Why Plus/Minus is the Worst Statistic in Hockey

BillDineen

Former Flyer / Extinct Dinosaur Advisor
Aug 9, 2009
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Argument could be used for Corsi as well. It has to be viewed in context just as +/- does. If you watch the Flyers you know Hartnell's high Corsi Rel is due to playing with Giroux and Voracek.

Let's assume you take a line in which all players have identical stats, but two are creating chances and the third is generating his production off of easy finishes, rebounds in front etc. If you took the 2 offensive catalysts and played them with multiple other players their stats would still be relatively good, but if you took the third player and played him on another line, his stats would be relatively poor. (This assumes all three are equally competent defensively as well).
 

skillhockey

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Feb 26, 2013
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Over many years it's good indicator of forwards 2-way game. When same guy is better than his teammate over several year period, it's sign of something, either he's doing great or some player he's playing with is. You can compare toews and kane, they play for same team and their +/- has huge difference over few years.

You can also compare stats of eric staal and alex semin before he joined and while they both played for the canes and times when semin was out(staal getting minuses). This is somewhat smaller scale but it anyhow looks pretty clear to me what huge difference it is for staal to play with semin.

It's not useless statistic especially when comparing teammates to another over long period of time.
 

Ohashi_Jouzu*

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Hmm, the article is actually quite bad. It is built on the strawman that +/- is a predictor of a player's ability overall, and not, say, whether he was used correctly and in an appropriate role. Instead of taking the stat as something the team can combine with other data such as minutes played and the opposition being played against, you took it as a characterization of an individual taken outside of the context in which a certain number was achieved.

Conclusion #1 is just silly. Of course you don't conclude player A is twice as good based on that stat alone. First of all, the absolute difference in +/- is merely ~1, and it's you and you alone who created the strawman that measures players' abilities by relative value in regards to their +/-. Secondly, the results of your analysis show that over the course of a season player A has been on the ice for 2.733 more goals for than against, and player B has been on the ice for 1.367 more goals for than against. Instead of looking at this from a perspective of the coach, who assigned them these different roles based on what his expectations were of the lines those players played on, you take it out of that context. The coach might very well have intended for player A to play on a dominating line, for which he was hoping to outscore the opponents by, say, 10 goals over the course of the season. On the other hand, he might have assigned player B to a shutdown role whose purpose was primarily to prevent opponents' top lines from scoring and give the top guys a rest. In that context, the +/- stat would have been useful in telling the coach that player B's line more than fulfilled its goals, whereas player A's line did not. In fact, since they're the same player, the numbers might tell the coach that he is better suited for that second role. In my opinion, that's useful to know.

Conclusion #2 is based on the assumption that in 1640 minutes played, the goalie just happened to have whiffed ~11 times more while player B was on the ice. This, with no regard given to the possibility that player A infuses more confidence. Or that player B was paired/grouped with different players, who might add to the explanation. Or that player A was playing against worse competition.

Finally, conclusion #3 is also based on luck. You have created this preconceived and unchangeable notion that nothing differs between the players. Fine. But you refuse to accept the fact that if two players are exactly the same, playing with and against exactly the same players and engaged in exactly the same roles, then the probability of such a disparity between shooting percentages over the course of a season is exceedingly small. Extending such generosity of doubt to other stats, then you pretty much can't take any of them as a predictor of anything. Because when plotting the distribution, pretty much any value for any stat will have a certain probability to occur, no matter how small. If, however, you know going into this that variability in +/- up to a certain number, determined by whoever wants to interpret the statistics, can be explained by chance, then that person will have no trouble realizing that the discrepancy that occurred actually could occur due to chance and that no firm decision will be made based on it.

This post pretty comprehensively summarizes how I feel about it. "I'm a lazy fan who is highly dependent on stats as a surrogate for my ability/willingness to put in the otherwise necessary observation time, and I need easily sortable and definitively descriptive numbers to rank players for me without the burden of context or developing my own understanding"...
 

treple13

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Sep 1, 2013
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You could theoretically write this exact same article using "goals" instead of "+/-" and end up concluding the exact same thing about goals being the most meaningless stat in hockey.

