Caprice was Vancouver's 9th round selection (178th overall) in the 1981 NHL Entry Draft. In the year following his selection, he improved his stock greatly, winning 24 games for the London Knights and representing Canada at the 1982 World Junior Championships. He won all three of his starts at the World Juniors, helping Canada to the gold medal. Following the season, he signed with the Canucks and turned pro.
Caprice spent most of his first pro season in the AHL, although he did make his NHL debut, playing the 3rd period in a blowout to the Los Angeles Kings. Caprice's big opportunity came in the 1983–84, when the Canucks' starting goalie Richard Brodeur was injured. In his starting debut against the Edmonton Oilers on Hockey Night in Canada, Caprice earned first-star honours in a 3-2 Canucks victory. He posted a solid 8-8-1 mark with a 3.34 GAA, the best performance of any of the three Canuck goalies that year.
Based on his fine performance in 1983–84, Caprice was given a chance to usurp Brodeur as the Canucks' starter in 1984–85, although he would struggle and then tear his hamstring, causing him to miss three months of action. He finished the season with an 8-14-3 mark and 4.81 GAA in 28 appearances, and would never seriously challenge for the #1 spot again.
In 1985–86, Caprice would again struggle, posting an 0-3-2 record and terrible 5.45 GAA in 7 appearances, and was demoted to the AHL in favour of Wendell Young. However, he would reclaim the backup job in 1986–87, and posted a 3.84 GAA in 25 appearances, his best since his rookie year. In 1987–88, he appeared in 22 games backing up 21-year old Kirk McLean as the aging Brodeur was relegated to 11 appearances.
In 1988–89, Caprice was relegated to the IHL as the Canucks decided to go with a goaltending tandem of McLean and Steve Weeks. For the 1989–90 season, Caprice was dealt to the Boston Bruins for a 9th round pick. However, he spent the entire season in the minors and was released at the end of the year.
Following his release from the Bruins, Caprice would spend most of the 1990s playing in Italy and later in Britain with the Cardiff Devils, before retiring in 1999 and returning to his hometown of Hamilton. He would come out of retirement in 2001 to represent the Dundas, Ontario team at the 2001 Allan Cup.
Caprice appeared in 102 NHL games over 6 NHL seasons, posting a 31-46-11 record with a 4.19 GAA and one shutout.
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