## Fancy Stat Summer School - Relative statistics

Tinordi had shockingly strong relative possession statistics in his call up to the big club. - Claus Andersen

Over the summer, EOTP is going to break down every fancy stat in order to help people understand what we're talking about all the time. Hopefully this series serves as a frame of reference throughout the future of the site.

##### What are relative statistics?

Relative statistics are a way to separate team talent from player talent. They're used both in possession metrics, and quality of competition metrics (which we'll cover later). The main purpose of relative statistics is to pull players out of the noise, on teams that are either really good, or really bad. This is a weakness of Fenwick and Corsi, as system and teammate effects can greatly change a player's raw numbers.

Relative statistics apply only to individual players, not to teams. They are calculated by finding the differential between a player's Corsi or Fenwick plus/minus per 60 minutes of ice time and the team's Corsi or Fenwick plus/minus per 60 minutes while that player is not on the ice.

##### Practical example

Once again we'll bring back Player A and Player B, and for this example we'll use Corsi. As opposed to the previous examples where we were looking at a fake single game of data, this time we'll be looking at a fake season's worth or so.

 Name Corsi +/- per 60 Team Corsi +/- per 60 while player is off the ice Player A 15.23 8.49 Player B 7.81 -2.65

Using this raw data which could be categorized as "Corsi on" and "Corsi off" for each player, we can calculate both players' "Corsi Relative".

(Corsi on) - (Corsi off) = (Relative Corsi)
Player A: 15.23 - 8.49 = 6.74
Player B: 7.81 - (-2.65) = 10.46

What we can see here is that even though Player A looked more impressive from the raw numbers, Player B ended up with a higher possession rate relative to his teammates.

##### What do relative statistics tell us?

In this specific example, they tell us that Player B was actually more impressive than Player A, in spite of the initial appearance that the opposite was true. This method is a good way to find good players on a bad team, or bad players on a good team.

##### What are the limitations of relative statistics?

Like we've said all along, you can't use them alone to evaluate a player. There are specific limitations as well though, as relative statistics lose a lot of their usefulness on teams that stack one line and don't have depth. Now you may think that's a bad strategy for any team, but it happens, and it happened in Montreal under Randy Cunneyworth in 2011-12

By the end of the season in 2012, David Desharnais was centering the team's two best wingers in Max Pacioretty and Erik Cole, while the Tomas Plekanec was stuck with rookie Louis Leblanc, and an injured Rene Bourque. Lars Eller was even worse off with Blake Geoffrion and Mike Blunden. Desharnais had the advantage of Pacioretty and Cole on his wings all season, which ended up giving him a positive Corsi Relative of 3.8, while Plekanec was a -3.8. Desharnais wasn't better than his teammates (including Plekanec), so much as he played with better players, while Plekanec took tougher competition with weaker linemates.

##### Criticisms

If you're looking to separate out a player's individual talent from his team's talent, relative statistics do a pretty good job. Where they fail though is in differentiating the player's performance from his linemates' performance. For that, we need to look at more intensive statistics.

As always, if you have questions, please feel more than free to ask. The comments section is an important part of this.

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