Standard deviation

The standard deviation is the square root of the variance. It is a measure of spread that indicates by how much, in order of magnitude, the results of a draw typically depart from their mean. A small standard deviation signals grouped, predictable results; a large standard deviation signals scattered and more surprising results.

The mental image is that of a radius around the center: the mean marks the aiming point, and the standard deviation gives the width of the cloud of results surrounding it. Most draws fall within a few times this width.

The calculation follows directly from the variance. You first compute the variance, that is the average of the squared deviations from the mean, then take its square root. For the series 2, 4, 6 with a mean of 4, the squared deviations are 4, 0 and 4, their average is 8/3, that is about 2.67; the standard deviation is therefore the square root of 2.67, that is about 1.63.

The major advantage of the standard deviation is that it is expressed in the same unit as the results themselves, whereas the variance lives in a squared unit that is not very intuitive. If gains are counted in dollars, the standard deviation reads in dollars too, which makes it far more meaningful.

It should not be confused with the range, which is merely the difference between the largest and the smallest result. The range looks only at the two extremes, whereas the standard deviation takes the whole series into account and how the values are distributed.

Concretely, if a game's gains hover around $10 with a standard deviation of $2, most rounds pay roughly between $8 and $12. For the site's draws, the standard deviation thus quantifies the expected regularity of a tool and the margin of variation from one series to another.