Analyses: observed versus expected

How close together are the five 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 39 on a circle where 39 touches 1: the draw 4, 5, 7, 37, 39 is then no longer spread over 36 positions but concentrated on 10. The bars show the distribution of draws by span, observed and expected.

The tightest draws

A circular span of at most 10 has a probability of 0.85% for a random draw. We therefore expected 25.9 such draws; there were 27.

What carries over from the previous draw?

For each draw, we count how many of its five numbers were already in the immediately preceding draw. The expected distribution is hypergeometric: 5 drawn from 39, of which 5 are marked.

The slip as a heat map

The 39 numbers in 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 39 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 5/39 ≈ 12.8% per draw: mean 7.8, and long absences are not rare, they are the rule.

15106 gaps measured · Mean: observed 7.79, expected 7.80

The longest absence in the data is 63 draws. The probability that a given number stays absent that long is 0.02%; with 39 numbers it is bound to happen eventually. The longest current absence is 23 draws. A number that has been absent for a long time is therefore not "due": the balls have no memory.

My combination

Enter five 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 575,757 possible combinations only a tiny fraction has ever come up.