SAN FRANCISCO — Litigation finance startup Legalist made a splash in the industry last year when it claimed it could estimate the likelihood of a case succeeding using a cutting-edge algorithm, no lawyers involved. It was quintessential Silicon Valley: just couple of young Harvard dropouts with some business savvy and software know-how.

Now, after launching a fund of $10.25 million—and with an eye on bankrolling about a hundred cases in the next year—it’s decided it might want someone with a legal degree on board after all.