The thing that stands out most to me is effort. All these advanced stats are really trying to quantify how hard a player tries, which is difficult because players of the same skill level with have different efforts, and effort can vary game-to-game and shift-to-shift.
Someone said in the other stats thread that the stats take the assumption that everyone is trying their hardest on each shift (or at least, all are trying equally as hard). This obviously isn't the case, but you really can't quantify the effort level of a player, who gives more and how much more often. Even if you strapped heart-rate monitors to each player and tracked each shift you still wouldn't be able to get an accurate picture of this (different body types/different heart rates, etc..). And even if you could, there is no way to measure how much the effort of one player has on the rest of the team. Advance stats basically ignore these things like they don't matter but they do, huge. How the captain of a team carries himself and applies himself to the game affects everyone else. How the star player applies himself affects the whole team. How the coach carries himself both in winning and losing affects the whole team. None of these "emotional" traits can be seen in the stats.
The stats can say what they will, but there are certain things that you will never be able to track. And, in hockey, because of how the game is structured with changes on the fly and necessary contributions from the entire group of players, these emotional traits play a very important role in team success. Stats essentially ignore them because they have too.
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