As a professional, his 38.7 net average led the league in 1986, and his 45.7 average yards led the NFL in 1991, and he set a Pro Bowl record with 10 punts in the 1985 game. His 58.5-yard single-game average on September 28, 1986 remains a Dolphin team record. At Rich Stadium, Roby punted the ball a team record 77 yards, but the punt was returned 70 yards. He completed the only pass attempt of his career, a 48-yarder to John Booty in 1995. Roby was selected as a punter for the NFL's 1980s All-Decade Team. In the Dolphins 1992 divisional round 31-0 win over the San Diego Chargers, he planted 4 of his 8 punts inside the Chargers 20-yard line, including 3 inside the 7. Roby played in Super Bowl XIX with the Dolphins, though he had a below average day, averaging just 39.3 yards per kick and failing to put any of his 7 punts inside the 20. "I was trying to kill the ball, and I kicked it bad", said Roby after the game. "I didn't hit one well. I was scared -- scared to make a mistake. It was the worst game of my life, counting high school, college, counting everything." Dolphins coach Don Shula said following the game "We're supposed to have the best punter in the football, but today, he didn't punt like he was the best." However, it is notable that despite Miami's #1 ranked offense during the 1984 season, which set numerous NFL records, he still made the Pro Bowl that year.