How To Calculate a Weighted Payout Table

Question

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.

score 1 · Accepted Answer · answered Jun 25 '13 at 13:24

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 $f, fp, fp^2 \ldots fp^{n-1}$

score 1 · Answer 2 · answered Jun 25 '13 at 15:32

Based on your answer @RossMillikan, I created a little excel spreadsheet to see if I could get the distribution to look right. The only thing I do to the numbers that is not obvious on the surface is I round each payout up to the nearest hundreds place. My payout distribution looks like the schedule below, but I cannot get the "check sum" to balance back to the overall Purse. Any thoughts I what I might be doing wrong? Thanks.

n:                 16      10      12      13      12
Purse = n * $10k    160000  100000  120000  130000  120000
top prize           40000   25000   30000   32500   30000
2                   30000   18800   22500   24400   22500
3                   22500   14100   16900   18300   16900
4                   16900   10600   12700   13800   12700
5                   12700   8000    9500    10300   9500
6                   9500    6000    7200    7800    7200
7                   7200    4500    5400    5800    5400
8                   5400    3400    4100    4400    4100
9                   4100    2600    3100    3300    3100
10                  3100    1900    2300    2500    2300
11                  2300            1700    1900    1700
12                  1700            1300    1400    1300
13                  1300                    1100    
14                  1000                
15                  800             
16                  600             
check sum =         159100  94900   116700  127500  116700
prize reduces by:   75%             
top prize:  25%

You can't set the top prize arbitrarily to $25%$ and set $p=0.75$ simultaneously. You would require $0.25 \frac {1-0.75^n}{1-0.75}=1$, which will be almost true for $n$ very large, but it will be in error by $0.75^n$. Then your rounding is coming into play. When I don't round the prizes in the first column, I get a sum of $158396.4.$ As $0.75^{16}$ is very close to $0.01$ and the leftover money is $1603.6$ this agrees. Good for you for checking. — Ross Millikan, Jun 25 '13 at 15:54

How To Calculate a Weighted Payout Table

2 Answers2