karen Howard | Canada |
Judge | Franco Benini | Italy | Franco Benini | Italy |
Judge | Birgit Foell | Germany | Birgit Foell | Germany |
Judge | Diana Stevens | UK | Zanna Kulik | Estonia |
Judge | Nobuhiko Yoshioka | Japan | Nobuhiko Yoshioka | Japan |
Judge | Katarina Henriksson | Sweden | Alla Shekhovtseva | Russia |
Judge | Adriana Domanska | Slovakia | Adriana Domanska | Slovakia |
Judge | Sung-Hee Koh | South Korea | Helene Cucuphat | France |
Operators | ||||
Data Operator | David Santee | USA | David Santee | USA |
Replay Operator | Alexander Kuznetsov | Russia | Alexander Kuznetsov | Russia |
Judges highlighted in yellow only participated in the short program. Judges highlighted in orange only participated in the free skate. Officials highlighted in red are from Russia.
We already know that Alexander Lakernik, the Technical Controller, is the Vice President of the Russian Skating Federation. There is an undeniable potential for conflict of interest here. We also know how two working together on the Technical Panel could have an enormous influence on the results of the competition.
Two of the four incoming judges for the free skate are also questionable. First, there is the Russian judge Alla Shekhovtseva, the wife of Valentin Piseev. Valentin Piseev is the ex-President of the Russian Skating Federation and its current General Director. Again, the potential for a conflict of interest to occur is undeniable. The second judge is the Ukrainian judge Yury Balkov, who was suspended for trying to fix the 1998 Nagano Winter Olympics. He was suspended for only a year after the 1998 incident. We have already demonstrated that just two Judges working together could also have a non-trivial impact on the PCS.
Without knowing how each judge scored, there is no way to prove one way or another whether the questionable appointments of these Judges had a biased impact on the results. However, unlike the previous two points, this one can be easily proven or disproven, if only ISU would release how the Judges scored.
Conclusion
So what have we demonstrated?
1. Had the mistakes committed by Adelina in her free skate been properly accounted for, her margin of victory over Yuna would have been 1.38 instead of 5.48.
1. Had the mistakes committed by Adelina in her free skate been properly accounted for, her margin of victory over Yuna would have been 1.38 instead of 5.48.
2. A margin of 1.38 could easily have been manipulated by as few as two people. For example:
- Two people on the Technical Panel could have misidentified, intentionally or unintentionally, the level of difficulty of certain elements, mistakes committed, etc.
- Two Judges simultaneously inflating one skater’s score while deflating the score of another could have an impact in the range of 1.20 to 1.50 on the PCS.
4. The selection of the competition officials is questionable with undeniable potential for conflict of interest.
If you have read this far, I want to thank you for your time. Also, I hope that even if you still think Adelina deserves the gold medal, you can appreciate why many people around the world find the results suspicious, to say the least. Despite the title of this document, my goal isn’t to convince anyone that Kim Yuna should have won. Instead, my goal is to demonstrate the peculiarities surrounding the women figure skating competition at the 2014 Winter Olympics, and how these peculiarities represent fundamental flaws of the ISU Judging System. For the integrity and future of figure skating, my hope is that ISU will:
1. Conduct an open and honest review of the women figure skating competition of the 2014 Winter Olympics, and2. Change the fundamentally flawed ISU Judging System to minimize judging bias.
Make no mistake, the future of figure skating is already dire. Similar to how MMA has taken over boxing in terms of popularity, a new generation of winter sport enthusiasts are flocking over to more modern winter sports such as snowboarding and skiing. Why do you think we keep seeing more and more snowboarding and skiing events added to the Winter Olympics? Does ISU really want to compete by generating controversy and forever staying in the shadow of the 2002 Salt Lake City Winter Olympics?
Call To Action
If you would like to actively participate in an effort to push ISU to take action on the items listed above, I urge you to:
1. Sign this petition on change.org:3. Join this Facebook group to connect with other people with the same goals:
0 Response to "Sochi Figure Skating Scandal: A (Mostly) Objective and (Somewhat) Mathematical Analysis of Why Kim Yuna Should Have Won the Gold Medal"
Post a Comment