The difference between plus/minus and even strength goal differentials

Earlier I had some discussions online, ending with myself being surprised with how many did not know the difference between the traditional goal plus/minus and even strength goal differentials.

Let’s take a look at the Jets as an example.


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Above I have separated most of the situations that go into the plus/minus statistic.

As we can see above, how a player performs at even strength serves as the bulk and then there are these additional situations that are incorporated into the statistic.

It should be noted, that the additional situations neither encompasses all other goals, and represents a very small ice time sample.

Some players can have their plus/minus heavily impacted by these additional situations, as we see here with Andrew Ladd:

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The Jets defenders offer some more interesting cases with the additional factors being larger, and in some cases having more impact than even even strength situations.

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The Problem

Goal differentials have issues with sample sizes. They are extremely rare: it takes over a season for a heavy-minute defender to experience over 100 events.

This is why we tend to see players fluctuate year-to-year with extreme values relative to their teammates.

This is also why Corsi, a shot differential including all shot attempts, both fluctuates yearly to a much lesser extent and also tends to out perform past goal differentials in predicting future differentials.

However, out scoring the opponent is the ultimate goal. Over a long enough period of time, goal differentials –with context– become valuable enough to where they should be a portion on how a player is evaluated.

Plus/minus though can be looked at two different ways.

It’s even strength goal differentials with some other situational goals added.

It’s all minutes goal differentials with some situational goals removed.

It is understandable what someone was trying to do when plus/minus was created long ago. They obviously were not a statistician, but the intent is at least obvious.

Plus/minus attempts to be a all minutes goal differential with context, but it fails as a useful number.

The Jets own Mark Stuart in this case functions as a serviceable example.

Stuart had the worst even strength goal differential for the 2014-2015 Jets. If one was to investigate further, this is due to three factors. Stuart has a poor impact on shot differentials and tends to be outshot significantly. He also played heavy minutes under difficult usage, although he had an exceptional partner help him out. Finally, there is some luck involved in shooting and save percentage variance.

Instead of being a negative plus/minus player, Stuart ended the regular season with a plus five score (plus three from above and then 4v4 situations).

A large portion of Stuart’s movement from the red zone to the black extends from the six goals the Jets scored while Stuart was on the ice as part of the penalty kill unit.

Stuart was on the ice for the most penalty goals for of all the Jets defenders. He was also on the ice on the penalty kill more than any other Jet defender. In fact, Stuart played more than nearly twice the amount of short handed ice time than any other defender not named Jacob Trouba.

While Stuart was on the ice for the most short handed goals for, he was also on the ice for the most goals against.

Plus/minus awards Stuart more than any other player on the penalty kill, despite not being the best performer on the penalty kill.

Since the move, the Jets have been their most porous with Stuart on the ice when down a player or two. The Jets have allowed more non-blocked shot attempts per minute than any other defender. Only Adam Pardy has allowed more scoring chances per minute.

It’s not just in the shot metric departments where Stuart has fared poorly. It is in goals as well.

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Hockey is a goal scoring contest. The ultimate goal is to out score the opposition.

Goal differentials, while flawed and susceptible to large variance without large multi-season samples, are a useful measure in figuring how players did in outscoring their opponent.

While the intent to adding context should be commended, plus/minus ultimately fails in this regard.

Adding only penalty kill goals for does not add the context of how well a player performs while short handed. Adding only power play goals against does not add the context of how well a player performs while at a man advantage. Adding pulled goalie situations sets a bias since particular players tend to play with a lead, while others tend to play while trailing (despite most evidence showing most players who are better at one are better at both).

We did not even touch on the aspect of ice time bias, with 1GF+8GA being the same as 151GF+158GA.

While goal differentials may be flawed, they are at least useful. Plus/minus though is fairly terrible.

Shot metrics are better than both anyways for most common situations anyways.