Basketball Statistics Blog

Statistician's Digest: How to Determine Standard Deviations ?

... How do I determine where a player who takes 1000 FGA in 2000 Min in a season, stands in terms of standard deviation as compared to the league rate of FGA/Min ? ...

Make the statistical computation FGA/Min for every player. Find the standard deviation of all those values. And then the formula is:

[ (1000/2000) - (Avg FGA/Min) ] / (stddev)

Also, it is possible to use to use percentiles. Sort all players by FGA/Min, give everyone a rank. Divide the rank by the total number of players in your sample.

Performing this calculation we must not mistake precision with accuracy. Nonparametric elements like percentiles make no hypothesis that is taken for granted about the shape of the distribution: they are more cautious measures and much less likely to return errors at the the highest degrees.
If you're searching leaders in a category, I recommend you to always use nonparametric measures with a common plan with parametric measure, merely to be sure there are no outliers into your results.

The weighted standard deviation doesn't succeed in seizing the unfairness between two players with the same rates in different quantities of playing time. Same rate is as if: that rate and no more. What it would succeed in catching is a significant change between the width of the distributions, having an effect upon the standard scores. The differences between player rates would be involved, but not if they have the same rate.

When analyzing numbers with measures that aren't well fully apprehended, I give preference to study at the numbers from multiple angles. In this case which you propose at your question, I would perform the computations using

1. Percentiles
2. Standard deviation
3. Weighted Standard deviation by minutes
4. Weighted Standard deviation by square root (minutes per game)

and examine and note the similarities or differences of them. There shouldn't be much significant change, but it would be holding the attention if there was.
( Prof. Roberto Azar )

Source: eBA Basketball Statistics Analysis System

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