ST. PAUL — The left-handed batter tried to check his swing in the first inning. In a reflex honed through thousands of innings behind the plate, Dwight Childs, a catcher for the St. Paul Saints of the independent American Association, pointed up the third-base line, appealing for a swinging strike call.

But there was no umpire there — or at second, or at first or even behind the plate at Midway Stadium. The game’s final arbiter, a man in a flowing black robe that flapped in the breeze, stood with his arms folded behind the mound. He pumped a fist, signaling a strike.

In the lightly attended exhibition game on May 11 at a creaky old stadium on a cold, blustery night, the Saints and the Gary SouthShore RailCats experimented with a revolutionary idea: a game without umpires. That the Saints were involved should not surprise anyone who knows that the team’s part-owner is Mike Veeck, a third-generation baseball executive and the son of Bill Veeck, the Hall of Fame owner and impresario.

Veeck, 62, inherited his father’s imagination and knack for inventive promotions. In more than 20 years running the Saints and other independent teams, Veeck has relied on off-the-wall gags and a festive atmosphere to create a new baseball genre outside the affiliated minor leagues. Independent leagues now operate coast to coast.