Wednesday, July 06, 2005

Wisconsin Lottery Ripping Off the Poor?

That’s the claim of the Journal-Sentinel, that asserts:
Nearly one-third of all state lottery tickets sold in southeastern Wisconsin last year were sold in poor neighborhoods, and players in these areas hoping to strike it rich have not seen as many big payoffs as the rest of the region, a Journal Sentinel analysis shows.
Sounds like another case of the poor being ripped off, right?

But as our colleague Lowell Barrington pointed out to us, the problem is the stipulation “big payoffs.”

The first hint that there is something wrong with the paper’s analysis comes in a chart that shows that “winnings to sales ratio” in various localities. Across the entire area the average payout in “winnings” is 6.4% of sales.

But in fact, the lottery pays out, in prizes, far more than 6.4% of all it takes in. In Fiscal 2003-2004, the lottery had (state wide) 482.9 million dollars in sales, and gave out 275.2 million dollars in prizes.

It returned, in other words, 56.9 cents on each dollar spent on a lottery ticket.

Then how does one explain the discrepancy between this figure and the 6.4 cents the Journal-Sentinel reports?

Simple. The Journal-Sentinel analysis included as “winnings” only prizes of $600 or more. But these come to only a very small proportion of total lottery winnings.

The discrepancy could easily be accounted for if people in poor neighborhoods disproportionately play games that have a high probability of payout, but only a modest payout if you win. And indeed, the article provides evidence that this is the case:
[Mike Edmonds, director of the Wisconsin Lottery] also noted that one of the most popular games in Milwaukee County is the Pick 3 game, which has a top prize of $500 - prizes that are not recorded and tracked by the lottery. Of the $23 million in Pick 3 sales statewide last year, he said, half of those sales were in Milwaukee County.
In other words, lottery tickets with a low top payout (but a greater probability of winning) are apparently more popular in poor neighborhoods.

This article was a prime example of statistical incompetence, and should never have appeared in the paper.

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