The +/- statistic in hockey is rightly denigrated for being flawed, but it still gets thrown around on broadcasts, the back of hockey cards, in player analyses, etc. The official stat credits every player on the ice for an even-strength goal with having exactly equal responsibility for every goal scored or allowed, which is rarely, if ever, an accurate reflection of any given goal. It also has the reputation of being an indicator of a player’s defensive abilities even though offense and defense are weighed equally in the figuring.
In light of the problems with official +/-, I have experimented with tracking what I’m calling a “subjective +/-” for the 2021 New York Rangers. Rather than giving every on-ice player the same amount of responsibility for goals, I have divvied up the credit for every 5-on-5 goal scored and allowed based on my own judgment of how much each player contributed to the play. My aims were to see how my subjective +/- compares to the official +/- and to get a sense for the relative contributions from players scoring a goal, earning an assist, and being on the ice for a goal without recording a point.
I only looked at true 5-on-5 goals, and had five units of responsibility to hand out for every goal for and negative five units of responsibility for every goal against. For example, on the below goal, I gave Phil Di Giuseppe a +0.8 for the forecheck pressure, Brett Howden a +1.9 for chipping the puck up ice and then making a nice pass, Colin Blackwell a +2.3 for the goal, and the Rangers defensemen received zero credit:
For an example of a goal against, on this one I gave Mika Zibanejad a -1.5 for losing the draw and failing to tie up the man in front, K’Andre Miller a -1.7 for failing to tie up the man in front, Adam Fox a -1.8 for getting caught on the wrong side of his man in front, and gave the two wingers no responsibility for the goal as they were covering their men at the points:
Add up all the responsibility from 115 5-on-5 goals for and 103 5-on-5 goals against, and here are the season totals (in the “subj. +/-” column):
| player | pos | subj. +/- | official +/- | subj/60min |
| Buchnevich, Pavel | F | 47 | 10 | 3.9 |
| Panarin, Artemi | F | 43 | 14 | 4.2 |
| Zibanejad, Mika | F | 24 | 2 | 2.0 |
| Chytil, Filip | F | 24 | 8 | 2.8 |
| Lafreniere, Alexis | F | 23 | -7 | 2.0 |
| Kakko, Kaapo | F | 21 | 3 | 2.1 |
| Blackwell, Colin | F | 19 | 2 | 2.0 |
| Kreider, Chris | F | 17 | -1 | 1.6 |
| Strome, Ryan | F | 17 | 6 | 1.3 |
| Di Giuseppe, Phillip | F | 13 | 2 | 2.4 |
| Rooney, Kevin | F | 8 | 0 | 0.8 |
| Lemieux, Brendan | F | 8 | 0 | 1.6 |
| Gauthier, Julien | F | 5 | -6 | 1.1 |
| Howden, Brett | F | 4 | -2 | 0.6 |
| Fox, Adam | D | -1 | 18 | -0.1 |
| Kravtsov, Vitali | F | -2 | -6 | -0.6 |
| Trouba, Jacob | D | -12 | 3 | -1.1 |
| Lindgren, Ryan | D | -15 | 20 | -1.1 |
| Hajek, Libor | D | -22 | 2 | -2.1 |
| Miller, K’Andre | D | -30 | 9 | -1.9 |
| Smith, Brendan | D | -37 | 3 | -3.1 |
The first thing to jump out at me is that the forwards are nearly all strongly in the positives while the defensemen are nearly all strongly in the negatives. That actually makes sense considering that forwards are counted on for offense more than defense and vice versa for d-men. In fact, I can precisely break down that division in responsibility from my subjective +/- numbers: On goals that the Rangers scored, I gave 77% of the credit to forwards and 23% to defensemen, while on goals allowed, I gave 62% of the responsibility to defensemen and 38% to forwards. (And even among forwards, centers carry more of the load than wingers, exemplified well by the second video above.)
This means that my subjective +/- stat is a totally different thing when it comes to forwards and defensemen. Depth forwards Brett Howden and Julien Gauthier come out ahead of team MVP Adam Fox in my numbers, but a -1 for a defenseman is much more impressive than a +4 or +5 for a forward. Official +/- operates as though forwards and defensemen are equally responsible for offense and defense, which is objectively not true.
And how about official +/-‘s assumption that all five players on the ice share responsibility for every goal? Well, I judged that exactly five players shared some of the responsibility on 25% of all goals. There were zero goals on which I judged five players to have had exactly equal responsibility. More often, I judged that three or four players contributed to any given goal:
| players involved | % of goals |
| 1 | 1% |
| 2 | 11% |
| 3 | 27% |
| 4 | 32% |
| 5 | 25% |
| 6 | 4% |
| 7 | 1% |
Even on goals on which five players shared responsibility, that responsibility was rarely close to equally distributed. I made a note on any goal that I felt was roughly, kinda-sorta in the neighborhood of being an equal contribution from five players, and that note appears on just 14 of the 218 5-on-5 goals from the year. So official +/- might do a good job telling the story about 6% of the time.
Here is the goal that I judged to be closest to a perfectly distributed responsibility of five players – four players touch the puck in quick succession and the fifth player helps screen the goalie:
(I gave Kreider, Lindgren, and Buchnevich a +0.9, Fox +1.1, and Strome +1.2.)
And just for fun, here is a goal to which I credited seven different Rangers contributing. The two Rangers that start the play in the d-zone then make a change while Artemi Panarin stalls while maintaining possession, and then the puck makes its way around four more players before finding the back of the net:
A few more takeaways:
- Pavel Buchnevich had a great year that seemed to fly under the radar a bit. I counted him as contributing to 48 5-on-5 goals for and dinged him on just 10 goals against. He and Panarin were in a class by themselves among Rangers forwards at 5-on-5. Buchnevich was also a key player on both the power play and penalty kill.
- Defensemen that stay partnered up for the majority of a year are naturally going to come out looking like equals in official +/-. For example, Ryan Lindgren ended at +20 and his partner Adam Fox at +18. And on goals against, I did rate Lindgren and Fox as being close to equals (-32 and -35 respectively). But when it came to generating offense, Fox did much more heavy lifting (+34 to +17), though you would never know it from official +/-.
- Once the season was over, Mika Zibanejad admitted that he was battling lingering effects from COVID at the beginning of the year. This chart of his cumulative subjective +/- could probably double as a graphic representation of how he felt throughout the year:
- Official +/- is worse than merely “flawed.” It is downright misleading while appearing to have some value.
- As for the relative contributions from goal scorers, assisters, and non-point getters…that will have to wait for another day!
Leave a Reply