WALTHAM, Mass. -- During a break in Friday night's intrasquad scrimmage in front of season ticket holders at TD Garden, Boston Celtics coach Brad Stevens presented Avery Bradley with his award for being named to the NBA's All-Defense first team last season. Bradley said the award looks exactly the same as the All-Defense second team award he took home during the 2012-13 season and while it'll find a safe place in his office in Austin, Texas, Bradley admits he wouldn't mind adding a more eye-catching trophy to his collection this year.

Bradley said over the summer that after being the highest vote-getter at the guard position in last season's NBA Defensive Player of the Year voting, he'd like to make a run at an award that no guard has captured in the two decades since Gary Payton claimed it during the 1995-96 season.

Now that the Celtics have added defensive-minded Al Horford to the back line on a team that finished fourth in the league in defensive rating last season, Bradley thinks team success could improve his chances. But he was also emphatic that he belongs in the conversation regardless of Boston's performance.

"If we’re playing well this year, I’ll give myself a chance [to compete for the Defensive Player of the Year award] because, to be honest, I feel like I should always be in that conversation," said Bradley. "I think I’ve [been left off the] defensive team because of our [lack of] success in the past. We weren’t winning as many games and I’m not going to name some players, but when I was looking at the list I’m like, ‘That person got more votes?’ It’s just because they had a better year, they played longer, they were on TV more -- all those things help you out. This year, I feel like the amount of TV games and how we should be playing this year should be able to help me be in that conversation.

"You can ask all the best players in the NBA -- there’s not one player in the NBA that guards them like me. I know [San Antonio Spurs forward] Kawhi [Leonard] is a great defender and [Golden State Warriors big man] Draymond [Green] -- to me, he’s a really good defender. For someone that plays defense, I appreciate watching him play defense. It’s really amazing."

Bradley clearly respects the big men that dominate the defensive award balloting, but he also feels he is peerless at the guard position, and, considering the talent he's often asked to check, he believes he has a strong case for earning the league's top defensive honor.

It probably doesn't help Bradley's cause that he flies so quietly below the radar, but that's simply his personality. He isn't all over social media like many of his teammates and typically avoids the spotlight. Bradley prefers to let his play speak for itself and, his efforts against some of the top backcourts like Portland and Golden State late last season, along with his teammates stumping hard for him, helped Bradley earn that All-Defense first-team honor.

Newcomer Horford noted that it's guys like Bradley -- and fellow defensive hound Marcus Smart -- who set the tone in practice each day for Boston. While Bradley is typically reserved off the court, teammates report he talks an awful lot of trash on the court while essentially challenging his opponents to score on him.

Maybe a nickname might help Bradley? Boston's roster is brimming with players who simply go by two initials -- IT, AB, JY. While making the rounds at Monday's media day, Bradley was asked his favorite superhero. After pondering for a moment, he answered Spider-Man, then later explained that used to be his nickname growing up.

"I think it was just because of the way I play defense, the way that I’m everywhere on the floor. And I was athletic," Bradley said. "We were playing our rival [AAU] team in Seattle -- Nate Robinson and all those guys played for a team called the Seattle Rotary Select. We ended up beating them, and they were like, ‘Man, this kid is like Spider-Man.’ I had just moved up to Washington from Texas, and they were like, ‘This kid, he’s around the floor like Spider-Man!’

"And it just stuck with me. Everyone called me that. All the people close to me always called me that."

Bradley smiled when asked if maybe it's time to bring back that moniker. Just think of the marketing opportunities and all the kids in the Garden crowd combining their Celtics green with Spider-Man's red and blue accessories. Bradley prefers to just do his job on the court.

Bradley is the longest-tenured member of the Celtics organization and outside of Kelly Olynyk, the only player that's been here for Stevens' entire stint. Bradley's impact on Boston's success is not lost on Stevens.

"We've asked a lot from Avery ever since I've been here. And I've been really impressed with his continuous improvement, where he's gone from an efficiency standpoint in the last four years," said Stevens. "And then not only to be -- he was already a very good defender, but I just think he's gotten better and better and better. He's just improved in every which way. We do ask a lot. He's a huge, critical, important part of our team, and he adds value to winning. And he does so most every night."

It seems impossible that this will be Bradley's seventh NBA season. Selected 19th overall in the 2010 draft, Bradley is still only 25 years old. He's eager to further distinguish himself this season, especially as Boston returns to the national spotlight for the first time since early in his career when he learned from the Big Three.

But Bradley knows that any individual award isn't possible without his teammates.

"Like Brad said, it’s important to recognize all the guys on our team that are able to accomplish some individual goals, like Isaiah [Thomas] last year with the All-Star [appearance]. That’s a big-time accomplishment," said Bradley. "I know [individual honors are] not possible without my teammates. The way I’m able to play defense night in, night out, they’re the ones that help me, they’re the ones that talk to me, they’re the ones that give me that confidence. So it’s really our team award.

"We know that, we talk about it. You can argue and say Marcus and Jae [Crowder] as well, they’re great defenders. Even Amir [Johnson], he’s a very good defender. We’ll all have a chance this year with what’s expected of us and the amount of opportunities we’ll have playing on TV to be able to show that."