Prior to the trade deadline, I wrote an article analyzing whether or not Robyn Regehr was a good fit for the Kings. Using some possession stats, I concluded that the Kings would be better served looking elsewhere. Beyond that post, which only included evidence from this season, his numbers historically suggest that he likely suppresses his team's ability to gain and hold the offensive zone. But that isn't what he's asked to do--nor is possession everything.
My purpose in writing that article wasn't to argue that Regher would be making the team significantly worse if acquired. It was to present evidence that he was likely being overvalued. Consider this: at $4MM, Regher has a larger cap hit than Alec Martinez, Slava Voynov, Keaton Ellerby, Davis Drewiske and Jake Muzzin combined. In addition, they gave up two second round draft picks to get him. Under Dean Lombardi, these are the players that have been taken in the 2nd round: Joe Ryan, Oscar Moller, Wayne Simmonds, Slava Voynov, Kyle Clifford, Tyler Toffoli, and Christopher Gibson. Not a bad group.
On the bright side, Regehr only has one year left on his deal, and if he's brought back it would presumably be at a cheaper price. It also gives them some flexibility in contract negotiations. It's likely that they'll only be able to keep one of Scuderi and Regehr-- and they'll probably take whichever will come cheaper. But the question is: are the Kings getting enough value in this trade? The narrative is that Regher brings toughness and a veteran presence to a defensive group that has little of it due to the losses of Matt Greene and Willie Mitchell.
The real reason the Kings don't block many shots isn't from a lack of grit, it is because they are one of the most elite puck possession teams of the last 5 years. The puck is rarely in their end. If the puck is rarely in your own end, there aren't going to be very many shots to block.
The player Regehr is currently replacing in the lineup is the poster child for this perceived lack of toughness, Alec Martinez. Martinez's weaknesses are in his defensive zone play. He appears soft in front of his own net, sometimes gets beaten on one-on-ones, plays looser in his gap control than the staff would like, and is slow to improve in these areas. He's just not comfortable yet (maybe never will be) in the Sutter/Stevens defensive philosophy.
It is evident, though, that he positively affects team offensive zone time. Using a variety of methods we have at hand and over large samples of data, we can conclude that Martinez provides a boost to his teammates' possession numbers. He is a sure handed passer and a strong skater which makes him an asset in break-outs and neutral zone play. These abilities fit in well with the flow of the Kings' offensive system, and his poor defensive zone coverage is made less dangerous by the fact that the Kings are insanely good at pushing the play forward. Thus his mistakes in the defensive zone are relatively infrequent, but when they do occur we tend to remember them and those instances shape our opinion of him as a player. It is hard to recognize and remember the small plays he makes (i.e. being first on the puck, making a solid first pass, deciding to skate the puck out of the zone at the right time) that positively affect the team. These small plays are enhanced by having very good teammates who then build on this first good play by making a series of others. By the time a scoring chance occurs, we probably have forgotten what started the play in the first place.
The problem with a player like Martinez could be that when he doesn't have the benefit of being on a top possession team, his defensive zone coverage might be more of a liability. On a team with forwards that aren't able to maintain control of the puck, Martinez's skills might not offset his defensive deficiencies.
But within the context of this team, Alec Martinez at a $700K cap hit and Davis Drewiske at $600K are far more valuable assets than Robyn Regehr at a $4MM cap hit (for more evidence that Davis Drewiske may have been undervalued, see this post). Robyn Regehr is at his most valuable when there is breakdown in the zone and the team needs someone to clear the crease or block a shot. For the Kings, these breakdowns don't occur very often relative to other teams. They already allow among the fewest shots against in the NHL.
That being said, Regehr is here. Was the trade a huge blunder? No. It would have been nice if the team could have used the cap space on an additional goal scoring threat, but in the current marketplace the cost of that was probably prohibitive. Yes, the team overpaid for him, but that in and of itself doesn't affect anything in the short term. The fact of the matter is whether you think Regehr or Martinez are good or bad players, they probably aren't going to be accorded roles in which they have anymore than a marginal impact on this team one way or the other. The Kings were an elite team due to rattle off some wins before the trade and they will continue to be so after.