ST. PAUL, Minn. — Make no mistake, Bobby Brink did the Minnesota Wild a solid on Tuesday.Arbitration is a tricky proposition for teams. It’s all based on the math, and at 0.46 points per game in his career (98 points in 214 games), the Wild discovered Brink could be staring at a $4 million award if he opted for arbitration next month.In most cases, the player and the club would compromise on a two- or three-year deal in the $3.5 million range before the player reached his arbitration hearing.But as we’ve documented all offseason, the Wild are suddenly up against it cap-wise again, with several holes to fill this offseason and about $12 million in cap space to go around.When free agency begins on Wednesday, it’ll be like they’re trying to row upstream with one oar.That’s why the Wild didn’t feel they could even allot $3 million or $3.5 million for Brink. So they engaged Brink’s agent in recent days and began working on a different type of contract — or, more accurately, a favor from Brink before not tendering him a qualifying offer on Monday.Brink could have become an unrestricted free agent on Wednesday at 11 a.m. and likely gotten more than the one-year deal he agreed to with the Wild on Tuesday, worth $2.75 million.