The game has never been played on paper. If it were, Erik Gudbranson would not have been re-signed by the Vancouver Canucks. But general manager Jim Benning and coach Travis Green work on ice, and the six-foot-five defenceman who can skate and physically punish opponents, who will stand up for teammates, was simply too big a fish to throw back to the rest of the National Hockey League. The Canucks are gambling on Gudbranson, but so is he after agreeing to a three-year, $12-million contract extension that’s probably less than what the 26-year-old could have leveraged as one of the top unrestricted free agents on July 1. Gudbranson is ground zero for the ideological war between hockey analytics and instincts. Few of his numbers are flattering, and a $4 million annual salary-cap hit represents overpayment for a guy who has been prone to both injuries and mistakes and, seven seasons since he was the third player chosen in the 2010 draft, hasn’t yet established that he is better than a third-pairing defenceman. But Benning looked at his team, which is light on defencemen and toughness, then looked into the future at all the skilled, offensive Canucks prospects scoring their way towards the NHL and asked himself this fundamental question: Would he rather have Gudbranson playing with them or against them? The answer came Tuesday.