NEW YORK—Chad Campbell lingered in the parking lot of a Dallas hospital as his wife waited inside to get the latest report on their first child, due to be born later this week.

He wanted a clear signal on his cell phone to hear the good news: Campbell is going to the Ryder Cup.

Paul Azinger completed his American team Tuesday with captain’s picks, adding Campbell, Steve Stricker, Hunter Mahan and Kentucky native J.B. Holmes to a team that will have six Ryder Cup rookies and no Tiger Woods.

“I think that we have rounded off this team with the best possible pl...

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