BOSTON –– Unlike most relief pitchers, when Dan Wheeler sits in the bullpen, most nights he’s actually paying attention to the game. He gauges who’s coming up, thinks over who he would bring into the game at that point.

His manager, Joe Maddon, is a numbers guru, and he plays the percentages on righty-lefty matchups. His relievers don’t know when they’ll come in, if they’re not paying close attention. Wheeler finds himself weighing baseball strategy the same way, and enjoying it.

“It’s fun, because I like to play manager, too. I love baseball. I try to think along with him. I like the way he thinks,” Wheeler said.

A guy like that is exactly what teams look for in a future major league pitching coach.

It’s a thought: the Warwick native is at the midpoint in his career, and thoughts of what comes next have started to float into his mind. He’s pitched since 1999, when he came up with the then-Devil Rays, and excepting a brief return to the minors, has spent almost 10 years in the major leagues. He would like to pitch until he’s 40 years old, much like one of his mentors, reliever David Weathers.

But in spite of how much he enjoys pondering the tactics of pitching, Wheeler doubts he’ll be one of those players who stays in pro baseball as a major or minor league coach.

“I doubt it –– never say never, but for me, I’ve spent so much time away from my family, traveling, that I don’t know if I’d like to go back and do all those bus trips again,” Wheeler said.

Wheeler expects that by the time he retires, another priority will loom large.

“I’m very lucky to do what I do, and hopefully someday I won’t have to do that, and I can watch my son play high school baseball,” he said.

Wheeler’s son, Gabriel, is now four, and much of his post-baseball daydreaming revolves around the little boy. Wheeler thinks about watching him grow up, and being around his team, as a former major leaguer giving pointers.

“I’d like to be a coach, but I’d like to be a high school coach, when my son is playing. Maybe not the head coach, but a guy out there helping,” Wheeler said. “I don’t think I’d like to be out there having all that responsibility.”

Could that mean a return to Pilgrim High School for the 1995 graduate?

Probably not. Wheeler thinks of splitting his years, with winters in Florida and summers in Rhode Island. His wife, Stephanie, is from Florida, where her father is play-by-play man for the Rays.

“My ultimate goal is to split time. I love living in Florida, but I also love living up here. When it’s all said and done, hopefully I’ll have a lot of free time, and I can make that decision, and spend a lot of time up here with family, and winters down there. Be a snowbird, 30 years early,” Wheeler said.

Wheeler made it back to Rhode Island three times this winter, but only briefly each time. On one visit, he was honored as New England Athlete of the Year by the Boston chapter of the Baseball Writers Association of America.

Since his Rays won the American League pennant last year, those kinds of honors have become more routine, as have the predictions of the Rays finishing ahead of the Red Sox or Yankees in the American League East. Coming into Opening Day in Boston, Wheeler likes having the target on their backs.

“Pressure’s a good thing. I view it as a good word. This is where we want to be. You look at the history of the Yankees and the Red Sox, they’ve done it year in and year out, that’s the time for us, now. We’ve done it, we want to establish ourselves as one of those teams that’s going to be there at the end of the year, every year,” he said.

The Red Sox and the Rays are even starting to view each other as legitimate rivals, he said. There has always been competition there, and for a while, there was true vitriol, after a series of brawls, the most notorious involving Pedro Martinez and Rays outfielder Gerald Williams. The dynamic between the two teams is different now. The Rays are upstarts, but they earned respect when they beat the Sox last fall in the Championship Series. Now the two trade blows as near-equals.

“It dates back to all those days, with Pedro, and Gerald Williams. But that was a different kind of rivalry,” Wheeler said.

“Now, there’s a rivalry where this team is right there, level talent-wise with us, and we’re not just a team that’s going to give them 12-15 wins a year. We’re going to try to get those wins,” Wheeler said.

Wheeler isn’t certain when he will come in during games, whether it’ll be the 6th, 7th, 8th or even sometimes the 9th. Wheeler has served as the Rays’ closer in the past.

“As of right now, Troy Percival is our closer. So until I’m told otherwise, I’ll just be ready to go,” Wheeler said.

Maddon said that Wheeler is “a rock out there,” and that having a veteran pitcher like him who can come into any situation is a huge asset. Wheeler, too, doesn’t mind, because it’s allowed him to hone his baseball mind, trying to guess when he’ll be brought in.

“We’re very fortunate, there are a lot of arms down there that can pitch in any situation. There might be situations where I pitch the 8th, the 7th, the 6th. I’ll just be ready to go whenever that phone rings,” Wheeler said.

dbarbari@projo.com