MOD EDIT: Posts 1 & 2 were moved from the Past Studies thread to reduce clutter in that thread. Please see post 3 for the actual beginning of this thread.
I studied the "with or without" effect (team results when player participating in game, vs when he didn't) for all players during all the last 25 or so seasons, lately even the goalies, also comparing (by game by game basis) to an "expected" game outcome. I also studied how some players' point production was affected when certain other players wasn't around. This is, as I see it, things that would be of great interest, considering all the debates upon how much different players were helped by each other, etc.
I've studied the strength of different year groups too. And lots on adjusted scoring, scoring distributions, the effect of faceoffs, situational adjusted goalie stats, penalty killing stats where attempting to taking away the goalie effect, different kinds of adjusted +/-, a combined overall player stat for ES+PP+SH, "how easy it was to produce points during a certain season", schedule adjusted standings, individual winning %, etc.
I find a problem with basically all studies here (including my own) in that they require a lot of work and time. There are usually many hours of boring research to have to be done, in order to learn and know about many factors leading up to the end results. There also seem to basically always be factors "biasing" things, including (of course) "randomness" or "circumstances".
(To use a common example, people often try to determine who produced more impressively between peak Gretzky and peak Mario. We can adjust based on mathematical methods, ending up with adjusted stats. But then we also want to know how much teammates affected their stats, or playing system. And in the end, we just end up with more or less arbitrary "feelings" of who did best.)
So, I think there needs to be done "boring" research in order to progress. To sort of lay foundations or reference to build upon. There are so many more or less automatic assumptions being done, and I think those too needs to be closely examined.