The frequency most typical of a fair drum (highest Bernoulli probability) in Powerball belongs to the numbers (sample: 20): Field 1: 1 (1.99%), 5 (1.99%), 6 (1.99%), 10 (1.99%), 19 (1.99%). Field 2: 1 (4.89%).Data includes draw #1970 of 09.07.2026.
A high coefficient means a number came up roughly as often as a uniform drum would predict — its frequency is statistically “normal”. It does NOT mean the number is more likely to be drawn next: the draw is random and all combinations are equally likely. The method is a distribution diagnostic, but as a selection system it works: clicking a number in the table adds it to the combination generator.
The Bernoulli formula gives the probability that a number is drawn exactly k times in n draws under a uniform chance p. The table shows this probability, normalised to %. Nearby, related views of the same frequency: Frequency →Z-Score →
P(k) = C(n, k) · pᵏ · (1 − p)ⁿ⁻ᵏ
where for each number:
- k — how many times the number was drawn over n draws; n — the number of draws;
- p — the chance of the number being drawn in one draw = (numbers per draw) / (balls in the drum);
- in the table each number is shown as the share of its probability P among all numbers (%).
Where to next
Winning odds
The chance of matching N of M numbers in Powerball — a combinatorial calculation, if what you need is the odds of winning rather than a frequency analysis.
OpenNumber frequency
How many times each Powerball number was drawn — the very frequency k the Bernoulli probability is built from.
OpenZ-Score
The deviation of a Powerball number's frequency from the norm in standard deviations — another view of “typicality”.
OpenPearson's χ² test
The drum bias of Powerball by each ball's frequency — a related uniformity test.
OpenFrequently asked questions about Powerball
What is the Bernoulli formula for the Powerball lottery?
It is the binomial probability formula: it estimates how likely it is that a number was drawn exactly k times in n draws under a uniform chance p. So for each Powerball number you can see how typical its observed frequency is for a fair drum.
What does a high coefficient for a number mean?
That its draw frequency in Powerball is close to what a uniform drum would expect — statistically “normal”. A low coefficient marks numbers with an anomalous frequency (very frequent or very rare). This describes the past, not a forecast.
Should I play Powerball numbers with a high coefficient?
The coefficient gives no future advantage — the draw is random and all combinations are equally likely; the Bernoulli formula cannot guarantee or increase the chance of winning. But if you want to pick numbers by a system rather than at random, use the method as a selection basis and the generator built on it.
How do I compute the odds of winning, of matching N of M?
That is a different question — the combinatorial probability of a match, not the frequency of individual numbers. The chance of matching the required number of hits in Powerball is on the “Winning odds” page.
How many draws are needed for the calculation?
The larger the archive, the more stable the probabilities: on a short window the coefficients jump around. Premium opens the full archive to compute across all draws.