The Bengals have neglected the strong safety position for a while. They have shuffled through several players and the strong safety position has possibly seen more turnover than any other position on the team. The Bengals tried a few players there in 2012 and still haven't found a clear starter. Possibly the team's third-round pick in 2013 will be the future of the position.
Mays started at strong safety to start the 2012 season, but lost his starting job after Week 4. While he has several very devout supporters, the coaches obviously weren't happy with his play. He is extremely athletic and has shown he can be a hard-hitting safety, something the Bengals want, but things just don't seem to be working out for him in Cincinnati. It's possible that he is having trouble learning Mike Zimmer's system, but it's anyone's guess. This year is a contract year for Mays, though, so maybe he'll turn it on to earn a decent paycheck in 2014.
Miles played in every game in 2013, but only started one. He was last on the depth chart behind Mays, Chris Crocker and Nate Clements and didn't see the field often aside from playing on special teams. He has a leg up in knowing the system, but he struggled in pass coverage and run support when on the field in 2012.
Williams is likely the favorite to start at strong safety despite the fact he's a rookie. There were higher-profile safeties on the board when the Bengals selected Williams in the third round, but they reportedly liked the fact that Williams was the quarterback of the Georgia Bulldogs' defense. That is what the Bengals liked so much about Crocker in his time in Cincinnati as well. Williams will have to prove he can outplay Miles and Mays as a rookie this offseason.