The Devils just signed Damon Severson to a 6-year $25 million dollar contract. The comments in our post about it seem to be pretty unilaterally positive. Furthermore, in my experience, the readers of AAtJ — or at least those who comment — tend to be quite statistically literate when it comes to modern hockey analytics. Therefore, you are unlikely to be highly concerned by the fact that Damon Severson had the 3rd lowest plus-minus in the league last year. That said, the average hockey fan still lives in a world almost exclusively led by individual, point-related stats. So when that Corsi-hater looks up Damon Severson on NHL.com this is what they see:

You see a player who got a lot of assists but can’t really score and has a bad plus-minus. While I mostly interact with analytically-inclined fans, I tend to believe that I live a sheltered life because when I step outside my typical social circles, I do run into people that live and die by the eye test and points almost exclusively. Due to the fact that shallow stats are likely to taint the view of Severson, I decided I’d attempt to dispel some of those rumors by explaining why Severson’s plus/minus is what it is.

The Failures of Plus/Minus

If you peruse hockey twitter long enough, you’ll find plenty of vitriol on the topic of plus/minus. It’s like the blue or gold dress of hockey if ESPN and NHL.com were the only people that thought the dress was blue and everyone else knew they were idiots (Side note: It is still and always has been white and gold. I’ll fight you). You will see a few articles on the topic with such sympathetic titles as Why Plus/Minus is the Worst Stat in Hockey and, slightly less sympathetically, Behind the Numbers: Why Plus/Minus is the worst statistic in hockey and should be abolished.

There are many reasons that plus/minus is a terrible statistic and if you’d really like to know them all in depth, I suggest you browse those articles. But some of them are really simple and I’ll enumerate them here and then explain how I’ll adjust for them.

Plus-minus is non-discriminatory about team quality and so players on a bad team will have lower plus-minuses regardless of how well they play. Plus-minus is inflated by time on ice. If Player A and Player B are of the same skill level and same team, but Player A played twice the minutes, the magnitude of his plus-minus will be twice as extreme. Players are punished for giving up goals on the powerplay and rewarded for scoring shorthanded. This unfairly benefits those who play on the PK and unfairly harms those who play on the PP.

As you can see from these issues, Severson is adversely affected by all of these intrinsic flaws in the stat. I have decided to look into a very primitive expected plus-minus statistic that utilizes only the situations and team that a player plays on.

Methodology for Expected Plus/Minus

The methodology is to calculate the team goal rates in all situations (even-strength, powerplay, and shorthanded), then use the time-on-ice of the player in those situations to predict what their plus minus should be. The thing to notice about this decision is that it has absolutely nothing to do with the quality of the player. This is calculated using only the quality of the team, and the situational deployment of the player. For those interested, the actual formula looks like this:

The results are pretty impressively correlated (R^2=50%) to the reality. The graph below shows the expected and actual plus/minus of every one of 888 players available in Hockey-References year summary except for those who were traded midseason because I refuse to spend that much time on a plus/minus-related statistic. Severson is at the lower left and was given a shoutout.

You’ll see he’s below the line, but not actually by THAT much. The major contributing factors to his ineptitude in this statistic were:

The Devils were a very bad team He logged the 2nd most minutes of any player on the team His special team usage was heavily weighted towards the powerplay — during which the Devils gave up goals at the fastest rate in the league.

If you are interested in the breakdown of how each of those stats contributed to his and all other Devils’ plus/minuses, I’ve attached the table of all Devils players and the components of their expected plus/minus below.

As you can see from the chart, Severson was expected to be a -16.08 during his even strength ice time (second only to Lovejoy’s -16.11), a -5.07 during his powerplay time (worst among defenders, but above Henrique, Zajac, Hall and Palmieri), and got almost no positive contribution (+0.33) from his limited short-handed time. This adds up to an expected plus/minus of -20.82 which is 11th lowest in the NHL behind basically the entire Colorado Avalanche team and Oliver Ekman-Larsson. Again, this means that any player given Severson’s situation should be expected to be around a -21.

Now a couple things to point about this metric that shoot my point in the foot somewhat. Firstly, I’m using team totals. Severson was a part of the team, and a pretty big one at that. So, I’m using a statistic to which he may have contributed significantly, in order to prove that it’s not his fault. To that, I say ... meh ... aright. As mentioned above, I refuse to spend superfluous time trying to fix this God-awful statistic. With Corsica down, I don’t have access to off-Ice stats and so I’m using team stats as a surrogate. He played about a third of each game and was one of only 5 players on the ice during those times so if he is responsible for 1/15th of that stat, I can sleep at night. Secondly, you may have noticed that we’ve not yet explained all of his stat. He was an astounding -31 which was third worst in the league. His expectation was only -21 and 11th worst. Where did the difference come from?

What’s Left

In browsing the players with the largest error in my model, the list is dominated by players with extreme PDOs. For those who are coming late to the stats show, PDO is on-ice Sh% plus on-ice Sv% and has been dubbed the “luck” statistic by many. Manny Perry and others have since created xPDO models that add a little context, but they are still highly variant and seldom predictable. Simplifying it to potentially treacherous degree — PDO above 100 indicates lucky and below means unlucky. Severson has the 19th largest negative error from the expected plus/minus model (you can download the full workbook above if you’re interested). And, of the 18 guys ahead of him, only 3 had PDO above 100 and only one was above 101. The average was 98.1 and Severson’s was 97. In other words, the common denominator in players that finished below their expected plus/minus was poor luck, not poor play.

At even strength, Severson was on the ice for 617 Shots For and 658 Shots Against for 1275 total shots. His PDO was 97% which is 3% below the expected. That 3%, if applied to his shots for, would give him 18.51 extra goals for. If applied to his shots against, it would remove 19.74 goals against. Let’s split the difference and say that his PDO was worth about 19 goals. His expected plus/minus had been roughly -20 and his actual was -31. So we had -11 left over, and accounting for the PDO differential of 19, he now gets brought all the way to a +8. Once again, it’s possible that I’m being too accommodating, though. After all, the entire Devils team only had a PDO of 99. If we regressed to that instead, it would still be worth about 13 goals making him a +2. I reiterate that regressing to the xPDO would be better, but Corsica is down and I cannot stress enough that I’ve already spent too much time debunking the steaming pile of randomness that is the plus/minus statistic.

Conclusion

To review here, the purpose of the exercise is to explain Severson’s -31 plus/minus. Of that around -20 can be explained by team quality and usage. There is -11 left, and regardless of which model we’re using, we can say somewhere between -12 and -19 goals is attributable to PDO. This moves Severson into the positive territory and should alleviate any huge concerns about his performance. This is not to say he is a great defensive player. DTMAboutHeart has is Defensive Goals Above Replacement as 4th on the team among just defenders — below Lovejoy, Greene, and Merrill. He definitely has work to do which is why even after adjusting, his plus/minus would still be rather low. But he is not the liability in his own end that the plus/minus atrocity would have you believe.

Your Thoughts

What do you think about the plus/minus statistic? Are you convinced that Severson’s is explainable using nothing but luck, team quality, and situational usage? Or do you still think Severson is responsible for some? Do you blame him for the Shorthanded Goals against on his watch? Do you think he was giving up higher quality chances? Thanks for reading as always, and leave your thoughts below!