The Powerball draw sums deviate from Benford's law: χ² = 22.1 against a threshold of 15.5 (sample: 20). Most often the sum begins with the digit 1 — 60%.Data includes draw #1970 of 09.07.2026.
Important: Benford's law describes numbers that span several orders of magnitude — from units to thousands and beyond. Lottery draw sums sit in a narrow band, so their deviation from Benford is expected and is NOT a sign of a rigged draw. This checks the shape of the distribution, not the honesty of the lottery.
Benford's law (the first-digit law): in “natural” multi-order data the digit 1 comes first about 30% of the time, while 9 does so only 4.6%, per the formula:
P(d) = log₁₀(1 + 1/d)
Where to next
Total draw sum
The distribution and range of Powerball sums — the very numbers whose first digits Benford examines.
OpenRuns test
Whether Powerball has non-random streaks and droughts — another view of randomness.
OpenShannon entropy
How evenly Powerball numbers are spread — a measure of unpredictability.
OpenPearson's χ² test
A χ² check of Powerball drum bias by the frequency of each ball.
OpenFrequently asked questions about Powerball
What is Benford's law?
Benford's law (the first-digit law) is the observation that in datasets spanning many orders of magnitude the leading digits are distributed unevenly: 1 appears about 30% of the time, while 9 only 4.6%. Formula: P(d) = log₁₀(1 + 1/d).
Why do Powerball draw sums deviate from Benford's law?
Because the law works for data spanning several orders of magnitude — units, tens, hundreds, thousands. The Powerball ball sums sit in a narrow band around the mean, so the first digit is set by that range, not by Benford. The deviation here is a normal consequence of lottery maths, not an anomaly.
Does matching Benford prove Powerball is honest?
No. Because of the narrow range of sums, the Benford test is weakly informative for a lottery: both a match and a deviation are possible for a perfectly fair draw. To check drum uniformity, Pearson's χ² on ball frequency and the runs test are more reliable.
What does the χ² test mean on this page?
χ² compares the observed distribution of first digits with the one expected under Benford. A value below the critical 15.5 (df=8, α=0.05) means the shape is close to Benford; above it, they diverge. This describes the shape, not a verdict on the lottery's honesty.
Can Benford's law predict Powerball numbers?
No. Benford's law is a tool for describing the distribution of first digits, not a forecast. It says nothing about which specific numbers will come up in the next Powerball draw.