17 December, 2013

The Dale Harder system

This is our second instalment of our foray into performance scoring. I would like to start with the work of Dale Harder

because it is the one that got me thinking in the right direction. In his book "Sports comparisons: you can compare apples to oranges"

Harder is laying the foundations for a universal, fair and efficient system which allows, in principle, the comparison of performances not only within a single discipline but between all possible sports. 
His starting points are stated as a collection rules of which I shall present only the first three (moreover, in my own words).

1. Sport is quantitative: a performance can, and must, be measured.
2. The basis of the comparison is the number of athletes achieving a mark: the fewer they are, the harder this mark is to achieve.
3. The comparison should be physics-based: a score must be attributed on the basis of the work performed.

I shall not go into the remaining ones. 
In fact, I would urge all readers of this blog to contact Mr. Harder (start at his website, strengthospeedia, and follow the links from there) and urge him to proceed to a new edition of the "Apples to Oranges" book. It is out of print for some time now and it would be a great loss if it were not made available to the new generation.
Of course, even the rules above must be refined. (It goes without saying that Harder is doing this in his book). For instance the number of athletes achieving a mark must be normalised by the overall number of participants in this sport. Concerning the physics-based scoring, I have argued in a previous post of mine that what matters is the energetic cost of a performance. This is most probably what Harder means by "work performed" but I prefer to use a physiological rather than a purely physical term at this point.

Harder's system is quantitative (as expected). He starts by attributing 1000 points to the perfect performance, which could be realised by a single person (out of the whole world's population) under ideal conditions. Then 900 points correspond to performances realised by the top-ten performers. Subsequently, for every 100 points the population concerned increases by a factor of 10 down to 100 points which correspond to the performance realised by the average human being. Harder is attributing 0 points to the lowest score that can be registered in a competition involving athletes aged 5 to 95. (On this last point, concerning the attribution of 0 points, I have some divergent opinion, but more on this in some future post). The factor of 10 increase of population for every 100 points is a clear indication of an exponential dependence of points on population. Starting from this remark I shall present, in future posts, my approach to scoring. However I must make clear from the outset that mine is a modelling approach, mathematically formulated, lacking all the statistical work needed if one is to present a working scoring system. Harder's monumental work contains a very detailed statistical analysis. Blending my approach to Harder's results would really give a most efficient scoring scheme. Well, no one knows. Perhaps one day ... 

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