I came to hockey late in life thanks to a hockey wise friend who took me to my first game and coached me along until I started picking up the finer points of the game for myself. But having grown up on football, the one stat I don't see but ought to be there is Time Of Possession.
You don't have to follow Jim Tressel to know that field position really matters in hockey. You have to be in the offensive zone in order to get the puck past a goalie. And so long as the other team is in your zone, scoring is a definite possibility. One really good measure of how your team game is working is how much time is spent in the offensive zone. Teams sometimes do win who lose on that stat (like in football) but it's a good indicator of how a team played.
So the stat I'd like to see is how much time each team spends in the other's zone. Calculate it from the moment it crosses the blue line, time in the neutral zone doesn't count. Power play time should also count, but perhaps be separated off like basketball stats differentiate between offensive and total rebounds. Maybe the NHl teams keep it, but I think it would be nice if they shared.