← Back to Blog

Stats Toolkit: Randomness Scores, Expected vs Actual, and Independence Testing

April 10, 2026  ·  6 min read  ·  Tool Guides

Three Tools in One Page

The Stats Toolkit brings together three statistical tools for exploring lottery data scientifically. All three reinforce the same message from different angles: lottery draws are random.

Tab 1: Randomness Score

The Randomness Score uses Shannon entropy to measure how evenly distributed each state's digit frequencies are. If all 10 digits appeared exactly 10% of the time, the score would be 100. In practice, scores range from 75–98 depending on sample size and window.

States near the bottom aren't "rigged" — they just have smaller sample sizes or shorter data windows, which produces more apparent variance.

Tab 2: Expected vs Actual

Select any digit (0–9) to see a bar chart of that digit's frequency in every US state over the last 90 days. A blue reference line marks the expected 10%. Most bars will cluster within 1–2% of that line — demonstrating the law of large numbers in action.

Tab 3: Independence Test

Select two states and click "Run Test" to perform a chi-squared contingency table test. The result shows whether the two states' digit distributions are statistically similar. In practice, nearly all state pairs will show p ≥ 0.10 — meaning the distributions are consistent with being independently drawn from the same uniform distribution.

For informational and educational purposes only. Past results do not predict future draws. Play responsibly.

Explore more with our free analytics tools:

Open Draw Analytics Dashboard →