Who's more valuable to their team? A quick look at Hockey Sabermetrics

This morning I was wondering which player is more valuable to his team: The player whose point total is through the roof? The player who scores the most goals? Or is it the player who has the highest +/- rating?

And thanks to a book I just picked up, I might have the answer.

In a seminal – and, for some reason, out of print – book on hockey and hockey statistics called “The Klein and Reif hockey compendium”, the authors Klein and Reif use a fairly simple method to get a players “true” +/- rating.

The main problem with counting goals or points is that it just measures the offensive output of a player – it says nothing of his two-way play. Goals for are just as, if not less, important as goals against are.

So the stat of Plus/Minus should be good, right?

But it’s not – it’s a good indicator, like using OPS for baseball, but it means almost nothing. A good player on a bad team can have a plus/minus in the toilet – and a bad player on a good team can have a great +/-.

So this is where Team Adjusted +/- (TA+/-) comes into play – it takes all goals scored (and goals scored against) by the team and filters out power-play goals, giving you what the team’s plus minus is. The formula is fairly simple: Team even-strength/shorthanded goals (Goals for – PPG) minus the even-strength goals for (total allowed minus PPG allowed).

Then, to get a player average, you divide by five (five skaters per side, right?)

So what does this mean? It’s easy – it shows what the average player on that team would have for a plus/minus. This, in effect, allows you adjust any player’s +/- so you can compare them equally.

All you have to do is subtract the player’s +/- from the TA+/- to get their adjusted +/- (PA+/-).

And there you go – an equal way to compare hockey player’s +/- without worrying about their team’s overall quality.

So how does this mean anything to anybody?

Let’s say I wanted to solve the question I posed above – which kind of player is better to their team? Would it be the point leader (Sidney Crosby, with 83 points)? Would be the goal leader (Vincent Lecavalier, with 35 goals)? Or would be it the regular +/- leader (Nicklas Lindstrom, with a +36 rating)?

Let’s work with the numbers, then. Here are the goals for each team.



Conversely, here’s what their goals against look like - Remember, the numbers go Pittsburgh, Tampa Bay and Detroit
Goals Allowed: 116 172 137
PP goals allowed:58 49 50
Even Strength Allowed Goals: 108 123 87

Now, here’s each teams adjusted +/- rating:
Even Strength Goals: 119 117 129
Even Strength Allowed Goals: 108 123 87
Adjusted Team +/- rating (AT+/-): +11 -6 +42

Now, remembering to divide by five, so we get a player average:
Raw AT+/-: +11 -6 +42
Average Adjusted Player +/- :+2.2 -1.2 8.4

So the average adjusted player +/- for Pittsburgh is 2, for Tampa Bay it's -1 and for Detroit it's +8.

So what does this mean? Simple: That’s the average +/- for any player on that team. We now can use that to adjust the raw +/- for any player. So, to go back to our original three players, we can just check their numbers by subtracting the average from their +/-:

So here, the numbers go: Sidney Crosby, Vincent Lecavalier and Nicklas Lindstrom
Regular +/-: +13 +6 +36
Average Adjusted Player: +/- +2 -1 +8
Player Adjusted +/-: +11 +7 +28

So, by looking at this – by seeing how much better a player is then his team’s average +/- and how important they are to the team - we can see three things: Crosby’s two-way play is a little overrated, Lecavalier’s two-way is a little underrated and Lindstrom, while playing on a team that inflates his +/- by a considerable margin, is still really good.

So there you go – Yes, Lindstrom is the most valuable of the three, since his two-way play (or perhaps just his defense skill) worth about 28 more points then the average player on Detroit.

Once again, thanks to the team of Klein and Reif for their formula here. It's a bit of a shame that they're not doing this anymore.