When the Numbers Don't Add Up: Benford's Law Analysis

How Benford's Law Works

In naturally occurring datasets — financial transactions, population counts, street addresses — the leading digit “1” appears far more often than “9”. This is because numbers grow logarithmically: it takes a 100% increase to go from 1xx to 2xx, but only an 11% increase to go from 8xx to 9xx. When someone fabricates numbers, they tend to distribute digits more evenly, violating this law.

Expected Leading Digit Distribution

The chi-squared statistic measures how far a provider's actual digit distribution deviates from these expected values. Higher values indicate greater divergence from the natural pattern.

Key Takeaways

• ▸200 providers show statistically significant deviations from Benford's Law in their billing amounts.
• ▸The highest chi-squared value is 4.14, far exceeding the threshold for statistical significance.
• ▸These 200 providers account for $3.71B in total Medicaid spending.
• ▸Benford's Law analysis is a screening tool, not a verdict. High chi-squared values warrant investigation but do not prove fraud on their own.