The Tampa Bay Rays recognize that if they ever expect to compete with the giants in their division, they must operate differently than the rest of the baseball world. They will never possess the financial resources to outspend the New York Yankees and Boston Red Sox, leaving them only one option: to outmaneuver them.

“If we occupy the wake of both the Yankees and Boston and our behavior is aligned with theirs, we’re never going to step out and pass them—ever,” one high-ranking Rays official said. “Never, ever, ever will we...