Thanks for the replies so far!
If you would attempt to quantify your thoughts, what would that result in?
I am thinking of a way of combining ES, PP and SH contributions into one stat. I have a plan for how to do it. I think/hope one can determine how much more difficult it is to outscore opponents in different situations, etc. But even if I would succeed with that, I came to think about the effect of tiring. It would have been nice if PP, ES and SH was about as tiring. If they're not, I suspect it might bias things. Ideally, I would like players' total ice times during games to not be biased.
Let's say SH is most tiring, while PP is least tiring. Do you think it will affect the total ice times? Or do players generally just rest for a shift or two and then become relatively restored?
Example... Player A played 20 minutes, distributed 0+16+4 (PP+ES+SH). Can one generally expect that the 4 minutes of SH had a negative (or for that matter positive) effect on his total ice time? (Would he have played say 4+18+0 if he had been used on the PP instead?)
Nice attempt plusandminus - but it might be a bit futile, too general, wouldn't address all the situational play that is the biggest influencer of the TOI, the goals for each player during that time, etc.
First, I completely agree with C1958: PK > ES > PP in terms of difficulty. On the PK, the amount of start-stop, physical play in front, fwds dropping to block shots, fighting for pucks along the boards in grueling. But not all players kill penalties that way. I watched Nielsen-Grabner on the NYI and they are thinking open ice = goals while killing penalties. Not all minutes are equal and not all players play them the same way.
Ryan Smith in front on the PP, battling down low, cycling - much tougher minutes than Lidstrom on the point.
Ovechkin can play the full 2min of the PP and still be somewhat effective. Mario easily could play the full PP because he moved in slow motion as much as he wanted to but was always dangerous.
I understand you probably will have a generic approach and over enough data, the outliers might become less relevant but I believe it's significant.
Another point is the context of the game.
Playing ES when you're up two goals is FAR EASIER than when you're down two goals.
Top offensive forwards on bad teams always have really poor +/- (Kovalchuk, Tavares, last year) They're typically tasked with scoring goals on teams that seem to trail most of the game. They also play against EITHER the best checkers or the opponents top line (typically harder to play against)
A 4th line player, playing against another team's 4th line - they're just there to kill time and allow the better players to rest. Lot of neutral play, uneventful forechecking, etc.
For me, the BIGGEST piece missing from stats, adjusted or not, is the contextual play that drives the game. Coaches coach to win games, not just to outscore a team in every minute of play.
Watching the trap-version of the NJD play you can see a guy like Elias (a gifted offensive player) simply dump the puck in and not forecheck hard because all he had to do was help protect the lead. As long as Marty was in net, Stevens/Niedermayer/Daneyko and friends on defense and every player clogging up the middle, hooking/holding players on the rush - the game was easily in hand.
Those became easier minutes for a NJD player and incredibly difficult minutes for the opponents.
Love the direction you're going with this and certainly the numbers will be interesting. But I think you lose a lot of the insights without the proper assumptions and context.