Goals scored depends on usage
Goals scored depends on goalie save percentage
Goals scored depends on shooting percentage

Certainly there are a lot of factors at play that make small sample size statistics more or less reliable, and plus/minus is certainly not the most reliable indicator especially league wide where those three have a wider variance.
However both goals and plus/minus are stats that hold better in team or in line comparisons as the variables are more likely to be evened out. Thus both statistics do hold value in determining a player's value (in conjunction with a lot of other numbers). A player with a lot of goals on a team that doesn't score a lot or a player with a good plus/minus on a team where most players are minuses are scenarios that may cause you to evaluate that player's value in those contexts.
So to say plus/minus is the worst statistic is so blatantly false. If you said most misused, I could see an argument for that. Even within hockey, there a number of stats that tell less of the story than plus/minus such as hits. Plus/minus tells you something for sure and over the course of a number of seasons on both good and bad teams, you are likely to get a picture of a player that tells you a more clear value.
Since the example is Alexander Ovechkin, his -35 can be viewed in a few ways. Certainly it tells us he had less 5-on-5 effectiveness this year than other years. His team was also much worse this year than other years, not making the playoffs so that would explain some of the drop. But his overall plus/minus numbers season to season tend to make you think that this season is an outlying statistic that will likely go back to the mean next season, closer to the 2 or -8 he was the two years previous.
 

JoelWarlord

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May 7, 2012
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This post pretty comprehensively summarizes how I feel about it. "I'm a lazy fan who is highly dependent on stats as a surrogate for my ability/willingness to put in the otherwise necessary observation time, and I need easily sortable and definitively descriptive numbers to rank players for me without the burden of context or developing my own understanding"...

Uh... what? The whole point of the post was that +/- is used that way and it shouldn't be. The entire point of this is that putting context into +/- shows that it's a very volatile stat with little predictive value. Ovechkin through his career has been +2, -19, +28, +8, +45, +24, -8, +2, and -35. He's been all over the map and his -35 tells us next to nothing about his performance this year or going forward.

People all over the hockey world are calling Ovechkin a bad player for his +/-, and the guy who writes an article putting the number into context and discrediting that idea is the lazy fan?
 
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Ohashi_Jouzu*

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Apr 2, 2007
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Uh... what? The whole point of the post was that +/- is used that way and it shouldn't be. The entire point of this is that putting context into +/- shows that it's a very volatile stat with little predictive value. Ovechkin through his career has been +2, -19, +28, +8, +45, +24, -8, +2, and -35. He's been all over the map and his -35 tells us next to nothing about his performance this year or going forward.

People all over the hockey world are calling Ovechkin a bad player for his +/-, and the guy who writes an article putting the number into context and discrediting that idea is the lazy fan?

Uh... what? The entire point of the article, and I'm directly quoting here, was:

"The take-away, friends, is that plus/minus is completely unreliable. It's meaningless. It's even worse than meaningless, because belief in plus/minus actively damages attempts at meaningful analysis. So please, let's stop using it."

Which is to say, the author is obviously still figuring out hockey on a fairly fundamental level if he's completely unable to glean any information from it, and thinks it actually - in and of itself - prevents anyone from understanding anything.

People who watch games the most still have more accurate "predicting power" than even the most ardent stats manipulators, btw, and I can understand how that frustrates the actuaries and pencil pushers who are trying to participate in such a great game on the level they're most comfortable - from the computer chair with Excel (and Youtube) loaded up, the morning after. And yes, attempting to use a spreadsheet and data set as a surrogate for experienced viewing is lazy, no matter how much of a chore that might be for others out there.
 

JoelWarlord

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Which is to say, the author is obviously still figuring out hockey on a fairly fundamental level if he's completely unable to glean any information from it, and thinks it actually - in and of itself - prevents anyone from understanding anything.
So wait, are you saying that statistical analysis is valid? And that people are misunderstanding the stat and using flawed assumptions to discredit it?
People who watch games the most still have more accurate "predicting power" than even the most ardent stats manipulators, btw, and I can understand how that frustrates the actuaries and pencil pushers who are trying to participate in such a great game on the level they're most comfortable - from the computer chair with Excel (and Youtube) loaded up, the morning after. And yes, attempting to use a spreadsheet and data set as a surrogate for experienced viewing is lazy, no matter how much of a chore that might be for others out there.
Ignoring this bizzare anger you harbour towards people who use stats in addition to watching games (the idea that people have stopped watching the sport in place of spreadsheets is laughable), score adjusted fenwick is now 71-33 in predicting playoff series wins since 2007-08. That's literally just fenwick numbers with no additional information. If you just blindly picked the higher fenwick team going in a playoff series you'd have been right 68% of the time. Is there a qualified game watcher that's matched that rate?

