I want to start out saying that I honestly don't know a lot about any advanced statistics in the NHL. I know more about baseball stats, but comparing baseball stats and hockey stats are like comparing cat owners to dog owners. One game has very clear start and stop points that makes it easy to gather objective data (pitcher throws ball, batter hits it to the shortstop, shortstop throws him out, next batter, MOVE ALONG TO NEXT DATA POINT, HUMAN), the other is a free-flowing and ever-changing game with fewer similarly produced setups that occur from a stoppage in play.
I also want to point out that I do like stats. That'll be apparent after you read the wall of text after the jump. I also like to take them with a grain of salt and understand that they are not actual predictors of any given situation. A shooting percentage of 20% doesn't mean that you must get the puck to that player and have him shoot 5 times per game.
Perhaps some of what I suggest already exists. Again, I know nothing about advanced hockey stats and really don't have the time to dig right now. I am going to attempt to look at the one stat I think has been getting a lot of attention lately: shots. They have become the new way to determine whether a team WINS OR LOSES THE FUTURE. Jump with me into your more immediate future to see some of my ideas in ways we could improve our understanding of the one stat I think we've seen beaten into the ground.
Next, you could add some flavors to the shot stat. Add the distance from goal to every shot. Longer shots should give the goalie more time to react. Each type of goal is often recorded in scoring, too, yes (wrister, slap shot, tip-in, etc)? Add that, but for shots. That slap shot from the blue line got re-directed into a tip in shot. They potentially have a greater chance of generating a goal since you are reducing the chance of the goalie reacting, but you are also potentially redirecting the shot wide. Another thing that is handy would be one-timers. Obviously a lot of goals are scored by a quick pass laterally across the goal to someone who one-times it past the goalie who can't react in time. Accounting for some sort of movement before a shot will help build a sense of what actually works.
From there I say you record EVERY shot, not just shots on net. How many shots end up going 3 feet wide of the net? Are deflected and go into the stands (or ideally the netting)? Slightly harder to do since it may be hard to deduce what was a shot and what was a dump behind to the boards just trying to maintain the zone. Or whatever. Stay with me, I'm going even more subjective.
From this I think you can get to the meat of what a lot of us are asking for: was the shot impeded in any way? Was there a defenseman's stick poking in at the shooter or the puck as it was shot? Was a defenseman standing in front of the shooter? Was the shooter being checked at all? The problem here is there is a lot of subjective data in what I just proposed. But hockey does have subjective stats already. What exactly is a hit? Why are some recorded and some not? (I could probably Google this, but please tell me in the comments what it is.) Is it when you knock someone off the puck, follow them into the boards, cause them to pass earlier than they wanted? Couldn't you bring that level of scrutiny to a shot? (Just how much impediment is a stick check vs a body check?)
Were there a way to get a reliable and third-party source (Nate Silver?), I think this would shed some light on how offensive and defensive systems actually work. Where are unimpeded shots coming from? Do those unimpeded shots result in goals or do they often get saved (or go three feet wide)? Where are the best places to park a defenseman? When is it best to let a shot happen and where do you absolutely want to stop a shot? Where should we be concentrating our shots on [Insert Enemy Goalie here]? This also just made me thing that you'd probably have to add another layer into each shot as well concerning whether or not the team gained the zone on a breakaway man-advantage, or if it was a play that developed through some clever forechecking, passing, and zone awareness.
Yes, I realize that teams probably already do a lot of things similar to this on their own. They probably have people pouring over tape every day seeing what other teams are doing, what's working, what's not, etc. Sadly we are not privy to team data for obvious reasons. Until our independent stat-trackers can catch up to this level and there are agreeable ways to quantify some of the subjective data, I still think we'll have people grabbing at stats that may or may not prove to be useful. Batting Average and Wins for pitchers used to be the holy grail in baseball. Now with other stats available due to an increased knowledge of the inner workings of the game and an increased use of technology and stat junkies to gather even more data from the game, their weight has been decreased.
I think shots are a good starting point because I don't believe that any two shots are the same. Nor does more shots necessarily mean more goals. I believe that is what a lot of us Wild fans are getting at. Maybe I'm completely wrong (and potentially missing a lot...I've had a lot of coffee today..). Perhaps after collecting data on everything I suggested would also suggest that the Wild are bad and OMG they are teh suck and GO FIGHTING STATS!! STATS WILL WIN THE CUP IN 16 STRAIGHT GAMES!!! If that's the case, well then, in the System I trust.