On Friday, I posted an article about using spatial statistics to detect whether a pattern of points is truly random. That day, one of my colleagues asked me whether there are any practical applications of detecting spatial randomness or non-randomness. "Oh, sure," I replied, and rattled off a list of applications in biology, materials science, manufacturing, and epidemiology.
On Monday, I read in Andrew Gelman's blog about a statistician who, in 2003, figured out how to pick cards in a certain scratch-off game so as to increase the probability of winning. When I followed the link to the original story in Wired magazine, I was astonished to discover that the statistician, Mohan Srivastava, is a geostatistician and that his technique uses spatial statistics that are similar to the ideas that I laid out in my blog post!
The basic idea, which is illustrated below and described halfway through the article, is to look at the distribution of numbers on the ticket and use a frequency analysis to determine which tickets have layouts that are less random than is expected by chance. In the example shown in the article, the ticket has infrequent numbers (numbers with a frequency of 1) in a winning tic-tac-toe configuration. (This is circled in the image below.) Such a configuration is unlikely to happen by chance alone, so you should buy the ticket. Srivastava experimentally showed that the ticket is a winner about 90% of the time.
So, add "picking scratch-off tickets" to the list of applications of spatial statistics.