Re: Is this a Probabilities Question?
It's twice as hard to win a 20 player tournament as a 10 player tournament, all other things being equal. Therefore, it should get twice as many points.
My guess is the formula you have also gives points for coming in below first place, and goes deeper for larger tournaments. As long as the total number of points is proportional to the number of players, the system makes some sense.
For example, suppose you gave 101 points for 1st in a 9 player tournament, and 70 points for 2nd. That's 171 total points, or 18 per original player. You should then give 360 points for a 20 player tournament. You might divide those up 150 for 1st, 100 for 2nd, 60 for 3rd, 35 for 4th and 15 for 5th.
There's no obvious rule for how to divide up points among finishers, although Fibonacci rules are pleasing (each place earns the sum of the points of the next two places; like 180, 105 ,65, 40, 25, 15, 10 for seven places).
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