On bad scoring tables

As my regular readers know, I am a fan of scoring tables. And that has been true since a very tender age of 10. I cannot explain why this subject fascinates me, but there we are. Whenever I see a scoring table I feel immediately an attraction. From the outset in this blog, scoring was at the centre of interest. Already the fourth published article talks about scoring, and a whole series entitled "Theories of Scoring" appeared in 2021-22. Scoring was the subject of several articles of mine published in the New Studies in Athletics (alas, now defunct, killed by the belt-tightening measures of Lord Sebastian). And it is, of course, the origin of my collaboration with G. Purdy. While writing these lines I realise that I have never published the article I had promised in "A brief history of the IAAF/WA scoring tables" explaining the relation of the World Athletics scoring tables to the Weibull distribution and moreover I have never presented the results of my collaboration with G. Purdy. One day I will keep my word and explain in detail the relation between performance distribution and scoring.

But let's go back to the current business. As you may know, I am a subscriber to the newsletter of Art of Manliness. Contrary to what woke-brainwashed persons might think, the site is anything but macho. Of course it caters to men's interests and lifestyle, and some people find that they tend to romanticize older stuff, but, frankly, most of its articles (shaving excluded) would be useful to women too. From time to time they publish Army-related articles and they always attract my interest. In case you didn't know, I am a big Army fan. I like the Army discipline, even when it verges on the absurd. Discipline, even exaggerated one, is better than no discipline at all. (I just hope that you are not taken aback by my militaristic tendencies). 

No, it's not modern pentathlon

In an article entitled "Are you combat ready?" (reprinted from one published in 2016) AoM were talking about the "Physical Combat Proficiency Test" of the US Army. The test was designed to assess the soldiers' agility, coordination, and ability to perform what the Army calls “warrior tasks”. The test was introduced in 1969 and was replaced by the Army Physical Fitness Test in 1980. Several iterations and modifications of the latter existed up to 2025 where the Army Fitness Test was introduced (but some people consider the PCPT to be the high-water mark for the Army’s physical training tests).  

What was most interesting in the AoM article was the inclusion of the scoring table for the mile run (the last of five events of the PCPT). Mind you, the mile was to be run in uniform pants and boots, so don't be hard on judging the times.

Once I saw the table I could not resist the temptation. I read off the points and the times and I converted the latter to mean velocity. As I have explained in my article "Theories of scoring: the energetic cost approach", the energetic cost of running is essentially proportional to the velocity, in particular for middle-distance running. But this is something that scoring-table builders are systematically ignoring. As a consequence, the creators of the PCPT mile-run scoring table produced a perfectly regressive table where the points grow roughly as a power 2/3 of the velocity. 

But they are in very good company. In fact, since the introduction of the 1985 tables, that were meant to repair the damages done by the Ulbrich tables, we are living with tables that are regressive for track events. Below I give the corresponding fit for the 1500 m of the decathlon scoring tables.

Apart from the initial part of the curve corresponding to very low velocities, the scoring is regressive, the points growing roughly as a power 3/4 of the velocity. 

I mentioned Ulbrich in the previous paragraph. In fact, he was the one who understood that the quantity in which the tables must be cast for track events is the velocity. His fatal mistake was to assume that velocity was the quantity that was determining the performance in field events. Well, it is, but not the velocity itself. The energy expenditure for field events is proportional to its square. By introducing a scoring proportional to the velocity for field events, Ulbrich introduced a counter-productive regressivity. You can read about this in my post on theories of scoring.

The scoring tables I proposed in collaboration with G. Purdy are strictly progressive for all events. On the same point of progressivity, my Décapassion friends, F. et P. Gousset, make the remark that the current tables for throws are only slightly progressive and this lack of strong progressivity throws the tables off balance. I have promised the Gousset that one day we'll write a joint article on this point. (And when this is done I will give here at least an "executive" summary).