The closest thing I've come up with was +/- per game adjusted for team save percentage. It's not perfect, but it's the easiest solution. Might not be the best. Real time stats are not a good statistical indicator for anything really. Only other things you can really look at are Shot-Dif, Fenwick, or Corsi, or time the amount of possession across the blue line for each team. In general the NHL is way behind when it keeps track of stats.
Best advice, is base as much as you can on coach's decisions. It's a coach's game now, everything is systems and structure. Coach's essentially decide statistics (especially for goaltenders) today. If a coach puts a player in a situation to defend a lot (whatever metrics we have to measure that), that's the guy with the best defensive attributes.
im pretty sure road hits/blocked shots (the only fair way to measure) are both negatively correlated with goals against. both of those are things you do to get the puck - therefore, if you always have the puck, you can't do them
Usually a combination of stats taken with context and a dash of judgement can paint a general picture of a players game.
Take a player like Paul Gaustad this year.
Starts 21% of his ES shifts in the defensive zone (as lopsided as there has ever been in the NHL since the stat was recorded). He plays against average competition with around the same level of teammates. Despite his zone starts, he manages a Relative Corsi of just -2.0, which is very respectable.
His GA/60 is merely 1.45, which is absurdly low given his zone starts. He also chips in with a GF/60 of 1.45, meaning he breaks even (give or take a lot of variance due to a small sample size) with his matchup over the long run. Add in that he is used on PK as well, usually first unit (highest TOI/60 among forwards) and manages a respectable 6.34 GA/60
Given how Trotz uses him, being able to break even given a 21% zone start and similar competition, Gaustad is essentially a get-out-of-jail-free card for his coaches.
He is a major reason Buffalo is struggling badly this year, especially defensively (3.2 GA/game compared to ~2.8 GA/game last year and ~2.8 GA/game the year before that as well). His injury is also costing Nashville this year, as their GA/game without him this year is 3.5GA/game, compared to ~2.0 GA/game with him in the lineup. Quite the difference (sample size is a factor)
Nashville gave up a first round pick to get him. Buffalo wouldnt let him go for less. Nashville then signed him to their 4th highest cap hit, longest term for a forward extension. Shows you what kind of value a player like this has. Almost every fan, though, considers Gaustad to be a 30-point player or an OK third-fourth line tweener when, in reality, this is a "franchise" caliber bottom 6 player.
From the stats, you can determine that this is a very valuable player, and when you watch him to figure out the how and why, you see it's because he's got size and he's a decent skater and he's just a very defensively aware player.
First off, stats like hits, shots blocked, and takeaways are useless on their own. These are indicative of style but not overall effectiveness. Some players rack up massive hit totals, often on the forecheck, but are lackluster to bad in the neutral/d-zone. Shots blocked can be just as indicative of bad performance leading up to lots of plays where shot blocking is necessity, or poor skating/other defensive skills with blocking as a necessity to make up for such. Takeaways are a little more directly valuable, as removing the puck from the opponent's possession is always a good thing defensively, but situation and resulting play are important to look at (If you take the puck away, but then immediately turn it over to the opposition because you were in a bad position to perform a takeaway where you should have went with a more passive defense, and this results in a goal against, was it a defensively good takeaway?).
+/- is worthless on it's own. +/- adjusted for save percentage is a bit better, but still doesn't take into account the quality of teammates or opposition. I'm more impressed by a guy with an adjusted +/- of 2 that plays with 3rd/4th lines vs top line opposition than the sheltered 3rd pairing d-man that has an adjusted +/- of 10 playing largely against the other team's checking lines.
Fenwick and Corsi both have a lot more to offer in terms of analyzing the impact a player has on the ice, but you still have the savvy to be able to understand just what all of the substats together are saying and most importantly be able to correlate what you see in the numbers with what you see from watching the performance.
Usually, Fenwick and Corsi are what I use when I need to get a rough idea of how a player performs with whom, against whom, and in specific situations.