(CNN) A former Miami Dolphins player apparently lived up to his old NFL team's name and says he swam nine miles in the ocean to shore after falling off his boat.

Fighting back tears, Rob Konrad, 38, recounted an incredible story Monday at a press conference in Plantation, Florida. He said he swam through cold water in the Atlantic Ocean for about 16 hours, alternating between the breast stroke and backstroke. Jellyfish stung him, and he was once circled by a shark, he said.

Appearing healthy, his wife sitting next to him, Konrad told reporters that, treading water in the moments after falling off his boat Wednesday off the South Florida coast, he knew how improbable his survival was.

He had read about what happens to the body under such circumstances. He figured that he had maybe three hours before hypothermia set in.

It might take him more than 10 hours, at best, to get to shore. But he told himself he would make it.

"I've got two beautiful daughters," he said, his eyes watering. "I was hitting shore."

Konrad said he departed alone in his 36-foot Grady White boat from Deerfield Beach, Florida, at about 10:30 a.m. Wednesday and went about nine miles offshore. He set the boat on autopilot for 5 mph and started to fish. He said he hooked a fish around 1 p.m. and while trying to reel it in, a huge wave smashed into the boat and he lost his footing and fell overboard. The boat was moving east, he said, toward the Bahamas.

He wasn't wearing a flotation device and didn't see any other boats around.

"I quickly realized I was in a real bad situation," he recounted. "I made a decision that I was going to start swimming toward shore, west."

Hope for rescue rises and falls

Over the next 16 hours, he said he had two opportunities to be rescued.

He saw a recreational fishing vessel. He was floating about 50 yards from it and tried to swim closer, but no one spotted or heard him.

A little later, a U.S. Coast Guard helicopter circled and shined its light on him, he recounted.

"They had come right over the top of me," he said. But the helicopter flew away.

"That was a difficult time. I realized at that point in time ... I was on my own."

Coast Guard Lt. Cmdr. Gabe Somma told CNN on Monday that Palm Beach authorities contacted the Coast Guard to report that Konrad was missing and that it had a helicopter out looking for the former fullback.

Down to his underwear, Konrad alternated between breast stroke and backstroke, mustering the strength to keep swimming.

He made it through the night, and managed to coach himself to remain calm despite seeing "glowing" creatures in the water.

When he heard waves crashing against the shore, he told himself: "At that point, you can't not make it?"

At around 4:30 a.m. Thursday, Konrad said he hit the shore in Palm Beach. He was shivering uncontrollably so he curled into a ball and tried to warm himself up.

He had trouble walking but eventually made his way to a home where a security guard was working. The guard notified that Palm Beach Police Department, according to a department report.

Konrad was taken to the hospital, where he said he was treated for hypothermia, severe dehydration and rhabdomyolysis, the breakdown of muscle tissue.

Even conditioned athletes would struggle

Konrad's remarkable experience has wowed distance swimmers.

Sid Cassidy , a nationally renowned distance swimmer, has swum the 22-mile course around Atlantic City, New Jersey, five times. He's trained in the same waters in South Florida where Konrad fought against the odds.

"If you're a good swimmer and you're faced with an emergency, you could be capable of doing what he did," Cassidy said.

The Florida Fish and Wildlife Conservation Commission said it is investigating the boat incident.

Depending on Konrad's location in the Gulf Stream, he would have had to swim west, across the water's south-to-north current, according to CNN meteorologist Chad Myers. The current could have been up to 4 mph.

Normally swimming a mile in the ocean could take 20 to 30 minutes -- if a person is very fit, Cassidy said. Most professional swimmers don't attempt that many miles without help from a team providing hydration and nutrition.

Konrad is the CEO of Alterna Financial, a South Florida financial services company. A fullback, he played at Syracuse University and was drafted by the Dolphins in the second round of the 1999 NFL Draft. He played his entire pro career for the Dolphins -- 82 games, according to Pro-Football-Reference.com . He was released from his contract in 2005.

"I can't imagine that swimming isn't part of his typical workout," Cassidy said.

Konrad said he judged which direction to swim by looking at the sun during the day and the stars at night.

But even if Konrad knew which direction to start swimming, he'd have to contend with constant saltwater in his eyes, intense muscle fatigue, wind and, of course, current, noted Bruce Wigo, president and CEO of the International Swimming Hall of Fame in Fort Lauderdale.

"From the salt alone, you'd have a tongue the size of a baseball," said Wigo.

It makes sense that Konrad stripped down in the water to lessen the drag, Wigo added.

A former pro athlete like Konrad knows what it takes to push past pain, Cassidy surmised. He would know how to focus and to stay calm, too.

Sitting next to her husband Monday, Tammy Konrad said he has always been the kind of guy who never gives up.

"Rob is a very powerful human being," she said. "He set his mind on something and he does go after it."