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"The excitement in Buffalo is so huge," Hutton told NHL Network. "I'm so excited to go to this market. I think the last few years they've just been dying for a team to win some games here, and they've been close. So I'm excited to come and be a part of that."
The 32-year-old goalie said six or seven NHL teams had interest in him, but some of those wanted him to be a backup instead of the starter.
"Buffalo right out of the gate was really strong, and they knew that I was their guy, and that was something that was real important for me," Hutton said.
Hutton was 17-7-3 with a 2.09 goals-against average, .931 save percentage and three shutouts in 32 games (26 starts) with the St. Louis Blues last season. He led the NHL in GAA and save percentage among goalies who played at least 20 games.
Hutton, who signed with St. Louis on July 1, 2016, was 30-15-5 with a 2.23 GAA, .923 save percentage and seven shutouts in 62 games (47 starts) with the Blues.
"I think for me my main goal right now is going in to win hockey games," Hutton said. "I'd love to get into the higher end of [50 starts] just to really give myself a goal. I think I play better when I get more minutes."
Signed as a free agent by the San Jose Sharks on June 1, 2010, Hutton is 63-39-17 with a 2.42 GAA, .915 save percentage and 11 shutouts in 138 NHL games (114 starts) with the Chicago Blackhawks, Nashville Predators and Blues. He was 0-0 with a 3.01 GAA in three relief appearances for Nashville during the 2016 Stanley Cup Playoffs.
The Sabres selected defenseman Rasmus Dahlin with the No. 1 pick of the 2018 NHL Draft.
"I'm pretty excited, he's a heck of a player," Hutton said. "... I think this young kid, he's going to be a difference-maker. It's going to be nice having him in front of me."