Among the various scoring tables that have been proposed over the years, the Letessier tables (known internationally as the "french tables") are worth mentioning. They have been of capital importance in France. When physical education became an essential component of the french educational system and students were to be attributed marks according to their performance in sports activities, various scoring scales were proposed. The first attempts were disastrous. In some events more than 50 % of the students were obtaining the maximal mark, while in some other less than 1 % managed to do so. It became thus clear that a serious overhaul of the scoring process was in order. Jean Letessier, a physical educator had already pointed out in 1951 the necessity of a systematic approach to the question.
What came to be known as the "Letessier tables" is the product of a close collaboration of Jean Letessier with his brother Pierre. The latter had a solid training in mathematics and this can be seen in the rigorous approach used for the construction of the tables. (This can be good and bad at the same time). Pierre Letessier explains the method used in the construction of the tables in the preface of the second, 1961, edition (the first edition was that of 1957 and the 9th (last?) appeared in 1992).
According to the Letessier brothers the construction of the tables must be based on a statistical approach. However, as they correctly remark, a statistical comparison has meaning only if the all the distributions of the performances follow the same law. They define two tasks, which they dub horizontal and vertical. The horizontal is to establish the equivalent performances between the various disciplines. The vertical one is to attribute points to the various performances. The authors of the tables are aware of the difficulties presented by these two tasks. While it is not so difficult to find equivalences between high level performances, when one gets to the bottom of the tables things can get iffy.
The Letessier make the assumption that the distribution of the performances follows a "log-normal" distribution. (I won't bother you with mathematical details here. If you wish to find more about the "log-normal" distribution you can simply consult the wikipedia article). This assumption of the Letessier leads unnecessarily to very complicated mathematical expressions. In my article (on the extension of Harder's method) I presented a much simpler approach which, as a matter of fact, I find more realistic. To put it in a nutshell, the implicit assumption of the Letessier is that nobody would score a zero in athletic events. My model allows for a small, albeit non-zero, percentage of the population being unable to register any athletic performance. But, of course, pursuing in this direction would be akin to counting how many angels can dance on the head of a pin, so I stop here.
Unfortunately the Letessier tables are not very useful as far as combined events are concerned. Their tables, which go from 0 to 500 points (why 500 and not 1000, nobody knows) are regressive. They know this and (try to) justify it. They say that a progressive scoring would incite the athletes to try to improve their strong events and neglect the weak ones (and they give the example of the 1500 m for the latter). Unfortunately the experience of several decades of regressive decathlon tables has shown that the exact opposite is true: the athletes would not make extra efforts for an ever diminishing reward. And by the way, the Letessier tables are regressive even for running events.
A correct scoring approach should lead to a table roughly linear in velocity for the track events.
So, while the Letessier tables had had a great success within the french educational system, they are not better than the Portuguese Tables (for which they formulate critiques in no uncertain terms) as far as combined events are concerned. In fact, while reading the explanations that Amado provides in his tables one can feel his love for athletics. In the case of the Letessier brothers, their approach is more rigid and thus less endearing.
PS1 This is the last post of the first season of the "Theories of scoring" series. A second season is in preparation. Stay tuned.
PS2 As you have certainly gathered from the phrasing of the previous postscriptum, I am a TV series fan.
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