13 November, 2013

Some thoughts concerning performance scoring

I was reading (again) the article of V. Trkal on the development of scoring tables for combined events and I felt the urge to post a short note with my criticism.
J. Thorpe, probably the best decathlete ever

V. Trkal is the coordinator of the working group which proposed the tables currently in use. His work is remarkable in the sense that the principles set for the development of the tables are really well-thought. I cannot resist the temptation to give them here:

1. The tables should only be used for combined events.
2. The results in different disciplines that are evaluated with approximately the same point value should be comparable as far as the quality and difficulty of achieving these results are concerned.
3. The tables in all disciplines should be:
a. a modification of current tables
b. linear in all disciplines
c. very slightly progressive in all disciplines (it was proposal 3c that was finally adopted)
4. The tables must be usable with combined events for beginners and juniors as well as top-class athletes.
5. There will be separate tables for men and women.
6. The tables must be based on decathlon statistics, taking into account the statistics of specialist athletes in the individual disciplines.
7. The tables should be usable now and in the future.
8. The sum of points scored by world-class athletes should remain approximately the same.
9. As far as possible, the tables should eliminate the possibility that an athlete specialising in one discipline is able to acquire sufficient points in that discipline to overcome a low scores in weaker disciplines and beat more versatile, all-round athletes.

V. Trkal's criticism of the previous tables, developed by Jorbeck, is based on the fact that the latter used as criterion the velocity v not only for the running events but also for the jumps and throws. Trkal's idea is that athletic performance is physical work (a correct assumption) and thus the kinetic energy, proportional to the square of the velocity, should be used for scoring (an assumption with which I disagree).

My point of view, presented in an article published in New Studies in Athletics, is that what matters is the energetic cost of the performance. As such the assumption of Trkal of a quadratic dependence on velocity is justified in the case of jumps and throws but not so for running. Indeed the energetic cost of the latter is essentially linear in velocity with a quadratic part multiplied by a very small coefficient, appreciable only at high velocities. Thus in the case of running what should be used for scoring is the velocity rather than its square.

Could this remark of mine make any appreciable difference concerning the combined events scoring tables? I do not know. Developing scoring tables has a large empirical component and thus a judicious use of data may prove more important than a simple scientific clarification.

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