testcenter

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Arved Klöhn
Admin
3. November 2022 07:47

To calculate the standard deviation for this example you first calculate the standard deviation for a single tournament.

In your example the net pay-outs for the tournament are as follows:

Position   | Net Win    | Prob.     
-----------+------------+-----------
1          | 490        | 1%        
2          | 290        | 1%        
3          | 190        | 1%        
4 - 100    | -10        | 97%       

First, you need to calculate the expected value μ via this formula:

μ = (490 * 1% + 290 * 1% + 190 * 1% - 10 * 97%) = 0

Next, you calculate the variance σ² via this formula:

σ² = (490 - 0)² * 1% + (290 - 0)² * 1% + (190 - 0)² * 1% + (-10 - 0)² * 1% = 3700

The standard deviation σ is the square root of the variance:

σ = sqrt(3700) = 60.83

This is the standard deviation for one tournament.

To calculate the standard deviation for n multiple identical tournaments X you use this formula:

σ(n*X) = sqrt(n) * σ(X)

In your example, this would be

σ(100*X) = 10 * 60.83 = 608.3

You can find the formulas for example on the Standard Deviation Wikipedia Page
I hope this helps 🙂

Last edited 1 month ago by Arved Klöhn

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