Steve Ballmer has always been an Excel guy. So when the former Microsoft chief executive’s wife, Connie, pressed him to be more philanthropic, he decided to do what he knew best: wade into vast repositories of government data to figure out where he could have the greatest impact.

Mr. Ballmer sought the government equivalent of a 10-K corporate report, the comprehensive business and financial document publicly held companies are required to file annually with the Securities and Exchange Commission. He realized no such singular...