13 October, 2013

My first foray into decathlon scoring tables

Those who have followed the previous entries of the blog are aware that my interest in athletics goes back to 1954 when I was 8 years old. By 1956 athletics were in the centre of my interests and when the time came for the Melbourne Olympiad I was ready to follow the events in detail. My pocket money was invested into buying the sports newspaper every day and I spent all my free hours dissecting all available information. The 1956 Olympiad reserved a happy surprise to the greek public: Giorgos Roubanis placed third in the pole vault winning an olympic medal in track and field, ending a 40+ year drought.

G. Roubanis competing in Melbourne

Decathlon had already attracted my interest and, for reasons that I cannot explain even now, I found the mechanism of scoring both intriguing and captivating. My joy was immense when in the newspaper I found that they were giving not only the performance by event but also the corresponding score. I set down to work and invented a method which much later I came to realise was a combination of interpolation and extrapolation. Here is an example of the data I had to work with:

Shot Put
Athlete distance points
Campbell 14.76 m 850
Kuznetsov 14.49 m 820
Johnson 14.48 m 819
Kutenko 14.46 m 817
Lassenius 13.45 m 715
Palu 13.39 m 709
Leane 13.26 m 696
Meier 12.99 m 671
Lauer 12.86 m 659
Richards 12.52 m 628
Bruce 12.30 m 609
Cann 12.18 m 598
Yang 11.56 m 544
Farabi 11.31 m 524
Herssens 11.12 m 509

I started by computing the successive differences in throw length ∆L and in points ∆P. Next I computed the values of L which would correspond to 800, 700, 600 and 500 points (interpolation). I found roughly 14.30 m, 13.30 m, 12.20 m and 11.00 m. Computing the differences I found that they increased regularly by 1 m, 1.1 m and 1.20 m. Thus I made the bold assumption that this tendency would continue all the way to 0 (extrapolation), since I was really interested in what was the minimal performance that would score a point. I found that the values of L for 400, 300, 200, 100 and 1 points should be 9.70 m, 8.30 m, 6.80 m, 5.20 m and 3.50 m. 

I repeated the same calculations for the long jump and the discus throw. I found that P=1 corresponded roughly to L=3.5 m for the long jump and L=13 m for the discus throw. My conclusion, upon seen these values, was that I had made some serious mistake. In my mind it was impossible that the decathlon scoring tables would attribute points to such ridiculously low performances. Well, if anything were wrong with my approach this was my conclusion and not the calculations. When I could lay my hands on a copy of the scoring tables (those were the 1962 tables and not the 1950 ones, valid at the Melbourne Olympiad) I discovered that my estimates were essentially right. (Not only this, but as the tables evolve, the minimal performance is being pushed backwards. With the current, 1984, tables the following performances suffice for P=1: shot put 1.53 m, long jump 2.25 m and discus throw 4.10 m). 

In the current distribution of IAAF scoring tables a brief history of decathlon scoring is presented and I could have access to the P=0 performance for the 1950/52 tables. (I prefer to think in terms of the P=1 performance, since P=0, would correspond to anything worse that this minimal scoring performance). To my great satisfaction I found that P=0 corresponded to: shot put 3.51 m, long jump 3.34 m and discus throw 11.25 m. Thus the interpolations/extrapolations of a 10-years-old scoring fan were not off the mark after all.

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