MIAMI GARDENS, Fla. — Stephen M. Ross swears he is not embroiled in a third-set tiebreaker with Larry Ellison, the billionaire co-founder of Oracle who bought the BNP Paribas Open in Indian Wells, Calif., a decade ago and transformed it into a tony desert party for tennis players and fans.

Still, when the moved and improved Miami Open begins this week at Hard Rock Stadium, home of Ross’s Miami Dolphins, it will not be hard to imagine Ross, a billionaire real estate developer, keeping a tiny scorecard in his back pocket.

“Larry’s done a great job,” Ross said. “He set the bar high, and it’s all great for tennis. But for us, it’s more natural not to compete, or at least to do so in our own way.”

Ross, who bought the Dolphins in 2008 and spent $550 million renovating the stadium, stepped in when IMG, which owns the Miami Open, found itself at an impasse with a Key Biscayne resident who controlled the land where the tournament had been played since 1987.