Hockey Analytics: Ditching Plus Minus

Plus-minus is the most useless and misleading statistic in hockey analytics today. Let’s address some of its problems.

If you read my angry writeup about goals against average, you will notice that I’m trying to keep it simple. Like GAA, plus-minus is a stat that only serves to mislead people in hockey analytics, at least relative to other superior measurements.

Many of its proponents will say that it was good for its time or it still has its use. This is simply not true. In any context, plus-minus tries to confuse people about how good a player really is. More often than not, no information is better than very, very flawed information.

The worst thing about plus-minus is that it pretends to be an advanced stat. When people see a terrible plus minus next to someone with impressive point totals, they tend to conclude the player isn’t that good. No! It’s just not that easy. Plus-minus is a terrible number for measuring how good a player is.

What’s Wrong With Plus-Minus?

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You might be wondering, how can plus minus be flawed? It measures how many goals are scored when you’re on and off the ice, right? Wrong.

Let’s take a look at Oliver Ekman-Larsson of the Arizona Coyotes. If you just look at his point totals and reputation alone, you might get the impression that he is a talented player; some would say one of the better defensemen in the league.

Well, that’d be incorrect. If we look at Oliver’s plus-minus, we can actually determine his true effect on the team. Look at that, his plus-minus is -28. This is why it is so important to look past point production and anecdotal defensive ability alone. When Ekman-Larsson is on the ice, more goals are scored against the Coyotes than for.

While he did have a -28, this hardly means anything. The Coyotes were one of the worst teams in the league last year. Even if he happened to be the best defender in the league, it is hard to maintain a good plus-minus when you are surrounded by an inferior team. Any player who plays a ton of minutes for a bad team is likely going to have a bad plus-minus rating.

This brings us to our first and biggest problem with plus-minus. The amount of control an individual player has over their own plus-minus is very tiny. Players make mistakes all the time. They can also excel at times. All too often, goals are scored, and you had nothing to do with it.

Similarly, all too often, someone messes up, and a puck goes into the net. Was it your fault? No. Does plus-minus care? No.

Another huge problem with plus-minus is that it doesn’t take goalie skill into account. Let’s create a scenario to expose this. Let’s say that two teams are identical, save the goaltender. On one team the goaltender has a .918 save percentage. In fact, he’s Frederik Andersen.

The other goalie is Scott Darling. He has a .888 save percentage. Let’s say that your team allows 30 shots per game, which is 2,460 over an entire season. Well, Darling would stop 2,184 while Andersen would stop 2,258. Through no fault of anyone but the goalie, the team with Darling would allow 74 more goals.

If you play, say, 20 minutes a game, and have a neutral impact on your team, then you would get 25 goals against because of the goalie. Because goaltending talent can vary so much from team to team, this is a huge issue. Plus-minus closes its eyes and pretends it doesn’t exist.

Additionally, a large variation also exists in goals scored. The Tampa Bay Lightning scored the most goals in the league this year, at 290. Meanwhile, the Buffalo Sabres scored the least, at 198.

Now, assuming every offensive line always scores the same amount, (obviously not the case, but we have to estimate sometimes) then you would lose the opportunity to gain 23 goals though, once again, no fault of your own.

The problem becomes even worse if you look at total goal differential. The GD between the Nashville Predators and Sabres is a 137 goal difference. Making the same assumption about scoring, this would put you 34 goals against in the hole.

So, at this point, it becomes clear that plus-minus is variable outside of your control. If you’re on a team that doesn’t like scoring or defending, or one with a bad goaltender (or vice versa) then it won’t really be possible to have significant independent control over it.

Because it doesn’t acknowledge so many variables, plus-minus is terribly flawed.

Replacing plus minus

Now it’s time for some wishful thinking. On TV, when they’re showing you a player profile, plus-minus is usually listed alongside other player attributes. This often misleads fans.

Now, unlike GAA, plus-minus doesn’t have a replacement that is commonly cited on broadcasts. However, if you read enough hockey blogs, then you’ll know about Corsi and Fenwick.

Corsi is like plus-minus, but it measures on-ice shot attempts instead of on-ice goals. A shot attempt is any shot at all: A shot on net, a shot that gets blocked, or a shot that misses altogether.

CorsiFor percentage is when you subtract Corsi allowed from Corsi for and turn it into a percent. If there are more shot attempts for than shot attempts against when you are on the ice, then you will have a positive CorsiFor percentage. Relative CorsiFor percentage also takes the team surrounding you into account, at least to an extent.

Let’s take another look at Ekman-Larsson. He has a CorsiFor percentage of 51.4, and a relative Corsi For percentage of 5.0 percent. This may be absolutely shocking, but, as we can see, Ekman-Larsson really is a talented player.

Corsi measures shot attempts instead of goals, which means that unlike plus-minus, it doesn’t have to worry about goalie skill. Additionally, since shots lead to goals, and there a lot more shots than goals,  shots are probably a better indicator of success than goals. Fenwick does the same thing but doesn’t count blocked shots as shot attempts.

Now, Corsi has its own problems that people are starting to address, but it doesn’t suffer from all of the uncontrollable variables that plus-minus does.  It would be wonderful if TV broadcasters replaced plus-minus with Corsi on TV. It truly is superior.

Anyways, use Corsi and Fenwick instead of plus-minus. They almost always provide more reliable results. Hockeyreference.com is a great place to start off your advanced stats career. If you really want to look at goals, even-strength goal differential is more accurate.

Plus-minus is very flawed. It really shouldn’t be used anymore, as Corsi and Fenwick are better indicators. Shots are inherently a far bigger sample size than goals, and we should acknowledge this.