# Distribute a number in an exponential way in a certain number of times

I have a number $X$ (let say it's 100). I want to 'split' it$N$ times in a 'exponential' looking way.

For instance $y = 0,2692x^{-0,925}$ with $x$ the integers between 1 and 16 is working fine.

The goal is to divide a number of points between all opponents of a competition. Obviously the first wins a lot more than the second, the second more than the third and the differences are getting less and less important.

I did this for 16 opponents by defining the values :

But the number of player will vary.

Thanks !

 This must be similar to: http://stackoverflow.com/questions/7224235/how-to-find-10-values-exponentially-distributed-which-sum-to-a-value-x

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If you like $y=0.2692x^{-0.925}$ for a shape, you can just scale it to give the total you like. For example, if you have $10$ competitors, it sums to $0.846257$. If you want to distribute $100$ points, multiply by $\frac {100}{0.846257}$. Then first gets $31.81$, second $16.75$ and so on. If you want to give whole numbers, you will need to round. If the total doesn't come to $100$, adjust the threshold of $0.5$ until it does.
By the way, this would be called a power law, not exponential. An exponential would have the place number in the exponent, like $e^{-x}$. The question you link to is following this.