Don't let the title deceive you, I am a giant nerd and I love advanced stats but let's be honest here Corsi stats have absolutely nothing to do with puck possession. Nothing. Zero. Zip. Zilch. Nada.
Corsi and her related statistics such as relative Corsi should be re-branded as shooting metrics simply because that is exactly what they are. They are not possession metrics so stop confusing people who can't understand this and call a spade a spade.
I'm a pirate. I don't have cable. I stream games for free and the other day I was watching an Islanders broadcast of the Leafs vs Islanders and the broadcasters were terrible on all accounts, but their understanding of Corsi was abysmal and it is not their fault.
I've watched feeds from Dallas and the broadcasters were great. Many MSG broadcasters are great so I'm not just an arrogant Canadian who thinks Don Cherry is the only man who knows hockey.(He's getting a wee bit senile isn't he?)
They were talking about possession metrics and mentioned that the Leafs were 5th in possession and the one guy said something ridiculous. I'm paraphrasing here: "Yeah, it's nice that we have the puck all the time but whenever we don't have it we give up goals." Then he said something brilliant. "You have to outscore your opposition." Bingo! That is the purpose of hockey. If you score more goals than the other team during the game you win the game.
These poor guys actually believe that the more shots and shot attempts a team makes somehow correlates to the amount of time a certain team or player possesses the puck. I don't blame them because Corsi is labelled as a possession metric which it absolutely is not. The underlying theory is that if a team or player attempts more shots on the opposition than the opposition attempts on them they must have the puck more often. The theory makes sense except that it is terribly presumptuous.
Let's look at the example of the Maple Leafs and specifically Nazem Kadri(because I watch every Leaf game so in this instance I am certain that I am right.) The Leafs are the 5th best team in shot differential but that doesn't mean they have the puck more often than the opposition. Nazem Kadri specifically shoots the puck often. He takes many shots that have almost no chance of going in the net and he takes shots that are guaranteed to hit the pads of the opposing defender.(Phil Kessel anyone?)
I remember back in October or November an interview with Naz in which he mentions that Babcock told him to shoot and shoot often. This is the reason he takes so many low-chance shots. This is also a great strategy for the Leafs or any team lacking high end talent. If you can't snipe, put the puck on net and get some greasy goals. The game tying goal in the Islander game was off a rebound of a low chance Kadri shot - so it can be effective.
How does this relate to Corsi and possession? In theory(I haven't tested it) but if you are shooting many low risk shots on net that means that in fact - you are possessing the puck less often. Rather than holding the puck to find a high quality scoring chance you are firing it and hoping to score on a rebound or regain control.
In some cases a high Corsi team will possess the puck more often because they are simply that good. In some cases a high Corsi team will possess the puck less often because they are not good enough to employ a high possession strategy so they shoot from anywhere and go for the greasy goals.
Long story short - Corsi is a very useful stat - but it has absolutely nothing to do with puck possession. Zero. Zip. Zilch. Nada.