Round Off Error in New Judging System

In the course of updating our analysis software to bring it in line with changes to the ISU judging system for this season, a curious artifact of the calculation method was noticed.  Skaters can exploit this quirk and gain up to 1/4 of a point by doing nothing -- or lose 1/5 point if they select their elements unwisely!

In the Ladies and Men's Free Skating events, the base mark for a jump is multiplied by a bonus factor of 1.1 if the jump is executed in the second half of the program.  When a jump sequence is executed in singles and pairs, the base mark of the sequence is the sum of the base marks for the two most difficult jumps multiplied by 0.8, while in Free Dance, a combination lift has a base value given by the sum of the base marks for the first two executed lift types multiplied by 0.7

Last season, calculations such as these were carried out to three decimal places and then rounded off to two places at the end.  Further, for the jumps these scale factors were applied to the full value of the jump element (base value plus grade of execution together).  This season, the scale factor is applied only to the base value.

While this change is an odd choice in itself, odder still is the fact that the product of the base value and the scale factors is rounded off to one decimal place before being added with the single trimmed mean of the grade of execution.  Consequently, depending on the jump or lifts involved, the skater may be cheated out of up to 0.04 points, or given a gift of up to 0.05 points on each element when a scale factor in employed, solely due to the strange (dare I say incorrect) way the program handles round off.

For example, a double Axel has a base value of 3.3.  If executed in the second half of a free skating program the value should be 3.63, but the skater is only awarded a value of 3.6, a penalty of 0.03 points.  For a triple flip, the base value is 5.5.  When executed in the second half of a program the value should be 6.05, but the skater is awarded 6.10 points, a gift of 0.05 points.

A few hundredths of a point is not a lot, but suppose, for example, a singles free skating program has five jump elements in the second half of the program (some skaters have indeed started to do that).  Depending which jumps these are, a skater could be cheated out of a total of 0.20 points or be given a gift of up to 0.25 points.  A range spanning nearly 1/2 of a point!

It is not uncommon under the new judging system for skaters to be separated by 1/2 point or less.  It happens about 10% of the time, and several medals have already been decided by this point margin, or less.  Thus, if one skater is on the losing side of the round off error and another is on the winning side, results will be determined by the round off error and not the skating.

What is the logic behind this calculation method?  It hardly seems fair to the athletes, and I can think of no other sport where the results potentially can be decided by the fact the technical experts Ottavio scoured the World to find can't get simple math right.

The rule says that the skater gets a bonus of 10% if the jump element is executed in the second half of the program.  Not approximately 10%.  Not sometimes 9% or sometimes 11% depending on dumb luck.  10%, no more, no less.

Whether the quirk is there by choice or by accident, the quirk is there, and skaters should exploit it in their programs.   Jumps in the second half of the singles free skating programs, jump sequences in singles and pairs, and combination lifts in dance should all be selected to insure that the round off error works in the skater's favor.  By judicious arrangement of the jump elements, a single's skater can boost their point total by up to 1/4 of a point, all for free.  1/4 point is not a lot, but because it can make a difference a significant fraction of the time skaters should try and exploit it, because the first fundamental rule of competing under the new scoring system is "Leave no Points on the Table!" 

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Copyright 2004 by George S. Rossano

12 October 2004