One of the largest problems we think that hockey statistics face is the problem of ice time. Regular hockey statistics are in terms of counting numbers, e.g. goals, assists, what have you. This misses the mark somewhat - a player who scores a certain amount of points in 12 minutes of ice time per game is almost certainly more valuable than one who scores the same amount in 20 minutes of ice time. So then, perhaps, we go to rates, as Behind The Net has done - Goals For (While On Ice)/60 minutes and Goals Against (While On Ice)/60 minutes. Almost all advanced statistics across sports are rate statistics, and these are no different. While they are certainly an improvement over nothing, there's still problems with treating all minutes the same, and they are as follows:
1. Level Of Competition
Whereas in baseball a batter (generally) faces the same defense each at-bat in a particular game, a hockey player may face a completely different set of players against him on any given shift. This problem explodes further when one considers that each player on a team may face different players on any given shift. This does not happen in football or baseball, generally - essentially, a player on a 4th line may rarely or never face a good line against him.
2. Quality of Linemates
A hockey player may have a different set of linemates throughout the season - ergo his stats may rise and fall depending on who he's playing with. Since this can change so often throughout a season, we cannot just throw this away as meaningless. Warren Young is the classic hockey example of being raised up by playing with great players - a career minor leaguer, Young got a chance to play with Mario Lemieux and led the league in shooting percentage on his way to a 40 goal season. He earned a lucrative deal with Detroit, where he flamed out - Young would only play 2 more full seasons in the NHL. Behind The Net has developed statistics for these two concepts, but they merely sort players in terms of how strong their competition is and how strong their teammates are - it has no meaning outside of that context, no coefficient to adjust other statistics by.
3. Denigrating the Strongest?
Some players are given much more ice time than others - how do we adjust for that? For example, Alex Ovechkin averaged 22:03 in even strength plus power play ice time, the highest in the league. Therefore, relative to every other forward in the league, his rate stats would be downgraded. But is there not some benefit to being able to play 22 minutes a game at forward? With a rate statistic, we are unfairly penalizing Ovechkin for being such a tremendous athlete that is he is capable of that much ice time - sure, there may be players capable of putting up similar rates to Ovechkin, but they're unlikely to be able to receive the amount of ice time he does.
The last problem is a problem of leverage, a concept that sabermetricians in baseball created to deal with relief pitchers and their usage. Some pitchers are routinely brought in with runners on base and are expected to put out the fire - others are only used when the team has a large lead or a large deficit. So we ask: How valuable were the player's minutes? A 4th line player might receive 13 minutes a game in a complete blowout, skewing his time on ice upwards, but would they be any more valuable than his normal 6 or 7? Furthermore, a tremendous scoring player might be left off the ice in the last 3 minutes when his team is ahead because he is a poor defensive player. We would have to come up with a way to quantify how valuable minutes are, likely looking at offensive and defensive zone faceoffs in the third period or overtime of close games.
Once again, we have no solutions for these problems, we are merely a gadfly. We have not even discussed just how much variance there is in a given season, which can also inject whatever statistics could come out of such an exploration with a great deal of uncertainty. It should still be instructive for general managers to observe these four items when considering a player for a team, however - buying a low-leverage player who got an inordinate number of shifts with excellent linemates is a good way to lose one's job.