Here’s the thing about brain aneurysms: They aren’t necessarily deadly, unless they pop. If that happens, there’s roughly a 50% chance that the patient will die—so it’s best to spot and treat them early.

To help in their aneurysm hunt, radiologists at Mayo Clinic use special software developed with IBM (IBM) that analyzes a three-dimensional brain scan. Computer algorithms process information in the images, pick out abnormal areas where fragile blood vessels might be hiding, and flag the potential trouble spots for Mayo doctors. So far the results are promising. In trials the software found 95% of aneurysms; a typical radiologist would have found 70%.

The technology used by Mayo Clinic is fairly new (the facility started using it last year), but the underlying science—advanced analytics—has been around for decades. Analytics, also known as “business intelligence,” sizes up and organizes vast streams of data to help institutions spot kinks in their supply chain, forecast where inventories should be next quarter—or detect serious health problems. The rocky economy has helped make business analytics, and the efficiencies it can produce, suddenly sexy. “Often these days companies can’t compete by just having a better product,” says Forrester analyst Boris Evelson. “They need to do things faster, at lower cost. Analytics software helps them do that.”

There’s a crowded field of technology companies competing in the $25 billion market for business analytics software, including SAS, based in Cary, N.C., which specializes in the stuff, and IBM, Oracle (ORCL), SAP (SAP), and Microsoft (MSFT), which have bolstered their portfolios in recent years by acquiring companies that focus on analytics.

What’s next? One fast-growing area is real-time analytics, which involves crunching numbers in fractions of a second and spitting out graphs that show how a factory is performing or whether the sales force is succeeding according to plan. Another is predictive analytics, which has a more ambitious goal: studying yesterday to figure out what’s likely to happen tomorrow.

Some companies are already reaping the benefits of predictive analytics. French retailer Carrefour (CRER.Y) recently used IBM software to dig through purchase patterns, figure out what each customer was likely to buy next, and offer targeted coupons that drew customers back into the stores. The outfit now has a better handle on customer demand, and the coupons give it a chance to win repeat sales and boost customer loyalty in a fiercely competitive environment. “Your batting average has to go up,” says Fred Balboni, global leader for IBM business analytics, “because your number of at bats has gone down.” It doesn’t take a brain surgeon to understand the value in that.