After years of rumors about pimply geeks with laptops plotting a takeover of English soccer, the game's statistical rebels have received a full-throated welcome into the hallowed grounds of the Premier League.

As a new season begins Saturday, all eyes will be on Anfield, where—10 months after Boston Red Sox owners John Henry and Tom Werner purchased Liverpool—the legendary club will flaunt the trappings of a $170 million spending spree that amounts to a pricey bet their data-driven approach can find value that others have...