During Kansas City’s decades-long playoff drought, Royals radio announcer Denny Matthews called thousands of meaningless games without ever sounding frustrated.

Now that the Royals are playing meaningful baseball, however, some critics complain that Matthews never sounds excited. “The man in the broadcast booth—who should be living it up with his fan base, much of which he helped create—seems to be off in his own world, unable to express joy and excitement,” Bob Lutz, a Wichita Eagle sports columnist, wrote amid last year’s...