Variance

Variance measures how much the results of a draw scatter around their mean. A low variance signals tight, regular results; a high variance signals spread-out results that often stray far from the central value.

The mental image is that of darts stuck in a target. If they form a small, compact group, the variance is low; if they are scattered across the whole board, even when centered on average, the variance is large. It describes regularity, not the position of the center.

The calculation follows a three-step recipe: take the deviation of each result from the mean, square that deviation so it always becomes positive, then average these squares. For the series 2, 4, 6, whose mean is 4, the deviations are -2, 0 and +2; their squares are 4, 0 and 4; the average of these squares is 8/3, that is about 2.67. That is the variance.

Squaring is not a mere detail: it prevents positive and negative deviations from canceling out, and it penalizes large deviations more than small ones. In return, the variance is expressed in a squared unit, which makes it not very meaningful on its own.

Variance should not be confused with expectation. Two games can share the same expected gain while having opposite variances: one pays out small, regular sums, the other alternates long losing streaks and rare jackpots. The expectation describes the center, the variance describes the agitation around that center.

Its square root, the standard deviation, brings the spread back into the original unit and is easier to read. For the site's draws, the variance explains why the same fair tool can produce sequences that are sometimes monotonous, sometimes highly contrasted.