Math Magician: At IBM’s Watson Research Center, Brenda Dietrich helps connect the work of the company’s research mathematicians to its consultants’ projects, generating enormous amounts of new business. Credit: Heather Johnson

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Five years ago, Brenda Dietrich started to investigate how IBM's 40,000 salespeople could learn to rely a little more on math than on their gut instincts. In particular, Dietrich, who heads the company's 200-person worldwide team of math researchers, was asked to see if math could help managers do a better job of setting sales quotas. She assigned three mathematicians at IBM's Thomas J. Watson Research Center in Yorktown Heights, NY, to work on new techniques for predicting how much business the company could get from a given customer.

The mathematicians collected several years' worth of data about every sale IBM made around the world. They compared the results with the sales quotas set at the beginning of the year, most of which were developed by district sales managers who negotiated them with sales teams on the basis of past experience. To spot opportunities the sales teams didn't recognize, the researchers collected external data on IT spending patterns by industry and combined that information with the internal sales data. Then they used a technique called high-quantile modeling--which tries to predict, say, the 90th percentile of a distribution rather than the mean--to estimate potential spending by each customer and calculate how much of that demand IBM could fulfill.