Startup investor Jason Calacanis took a $25,000 gamble five years ago on a company almost no one had heard of called UberCab. That investment in what is now Uber Technologies Inc. has ballooned to roughly $110 million.

Mr. Calacanis has never said publicly where the money came from: Sequoia Capital, one of Silicon Valley’s biggest venture-capital firms. Since 2009, Sequoia has funneled millions of dollars to scores of well-connected entrepreneurs, academics and other people known as scouts.

Scouts...