But that's not what makes them most proud.
"My Mohawk name is Dayodagonay," Ty says. "It means 'He carries the fire.'"
"My name is Guyagoyah, 'He strikes the sun,'" says Miles.
"Dayhausinonday, and it means 'He is flying over us,'" Lyle says.
"Lacrosse is more than just a game for our people," Ty says. "When I was growing up, me and my friends, that's all we did."
Their ancestors invented the sport. European settlers first documented Native Americans playing the game in the 1600s. Even now, lacrosse is deeply symbolic for Native Americans, who believe the game's purpose is to entertain the creator and to heal the sick.
That philosophy has delivered unprecedented results. The three Thompsons scored more points last season than the entire teams of 40 Division I schools.
"They really are, in a sense, on a different level," head coach Scott Marr says. "They are just so creative, they are just so much fun to watch."
The Thompsons say Albany feels like home, because their team has embraced their culture.
"It feels like I'm in the right place, because there, we go and get water, and we call it onaganos, and we got the whole team calling it -- 'Let's go get some onaganos,'" Miles says. "They are open to us and we are open to them, and it feels like a family here."
"It just shows they respect us and we respect them, and it is a family here," Lyle says.
A family that recognizes and honors its rich history.