Analyses: observed versus expected

How close together are the six numbers?

The linear span is the distance from the smallest to the largest number (end positions included). The circular span reads the numbers 1 to 90 on a circle where 90 touches 1: the draw 2, 3, 5, 87, 89, 90 is then no longer spread over 89 positions but concentrated on 9. The bars show the distribution of draws by span, observed and expected.

The tightest draws

A circular span of at most 12 has a probability of 0.01% for a random draw. We therefore expected 0.3 such draws; there were 0.

What carries over from the previous draw?

For each draw, we count how many of its six numbers were already in the immediately preceding draw. The expected distribution is hypergeometric: 6 drawn from 90, of which 6 are marked.

The slip as a heat map

The 90 numbers in nine rows of ten. The darker the cell, the more often the number was drawn. The expected value is the same for all; the differences are the normal spread of a binomial distribution.

The gap between the rarest and the most frequent number looks large, but it is exactly what you expect from 90 independent counts. Over the last 100 draws the relative spread is even larger because the sample is smaller.

How long does a number stay absent?

For each number we measure the gap in draws between two appearances. If the draws are independent, this gap follows a geometric distribution with probability 6/90 ≈ 6.7% per draw: mean 15.0, and long absences are not rare, they are the rule.

25638 gaps measured · Mean: observed 14.95, expected 15.00

The longest absence in the data is 148 draws. The probability that a given number stays absent that long is 0.00%; with 90 numbers it is bound to happen eventually. The longest current absence is 72 draws. A number that has been absent for a long time is therefore not "due": the balls have no memory.

My combination

Enter six numbers: has this combination been drawn before? Which draws came closest?

Everything runs in your browser; nothing is stored or sent. That a combination has never been drawn is normal: out of 622,614,630 possible combinations only a tiny fraction has ever come up.