PECOTA, Baseball Prospectus’ sophisticated computer model for forecasting on-field performance, is impressively accurate. Half of teams have, on average, finished within 2.75 wins in either direction of PECOTA’s predictions since 2013, with nearly two-thirds of teams coming within 3.25 wins.

But there’s still one team PECOTA can’t figure out: the Kansas City Royals, the unexplained mystery of the major leagues. The Royals outperformed PECOTA by an average of 12½ games from 2013 through 2016, the most in the sport over that...