What it Takes to Become a Two-time Olympic Champion

By: Nora Liu

Yuzuru Hanyu at 2018 Pyeongchang Olympics Free Program. He won his second Olympic Gold medal with a score of 317.85. Source: NYTimes

Yuzuru Hanyu, two-time Olympic Champion in men’s figure skating, two-time world champion, and 4 time champion of GPF, is by all means a great skater. He is the first skater to land a clean quadruple loop, and the first skater to surpass a total score of 300 points. Other than technical skills, Hanyu also excels in his performance. He gives us new interpretations of music every season, proving that technical and artistic perfection are compatible. Hanyu is the first man since Dick Button to win back-to-back Olympic gold medals, and this article analyzes how he got to this point.

Hanyu’s signature Hydroblading. Source: Skating Things

Lead in Junior Group

Hanyu debuted in the junior group competitions in the 2008-09 season. He finished 12th place in the World Junior Figure Skating Championships (WJC) in 2009. In the next season, he skated to Paganini in the free program and won his junior world title just two years into the junior group. As young as 15 years old, he showed excellent skating skills and wonderful jump quality. It can be seen from Figure 1 two graphs of free program scores in WJC 2010 that even if Hanyu’s base values (BV) of his technical elements were about the same as the other top 5 skaters, he had very high Grade of Execution (GOE) score, which indicates that he was able to finish every jump, spin, and skating element with high quality. His program component score (PCS) shown in the first graph also ranks number one among the top ten skaters.[1]

Fig 1: World Junior Figure Skating Championships 2010 Male Free Program Score. (1) Technical element score consists of base value and GOE. BV shows the level of difficulty of the skaters’ planned combination of all technical elements, and GOE is based on the quality of these elements done during the competition. (2) total score consists of TES and PCS. TES is the technical score, and PCS is the performance score. More detailed explanations are at the end of the article.

2011-2014 Senior Debut

Hanyu progressed to the senior group in season 2010-2011, where he clinched the Silver medal at Four Continent Figure Skating Championships (4CC) 2010. In the 2014 Sochi Winter Olympics, he got his first Olympic Gold medal. It can be seen from the following graphs that he never stopped exploring more difficult jumps in this Olympic cycle. His technical scores were also rising over the years (Fig 2.(2)). Yuzuru Hanyu clearly knew that one can only maintain his or her competitive edge by constantly improving. He should not wait for other skaters to make mistakes to win the game. As such he put in more quad jumps every season (Fig 2.(1)). PCS scores are given by how judges feel about your performance, which is actually highly uncontrollable and subjective, thus the only way to win the game without being questioned about fairness is by outperforming other skaters by solid jumps and spins.

Fig 2: (1) Yuzuru Hanyu’s number of quad jumps in both short and free programs; (2) Yuzuru Hanyu’s free program technical score from season 2010-2014, with separate scores of base value and GOE

It was a surprise to most of the people when he won the 2014 Sochi Olympics. Many people thought that Patrick Chan would win that gold medal because he is a very mature and elegant skater with relatively high technical difficulty and good skating skills. As shown in the graph below, Hanyu had higher TES than Chan and lower PCS score in the game. Hanyu’s PCS score is perfectly reasonable (performance score is usually higher when you get higher technical scores as well so there is generally a linear relationship between these two components). The scores of all skaters fit the linear model (Fig 3). The residuals are mostly scattered around 0 as seen in the residual vs fitted value plot (Fig 4). From the outlier test, the only score that seems abnormally high is Takahashi’s score (Table 1). Hanyu clearly deserves this gold medal.

Fig 3: Plot of PCS against TES in 2014 Sochi Olympics Men’s Figure Skating Free Program. The red line is the best fit line. The linear model can be used to predict PCS. The P-value of the variable TES is 0.046 which is smaller than 0.05 suggesting that the variable TES is statistically significant. This model has R^2 value at 0.2387, which is understandably low since there are multiple other factors that might influence one’s PCS, including the performance itself, skaters’ starting order, nationality, etc. But this model tells us that there is a valid positive relationship between PCS and TES.

Fig 4: Residual plot does not show much pattern. Points are scattered around 0. The NCV test gives a p-value at 0.44542, which is much larger than 0.05. This model does not violate the assumption of error variance.

Table 1: outlier test of the linear model created to predict PCS from TES. The number 6 here refers to the index of skater Takahashi. This score is a bit extreme based on the model created above. Hanyu’s score fits the model.

