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Numbers, STEM

Numbers: Would the New Math for Figure Skating Have Changed the Outcome for Harding and Kerrigan?

Source: Shared Photos from the International Olympic Committee

Source: Shared Photos from the International Olympic Committee

Prior to the start of the 2014 Winter Olympics in Sochi, Russia, I toyed with the idea of creating a post to discuss at least one STEM related concept associated with this quadrennial event. Although curling is not a new sport, it is relatively new to the Olympics and, I have to admit, is a bit of a curiosity to me. Then there’s bobsledding and the luge for both men and women. My eyebrows went up when I heard that BMW had designed a bobsled for our U.S. Olympic team. Then there is the question of what impact, if any, the new suits for our speed skating team had on their performance in Sochi? And of course, there is figure skating.

I stumbled upon a video, Mathletes, that reminds the viewer that a lot of math, both simple and complex, can be found in Olympic sports. Figure skating has always been one of my favorite Winter Olympics sports, and therefore, the topic of this post. No sooner than I had finished watching the women’s figure skating program on Thursday evening, February 20, 2014, I awoke the next morning to find that not everyone is in agreement with the judges’ decisions for all three medals that were awarded for ladies’ single figure skating. The outcome has left many fans definitely questioning the process. In less time than it took for one skater to perform her free-style program, this latest controversy – and possible scandal – had gone viral and was being picked up by media outlets around the world prompting the International Skating Union (ISU) to issue a statement on the ISU Judging System [Ref. 1] related to figure skating events.

Add to that on Sunday, February 23, 2014, the last day of the winter program, NBC aired a special documentary, Nancy & Tonya, just before the start of the closing ceremonies. I hadn’t thought of either person in years, and 20 years after the famous clubbing of Nancy Kerrigan’s knee at the 1994 U.S. Figure Skating Championships – an attack that was designed to maim Kerrigan by Harding’s now ex-husband Jeff Gillooly, and carried out by his friend Shane Stant. I had hoped that the 1994 incident was the last time we would hear about a scandal in figure skating, but that was not to be.

club-billy-stick-2Both Kerrigan and Harding expressed surprise that people are still talking about the 1994 incident in U.S. Figure Skating today. Each is married and has children – Kerrigan, three, and Harding, one. While I was surprised to see NBC revisit this figure skating story from 20 years ago, one thing that wasn’t ignored is that figure skating has had three (3) scandals and/or incidents that generated an awful lot of heartburn in as many decades.

Figure skating is the favorite sport for Winter Olympics. It has a huge following! The new judging system has alienated a number of viewers and fans. Some have referred to it as a rejiggered scoring system. If you remember the old days, a perfect score was a 6.0. The sport overhauled its scoring system after a 2002 vote-trading scandal, and has been in existence since 2004. The scoring system was implemented after a French judge and a Russian judge colluded at the 2002 Olympics.

Figure Skating "Code of Points", Source: Wikipedia

Figure Skating “Code of Points”, Source: Wikipedia

The familiar 6.0 perfect result has been replaced with advanced math equations where skaters now accumulate scores for each piece of work that they perform. How do they do this? [Ref 2, 3] Skaters receive a base value for every single move they execute in a program. The more difficult the move, the more points they receive. Something that viewers may not have been aware of is that a skater gets points just for attempting a move even if they do not complete it 100%.  This better explains why a person can stumble or even fall and still end up with more points than another skating that may have delivered a flawless program. The system is designed to help prevent judges from fixing a competition and make scoring less subjective.

The skaters receive a “segment score” for both the short program and the free skate program. [Ref 2, 3] For ladies figure skating:

Total Competition Score (TCS) =

            Segment Score Short Program + Segment Score Free Skate

Nine judges provide input to the TCS. We now need to define the segment score to complete the equation above. The segment score is made up of a Technical Score and a Program Component Score.

Segment Score: Technical Score and Program Component Score

Program Component Score:  The judges give points on a scale from 0 to 10 for program components. The five components are:

§         Skating Skills

§         Transitions

§         Performance

§         Choreography

§         Interpretation

Judges award marks on a scale of one-fourth of a point to 10 points, in increments of quarter-points.

Technical Element Scores: Each move in a skater’s program is given a base value. Jumps, spins, and moves all have assigned base values. Judges give grades of execution (GOE) – the number of points a judge adds or subtracts from each move’s base value. The skater can gain or lose + or – 3 points for each assigned base value. A fall carries a mandatory deduction of 1 point.

Tallying the Final Score: A computer randomly selects the scores awarded by seven out of nine judges. Of those scores, the lowest and highest are thrown out and the remaining five are totaled to get the final score. The marks of all nine judges are displayed, however, the judges don’t know whether or not their marks contributed to the score. [Ref 4]

What is also clear from the more recent Olympics is that judges are using computers to calculate the scores. In the past, it seemed like it took an eternity for a skater to get her scores. Now much of the tallying is done automatically, including tossing out the random scores, and the low and high scores. Very little if any math is done by hand. This ensures that fewer errors are made during the evaluation process, and the results for each program are tallied very quickly after the skater completes her program.

Silver, Gold, and Bronze Ladies' Figure Skating Medal Winners, Source: IOC

Silver, Gold, and Bronze Ladies’ Figure Skating Medal Winners, Source: IOC

So, here’s what I saw on last Thursday evening: I thought both Adelina Sotnikova of Russia and the gold medal winner for women’s figure skating, and Yuna Kim of the Republic of Korea, silver medal winner, both skated well. Although Ms. Sotnikova’s program was not pitch perfect and she stumbled in her free skate routine, she also made more difficult techniques in her program, especially the last 60 seconds. If there was any surprise for me, I expected their final scores to be very close, perhaps less than one (1) point. Instead Ms. Sotnikova (224.59) final score was greater than 5 points over Ms. Kim’s (219.11).

In their carefully worded statement, ISU stated “…the organization has not received any official protest with regard to the Ladies’ Free Skating event or any other event held during the Sochi 2014 Olympic Games and is confident in the high quality and integrity of the ISU judging system. [Ref 1]

However, I can’t help but ask myself, if Nancy and Tanya were skating under the new rules – you know, that rejiggered scoring system – would the results have been different in 1994 at the U.S. Figure Skating Championship? and the Winter Olympics? In closing, I commend all participants in the ladies’ figure skating competition and all other winter sports for their hard work and efforts.


1.      ISU Statement on the ISU Judging System, February 21, 2014, Sochi, Russia, http://www.isu.org/en/news-and-events/news/2014/02/isu-statement-on-the-isu-judging-system

2.      How to Understand the Olympic Figure Skating Scoring System, http://www.howcast.com/videos/317576-How-to-Understand-the-Olympic-Figure-Skating-Scoring-System

3.      International Judging System (IJS), http://www.usfsa.org/New_Judging.asp?id=289

4.    Figuring The Skating Math – Watching & Teaching The Sochi Olympics, February 7, 2014, http://theasideblog.blogspot.com/2014/02/figuring-skating-math-watching-teaching.html 


About Vi Brown

Vi is principal and CEO of Prophecy Consulting Group, LLC, an Arizona firm that provides business and engineering services to private and public clients. Prior to establishing her consulting practice in 2001, Vi worked with Motorola, Maricopa County Government, Pacific Gas & Electric, CH2M Hill, and Procter & Gamble. As an adjunct faculty member, Vi teaches undergraduate calculus classes and graduate level environmental courses. She is also a professional speaker.


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