I don't distinguish between 'advanced' and 'regular' stats. They're all stats...
Should we say JVR is a crappy player because his rel CA stats suck? I don't think so, esp when the rest of his numbers are pretty good. But it's a good start to a discussion...
Well, what they tell you is that JVR played on what was probably the worst defensive line in the league in JVR-Bozak-Kessel for a number of years.
You can reasonably infer on that basis that JVR is a poor defensive forward. Although you make allowances for position as JVR is a winger, thus typically has less defensive responsiblities, thus likely can be put in a position where he is sheltered defensively by his center and defenseman teammates. Regardless, his numbers suggest a player that you'd only want for his offense and probably needs to be carefully managed to be useful, something any close observer of JVR in Toronto would likely agree with.
Gallagher on the other hand, has the numbers of a player that can be plugged into any 5 on 5 line and make it better all over the ice, and does this at an elite level. Which close observers of Gallagher's past 4 seasons should also agree with, although he typically doesn't get enough credit do to the persistant bias against players of small size.
Straight shot differntials aren't as effective at evaluating forwards becauses there are significant differences in finishing skill and quality of chance generation that need to be accouted for which will effect the ability to produce goals. In Habsland terms there are Gomezs (awful shooters, great at territorial play), Moens (mediocre territorially, bad shooters), Vaneks (great offensive zone players, awful at territorial play) and Coles (above average shooter, good territorial players).
Defenseman are quite a bit different, their affect on team shooting percentage is pretty small and sometime counter-intuitive (both Erik Karlsson and Shea Weber are probably on balance bad for team on-ice shooting because despite having good shots for defensemen, they take so many shots it changes the balance of shooting towards the outside of the offensive zone and away from the forwards in a better position to convert). Meanwhile save percentage is driven primarily by goaltender skill and team defensive structure, neither of which an individual defenseman has a strong control over (even the ultimate man-mountain in Zdeno Chara didn't have a save percentage all that different over the long hall than his teammates, his defensive brilliance was in shot-supression). So shot differentials do a pretty good job of looking at defenseman contributions to even strength play, and even more strongly converge towards goal differential in the long run.
Goal differential is what you actually care about, because its what actually wins hockey games, but over the short run goal differential is controlled more by random factors and shot differentials give better information about the trends in play.
You can off course, build even better models if you correctly weight the expected goal value of a shot, most of the public systems that try to do that don't work very well because
1) NHL play by play information records who made a shot fairly reliably, but not the information surrounding it well at all (i.e. location etc.)
2) they are usually based on shot location, which is something of a factor, but the most important element of shot quality is puck movement prior to the shot, not where it came from so its less effective.
Also, for those holding out that wise NHL front offices have gigantically superior systems that make all outside analysis look like chumps playing number games, everyone I've talked to who went from outside the system to inside it to "look under the hood" so to speak intimate that the NHL systems really aren't that sophisticated (no, NHL teams didn't secretely hire brilliant data scientists to do their work, the reason they hired bloggers to do it was that the bloggers were the cutting edge at the time).
