Benfords Gesetz — Anfangsziffernanalyse
Benfords Gesetz besagt, dass Anfangsziffern in natürlichen Datensätzen ungleichmäßig verteilt sind: die Ziffer 1 erscheint ~30% der Zeit, während 9 nur ~4,6% erscheint. Wir prüfen, wie sich die Anfangsziffern der Ziehungssummen der Lotterie «Пять-О-Пять» zu diesem fundamentalen mathematischen Gesetz verhalten.
How to Use Benford's Law Analysis for Пять-О-Пять
Choose the data source
Switch between "Ball sums" and "Draw numbers" modes. Ball sums are better suited for Benford analysis as they cover a wider range of values.
Evaluate the chi-squared test result
If the χ² value is less than the critical value (15.507), the data conforms to Benford's Law. This indicates a natural distribution of first digits.
Study the histogram
Compare the expected and actual value bars. Significant discrepancies may indicate anomalies in the data.
Analyze the deviations
The deviation chart shows which digits appear more or less frequently than expected. Positive deviations mean the digit appears more often, negative — less often.
Was ist Benfords Gesetz?
Benford's Law (or the first digit law) is an observation from probability theory about the distribution of leading significant digits in numerical data sets. It was discovered by astronomer Simon Newcomb in 1881 and independently rediscovered by physicist Frank Benford in 1938.
Benford's Formula
P(d) = log₁₀(1 + 1/d)
where d is the first digit (from 1 to 9). This gives: P(1) ≈ 30.1%, P(2) ≈ 17.6%, ..., P(9) ≈ 4.6%.