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

April 11, 2026  ·  6 min read  ·  Tool Guides

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Hot & cold numbers, patterns, and frequency-ranked combinations

Free analytics dashboard with frequency charts, long-gap numbers, and pattern tools — updated after every draw.

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.

DrawAnalytics is an informational service. We do not sell predictions or guarantee outcomes. Lottery drawings are random — past results do not predict future drawings. Play responsibly. 1-800-GAMBLER.

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Hot & cold numbers, patterns, and frequency-ranked combinations

Free analytics dashboard with frequency charts, long-gap numbers, and pattern tools — updated after every draw.

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DrawAnalytics is an informational and entertainment service. We provide historical lottery data analysis and pattern exploration tools. We do not sell predictions, we do not guarantee any outcome, and we make no representation that any tool on this site improves a user's probability of winning any lottery game. Lottery drawings are random. Past results do not predict future drawings. DrawAnalytics is independent and is not affiliated with or endorsed by any state lottery, the Multi-State Lottery Association, Powerball or Mega Millions. Game names are trademarks of their respective owners. Results are collected from public sources and may contain errors; official lottery results prevail. You must be 18 or older (21+ in some states) to play state lottery games. If you or someone you know has a gambling problem, call 1-800-GAMBLER or visit ncpgambling.org.