Bob Edmonds bought a lottery ticket in Ontario and took it to a shop to be checked. He was told it was not a winner. It was worth $250,000, and the people who told him otherwise kept it.
That is one story, and on its own it is a crime rather than a statistic. What turned it into a statistic was somebody asking the obvious follow-up: if this happened once, how often does it happen?
In October 2006, CBC's the fifth estate put the question to Jeffrey Rosenthal, a statistician at the University of Toronto. He did not need access to anything confidential. He needed two numbers: roughly what share of lottery tickets are bought by the people who sell them, and how many major prizes those people had won.
The Insider Meter
The question Rosenthal was asked, with the arithmetic in your hands. The sliders are illustrative inputs; what is documented is the shape of the answer — fewer than about sixty insider wins expected, more than two hundred observed.
200 wins against 57 expected is 19.0 standard deviations above what honest play produces. At this distance the question stops being statistical and becomes a matter for investigators.
Retailers are a small fraction of the ticket-buying public, so their share of major wins should be correspondingly small. Rosenthal's calculation put the expected number of insider wins since 1999 at fewer than about sixty.
More than two hundred had been recorded.
The gap is not the kind that argument can close. It is not a matter of interpretation, or of methodology, or of what counts as a major prize. Two hundred against sixty is a distance that random chance does not cover, and the arithmetic that says so is the same binomial distribution taught in a first statistics course.
He presented it on television. The Ontario Lottery and Gaming Corporation, which had maintained there was nothing to investigate, found there was something to investigate. The provincial ombudsman produced a report. Refunds followed, and so did a restructured system of checks on how tickets are validated.
No new mathematics was invented that year. Somebody simply computed an expectation, compared it with a count, and refused to be talked out of the difference.