Era of Quad Jump

It is absolutely amazing that Hanyu was able to stay competitive all the time, especially after the Olympics. It is totally normal to see athletes experience ups and downs in terms of their performance over the years, but this did not seem like a problem for Hanyu. As an “old” skater, he did not have the strong physique of young skaters, but he also did not seem to fall behind in learning more difficult quadruple jumps. The following graph shows a very clear increase in base values of top 10 skaters in WC free program technical components in the past few seasons (Fig 5). The purple line represents Hanyu’s base value, which clearly shows that he constantly remained at the top in terms of technical difficulty.

Fig 5: boxplot of free program base values of top 10 skaters in WC and olympics. The purple line represents Hanyu’s base value.

In Season 2016-2017, a large group of young skaters entered the senior group. Nathan Chen’s short program consisted of 4Lz+3T, 4F, and 3A [2], which is really the most difficult combination of jumps in the short program. Boyang Jin also amazed us with his clean and nice 4Lz+3T. Even though these young skaters were not able to get high performance scores, they won various games by getting high technical scores and doing much more difficult quad jumps than other skaters. The following table shows the number of quad jumps of some skaters in the 2017 WC (both programs). Back in the last Olympic season, it was enough to have 2 quad jumps in both programs to become one of the top skaters. But it can be seen from table 2 that the skaters need on average more than 5 jumps in both programs to compete for the podium, and having three triple Axels in both programs is almost required for all skaters. Facing the pressure from the young skaters, Hanyu broke the record of free program score in 2017 WC and won the gold medal by both high technical difficulty and performance.

Table 2: Quadruple jumps in both programs in 2017 WC

Hanyu’s beautiful Triple Axel. Source: Tumblr

The King

Hanyu suffered an ankle injury a few months before the 2018 Pyeongchang Olympics. He planned to put a 4Lz in his free program, but this jump caused too much stress to his ankle. He eventually only had 4 quad jumps in the free program. As such Hanyu had no upper hand in this game due to a lower base value of technical elements. Even though he only ranked second in the free program, he beat the top scorer by outperforming him in the short program.

Fig 6: (1) Base value and GOE (2) TES and PCS scores of free program in 2018 Pyeongchang Olympics.

It can be seen from the graphs above that Hanyu actually had very high GOE compared to other skaters, which suggests that he was able to complete every jump and spin element with high quality. This is also the part young skaters should focus on. While it is true that young skaters have the body strength to finish more difficult quad jumps, one cannot simply beat others by doing this, especially when the top 5 skaters have very similar technical components. During practice, every jump needs to be perfected, from how to enter the jump, to the posture in the air, to ultimately landing. Skaters need to spend time on these details instead of just knowing how to land the jump very roughly. Pursuing high levels of difficulty without completely honing the skills is not enough to become a top scorer. For example, the 6th scorer, Vicnent Zhou, had very high base value, but had the lowest GOE. His jumps had many problems that needed more practice, including under-rotation. And subsequently, low GOE can also affect PCS score as the judges might feel that you are not proficient in your skating at least in this program.

Yuzuru Hanyu is 26 years old now. He suffered injuries that might have not completely recovered yet. However, he is a legend to all of the fans. His constant pursuit for more difficult technical elements, his extreme attention on details, and his music interpretation are still amazing. Hopefully he can do what he wants on ice, and the fans will always look forward to every program he meticulously prepares.

Finally, I would like to share one of my favorite skating programs:

Thanks for reading!

Additional Notes

[1] Some technical terms:

1. Base value (BV): raw score of technical elements. It reflects the technical difficulty of this skater

2. Grade of Execution (GOE): before 2019, GOE ranges from -3 to +3. It is given based on the quality of the technical elements.

3. Total Element score (TES): BV + GOE

4. Program Component Score (PCS): basically performance score. It consists of 5 parts: skating skills (SS), transitions (TR), performance (PE), composition (CO), and interpretation of the music (IN). Each part score ranges from 0 to 10.

5. Total Segment Score (TSS): TES + PCS

[2] Brief summary of jump elements in figure skating: there are 6 types of jumps: Toeloop (T), Salchow (S), Loop (Lo), Flip (F), Lutz (Lz), and Axel (A). The first 5 jumps usually can be 1-4 rotations, and Axel jumps for now only have till 3 rotations. This is because Axel jumps have extra half rotation than other jumps. Different jumps carry different scores based on level of difficulty.

Sources: isu.org