I want to start with this: advanced stats are not perfect and are mostly useless as evaluators of talent (like pretty much any other stat) without context, and the bigger the sample size the more accurate a stat will become-ideally, for hockey, this means at least an 82 game season.
I understand some people might have issues when we bring up things like PDO, GVT, CorsiREL and other non-traditional ways of evaluation. In my opinion, these stats add to the game, and I don't want someone to be lost when they read an article here because they don't know what the hell Zone Start is or how it impacts a player's stature.
By no means am I an expert when it comes to these things: I, too, still have a lot to learn. These are my interpretations; if I have something wrong please bring it up and I'll edit the article accordingly.
With those things in mind, I present to you part one in a glossary of advanced stat terminology.
Corsi: the most popular advanced stat in the hockey blogosphere, Corsi is a possession metric developed by former Buffalo Sabres goaltending coach Jim Corsi. At its most basic level, Corsi is the plus/minus amount of shots directed at a net while at even strength-blocked shots, shots high and wide, shots that hit, shots that get tipped, etc. A player who has a positive Corsi has more shots directed towards the opponents net while he is on the ice at even strength then shots directed towards his own net under the same criteria. All 10 players on the ice are used when calculating this metric.
For example, if Mark Giordano is +7 in Corsi over the course of the game, that means he & Flames players he was on the ice with at even strength directed 7 more shots towards the opponents net then were directed by the opponents towards the Flames' net.
Most of the time we'll stop there, as any score effect bias generally evens out over the course of a season (unless a team really sucks or is really good, but there's that context thing). Basically, score effect means that a team will play differently depending on how far ahead/behind they are in a game-if a team is 3 goals up, they'll sit back and take more shots against then they would if they were 3 goals down.
So, to combat score effect, we can break down Corsi into 4 categories: Corsi Ahead (Corsi while the subject's team is leading the game), Corsi Even (Corsi while a game is tied), Corsi Close (Corsi while a game is within 1 goal either way relative to a subject) and Corsi Behind (Corsi while the subject's team is losing the game). With these tools, we can eliminate most scoring bias within the stat. All of the breakdowns have their purpose, but when trying to evaluate a player, the most important breakdown is Corsi Even-a team won't be taking risks and won't be sitting back when a game is tied, they'll be playing as "normal" as possible.
Fenwick: Named for Battle of Alberta writer Matt Fenwick, Fenwick is almost the exact same as Corsi, but it doesn't count blocked shots-the reason for this is that it is entirely possible that blocking shots is a skill, and not just a series of random events.
Why Only Even Strength?
First, because about 75% of the shots taken over the course of an NHL season are at even strength.
Second, the amount of PP and PK shots directed towards the net generally cancel each other out over the course of a season, rendering them unnecessary for calculations. Besides, a team is expected to bleed shots when down a man and vice versa. (Edit: It's more individual then anything. Someone who is a PK specialist but never features on the PP would be unduly penalized by the stat. Thanks for bringing that up, Mike.)
What do these stats tell us?
These stats are reliable metrics for possession-logically, the more shots a team is able to direct towards the net, the longer they have the puck. The term "direct" is important here, since a team could be +30 in Corsi collectively, but because of bad luck, be behind in the shot count. Plus, there's the ever present scorer bias in NHL arenas-home teams generally get more shots recorded.
Corsi is used in many other stats, and we'll take a look at those down the road.