Which 6D Lotto numbers deviate from expectation the most? Z-Score over the last 20 draws: Field 3: 8 (Z=2.98). Field 5: 8 (Z=2.98).
The Z-Score describes past skew, not the future: a positive Z means the number appeared more often than expected, a negative one — less often, and it does not affect the odds of the next draw. But as a selection system the method works: if you prefer picking numbers by statistics rather than at random, clicking a number in the table adds it to the generator below, and the underlying frequencies are shown in the frequency table →
The Z-Score (standard score) is a measure from mathematical statistics: how many standard deviations σ a number’s observed frequency differs from the expectation of an equiprobable draw. In a fair drum the values cluster around zero: |Z| > 2 occurs in about 5% of numbers, |Z| > 3 — in 0.3%.
Z = (f − E) / σ
where:
- f — the observed frequency of the number over the selected draws;
- E = n·p — the expected frequency (n — number of draws, p = how many numbers are drawn from the field ÷ total numbers in the field);
- σ = √(n·p·(1−p)) — the standard deviation of the binomial distribution.
Where to next
Number frequency
The actual 6D Lotto number frequencies — the raw f the Z-Score is computed from.
OpenPearson test (χ²)
The skew of the whole 6D Lotto drum in a single number — the sum of squared deviations of all balls.
OpenBernoulli formula
The same frequency through binomial probability: how typical a number’s hit count is for a fair 6D Lotto drum.
OpenHot numbers
6D Lotto numbers with an upward frequency skew — a ready-made list of leaders without formulas.
OpenZ-Score questions
What is the Z-Score in a lottery?
It is the standardized deviation of frequency: we take how many times a 6D Lotto number has actually been drawn, subtract the expected frequency of a fair drum and divide by the standard deviation σ. The result is “how many sigmas” the number deviates: Z = 0 — exactly as expected, Z = +2 — noticeably more often, Z = −2 — noticeably less often.
Which is “worse” — a negative or a positive Z-Score?
Neither: the sign only shows the direction. A positive Z means the number appeared more often than expected (“hot”), a negative one — less often (“cold”). What matters is the absolute value |Z|: the larger it is, the more the number’s frequency differs from the expectation of a fair drum — in either direction.
Why are the thresholds exactly 2σ and 3σ?
In a normal distribution about 95% of values lie within ±2σ and 99.7% within ±3σ. So |Z| > 2 is expected for roughly 5% of numbers even in a perfectly fair lottery — not yet a signal; |Z| > 3 — for only 0.3% and deserves attention. On a short sample large |Z| values appear more often — that is a property of a small number of draws, not of the drum.
Can you pick numbers by Z-Score?
The Z-Score does not increase probability: in a fair drum all combinations are equally likely, and strong deviations smooth out over time. But as a selection system the method works: if you want to play the 6D Lotto numbers with extreme deviations, mark them in the table — the generator on the page will build combinations from them.
How does the Z-Score differ from the Pearson test (χ²)?
The Z-Score rates each number individually: its own deviation in units of σ, with a sign. The Pearson test adds up the squared deviations of all numbers into a single total χ² and speaks about the drum as a whole. Use the Z-Score to find specific “outliers” and χ² to assess the skew of the entire drum.