There is a theoretical justification, although it's a bit confusing, but if you want, take a look.
Forgot to mention that I performed preliminary calculations using the formula, and it seems okay. Maybe someone can double-check?
In general, the calculations showed that:
In case of 08 participants:
The participant who took 01st place will receive 539 rating points.
The participant who took 02nd place will receive 490 rating points.
The participant who took 03rd place will receive 415 rating points.
The participant who took 08th place will receive 141 rating points.
In case of 16 participants:
The participant who took 01st place will receive 641 rating points.
The participant who took 02nd place will receive 583 rating points.
The participant who took 03rd place will receive 493 rating points.
The participant who took 16th place will receive 49 rating points.
In case of 64 participants:
The participant who took 01st place will receive 907 rating points.
The participant who took 02nd place will receive 824 rating points.
The participant who took 03rd place will receive 697 rating points.
The participant who took 64th place will receive 004 rating points.
Yeah... Dirty_Player says that the formula is too cumbersome.
Well, what can you do? I considered all the suggestions and included the tournament rating in the formula.
If we don't need it, then we can simply modify Dirty_Player's formula.
Then it turns out like this:
