I am looking to see if there is some sort of formula I can use to calculate weighted payout tables. I am looking for something similar to the PGA payout distribution, but the problem is I want my payout table to be flexible to accommodate a variable or known number of participants.
As in golf, the payout distribution goes to 70 players. So that payout distribution, while weighted, is pretty mush constant from tourney to tourney.
With my calculation, I want the weighting to be flexible by having a variable as the denominator for the payout pool.
In other words, I would like the formula to handle 10 participants, or 18 participants, or 31 or 92, etc.
Let me know if there is some sort of mathematical payout weighed formula I could use.
Thanks.
Best Answer
There are lots of them. You haven't given enough information to select just one. A simple one would be to pick $n$ as the number of players that will be paid and $p$ the fraction that the prize will reduce from one to the next. The winner gets $1$ (times the top prize), second place gets $p$, third $p^2$ and so on. The sum of all this is $\frac {1-p^n}{1-p}$, so if the winner gets $f$ the total purse is $f\frac {1-p^n}{1-p}$. Pick $p$, and your total purse, and you can determine each prize as $f, fp, fp^2 \ldots fp^{n-1}$