Re: Is this a Probabilities Question?
Yes, keeping points proportional to number of players and using Fibonacci shares makes sense.
To award more places (and I agree with you that's a good idea) start your series smaller. Say you want to give points for 40% of the places. You just take that many Fibonacci numbers.
So if you want 8 players to get points (20 player tournament), your payoffs will be proportional to 1, 2, 3, 5, 8, 13, 21, 34. That adds up to 87. If you want 18 points per original player (that's arbitrary, you could use any number you wanted), you need to scale that up to 360. 360/87 is about 4, so you could start with 4, 8, 12, 20, 32, 52, 84 and 136. That adds up to 348, so you have 12 extra points which you could ignore, or add to first place, or distribute somehow.
It may sound complicated, but with a little Excel trial and error, you should be able to come up with point distributions for all tournament sizes from 2 to 10,000. You only have to do it once, then make that the official list. You can use round numbers if you want, or stick to strict mathematics.
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