ST. PETERSBURG, Fla.—Even with a healthy Evan Longoria and Carl Crawford, the Tampa Bay Rays knew it would be a challenge to stay atop the AL East. Without them, help will have to come from every corner of the clubhouse.

“You go around and there’s been a lot of guys who have helped us get to this point, some with limited playing time,” executive vice president of baseball operation Andrew Friedman said Monday after rookie All-Star third baseman Longoria joined Crawford on the 15-day disabled list because of a broken right wrist.

“A few of these guys are going to get mor...

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