The point system equations for the heptathlon are listed at the following question - Heptathlon point system calculation
My question is how did the founders of this scoring system come up with the numbers for a,b and c?
In the iaaf document about the scoring tables they just state the basic rules which they tried to meet with the system from 1983 (p.18):
- The new set of tables should be used for combined events only.
- Results in various events should, as far as possible, yield about the same number of points if the results are comparable as to quality and difficulty.
- The new tables should be either:
- a modification of the existing ones
- a straight line in all events
- slightly progressive tables in all events.
- It must be possible to use the scoring tables for beginners, juniors and top athletes as well.
- There will be a special scoring table for men and another table for women.
- All the new versions of the scoring tables should be based on the statistical data for the combined events by paying due regard to the statistical data for performances by single event athletes.
- The new tables should be applicable now and for the future.
- It is desirable without creating other problems, that the total scores using the new tables for the top world class athletes should remain approximately the same. That is about 8500 points for the decathlon and about 6500 points for the heptathlon.
- As far as possible the new tables must insure that a specialist in one event cannot overcome performances in the other events.
It also says that it was created in a meeting with "several statisticians".
Wikipedia says for Decathlon scoring (which it seems uses the same factors) the 1934 scoring system was based on exponential functions fitted for 0 Points based on the results of untrained children to 1000 Points closely to the world records with a limit at 1150 Points per event.
Since all newer systems seem to have evolved from this one I guess the procedure was the same with changes to the functions used (throwing events changed from progressive to regressive) and the data used for fitting.
That was all I could find so no data or statistics but if you google you find several papers by statistician that propose different scoring methods to replace the old one.