9.88 7.10 5.81 4.96 4.33
The lowest overall winner receives a lot more than the next finisher, who receives nothing (except section or match awards). This is called a cliff. The cliff is at least slightly ameliorated by the fact that the next finisher will receive section awards.
Cliffs are common. In the Olympics, there is a huge cliff between 3rd place (bronze medal) and 4th place (nothing). In football, there is a huge cliff between just making the playoffs and just missing the playoffs.
Nonetheless, it is a little odd that the difference between 5th and 6th is larger than the difference between 1st and 2nd.
log (n/ (m * (r - .5)).
In the club formula, m equals 1 and the zero award goes to the last place finisher in an infinitely large field. In the tournament formula I proposed, m equals 2 and the zero award goes to the competitor in the exact middle of the field. If m is equal to a higher number, that reduces the cliff. For example, suppose m was 3. The awards would now be
10.52 7.24 5.68 4.70 3.94
Setting m equal to 3 makes the players who are 34th out of 100 receive a zero award. That is not mathematically elegant. But the formula does not violate any of the other, more important principles.