Cory Conacher is a 5-foot-8 center in a league that still looks askance at small players. He played four years at Canisius College, which had never sent a player to the N.H.L. Undrafted, he tried out with three minor league teams before signing a pro contract. He has Type 1 diabetes. Yet there he is, racing all over the ice for the Tampa Bay Lightning and becoming the N.H.L.’s top rookie scorer this season.

“I’ve been given so many awesome opportunities, I’d like to take advantage of those opportunities and prove to people that I’ve made the right decisions — and then also prove other people wrong,” Conacher, 23, said. “Back when I was a young kid, I got cut from my AAA team because I was too small.”

Entering Tuesday night’s game against the Buffalo Sabres, the cheerful and shaggy-haired Conacher leads N.H.L. rookies with 23 points in 32 games, ahead of such highly regarded prospects as Florida’s Jonathan Huberdeau and Edmonton’s Justin Schultz and Nail Yakupov.

“I’ve got to be that fearless guy out there,” Conacher said. “I can’t show that I fear these guys, because that’ll cost me. Right now I play as big as I can. I play like a 6-foot-7 guy. I try to challenge those guys as much as possible just to show I’m not scared to go in the corners with them.”

Conacher’s unlikely, I-think-I-can path to the N.H.L. started in his hometown, Burlington, Ontario. At 8, he was found to have diabetes. At 12, he got an insulin pump, which he wears like a beeper. It attaches to a permanent port in his abdomen. He takes the pump off during games.

“It really hasn’t gotten in the way,” Conacher said. “As long as you control it, it’s not a big deal.”

The diabetes did not faze him; Bobby Clarke, the Flyers’ captain in the 1970s and ’80s, also had diabetes. Nor was Conacher fazed by the expectations raised by his surname, which is famous throughout Canada. The Conacher brothers — Lionel, Charlie and Roy — are each in the Hockey Hall of Fame. Lionel, also a champion in boxing, wrestling, football, baseball and lacrosse, was voted Canada’s top athlete of the first half of the 20th century.