I said "+/- has little predictive value". You went off about nerds and spreadsheets using numbers and said that +/- does have value. Get a new schtick man, nerds aren't going to take hockey away from you. If you're correct and the stats are meaningless, nobody in the NHL will use them and the game watching experience will be unchanged. If stats don't help analysis then you'll be more successful with predictions than Bob in accounting.

Moving on, what can be gleaned from Ovechkin's -35? What can be gleaned from his years of +45 and +24? What does his +/- tell us about him as a player? If you were the GM of the Capitals, how would his +/- factor into what you decided to do with your roster?
 
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Ohashi_Jouzu*

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So wait, are you saying that statistical analysis is valid?

Of course, lol. And +/- doesn't have to be predictive as long as it's descriptive - which it is. It means something to be almost doubly minus the next "worse" player on your team whether it happens repeatedly/reliably in the past or not. It also means something to have scored 30 or 40 goals in the past, even if you never quite get there ever again. Everything is a function of all the skills and circumstances that are more easily understood by those observing them on the regular than those trying to glean similar things through number crunching.

"Controller disconnected" is synonymous with Ovechkin at this point for a reason.
 

Novak Djokovic

#24 and counting... #GOAT
Dec 10, 2006
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I disagree with the conclusion. Plus-minus, when adjusted properly, is an excellent indicator. I think it's less reliable over a single season, but over several seasons, the ratio of ES GF/GA when a player is on the ice vs. when he's off the ice is very telling.

The author gives 3 examples:

1) Playing time: The fact that a team would put a player on the ice much more than another player speaks to the value that team puts on that player. Also, it's generally more difficult to sustain value per unit of time as playing time increases.

2) Save %: This is a more legitimate factor. However, he neglects to mention that a player's defense contributes to the SV% while he's on the ice. The amount he affects SV% could vary dramatically depending on his defensive role. This type of effect should mostly even out over multiple seasons.

3: Shooting %: Again, he neglects to mention how a player's offensive abilities affect both his own S% and the S% of the players with him on the ice. Again, this effect should mostly even out over multiple seasons.

Exactly!

As a star player (won't name names), isn't it also your job to increase the S% of your line-mates? Isn't that called "making players around you better?"

As a defenseman, shouldn't you play a role in increasing goalie's SV%?

I agree that sometimes a goalie will let in a bad goal and there's nothing that player could have done, but if it is a trend over time (or if you stand out against rest of your team-mates), something is up.
 

EdzosCrayon

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Apr 4, 2013
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Argument could be used for Corsi as well. It has to be viewed in context just as +/- does. If you watch the Flyers you know Hartnell's high Corsi Rel is due to playing with Giroux and Voracek.

Let's assume you take a line in which all players have identical stats, but two are creating chances and the third is generating his production off of easy finishes, rebounds in front etc. If you took the 2 offensive catalysts and played them with multiple other players their stats would still be relatively good, but if you took the third player and played him on another line, his stats would be relatively poor. (This assumes all three are equally competent defensively as well).


This is what I always wonder about whenever the +/- debate comes up. I don't understand why +/- is the worst stat in hockey yet people get a boner over Corsi when they're basically the same thing.
 

DTMAboutHeart

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Jun 25, 2014
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+/- is one of the worst statistics currently used in hockey. Period. Well then, why is it still used? Its simple, pretty and everyone can understand that. Yes it a statistic that tells you what happened in a game, but that in and of itself doesn't justify using it for anything productive. Heres a statistic, how many times Sidney Crosby blinks during games that take place every other Thursday in the southeast region?

That is a stat. Everyone knows what its measuring. It could be easy to track if someone wanted to. Does it add anything meaningful and valuable to a discussion about evaluating individual hockey players? No. So just stop.
 

Hank Chinaski

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May 29, 2007
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Of course, lol. And +/- doesn't have to be predictive as long as it's descriptive - which it is. It means something to be almost doubly minus the next "worse" player on your team whether it happens repeatedly/reliably in the past or not. It also means something to have scored 30 or 40 goals in the past, even if you never quite get there ever again. Everything is a function of all the skills and circumstances that are more easily understood by those observing them on the regular than those trying to glean similar things through number crunching.

"Controller disconnected" is synonymous with Ovechkin at this point for a reason.

Ok. What does it mean?

It could mean that you were on the ice for double the amount of ice time. It could mean that you created or gave up the same amount/quality of shots, but your goalie allowed double the amount of goals, or the opposing goaltender happened to allow double the amount of goals.

You haven't really refuted anything in that article.
 

Ryker

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Oct 3, 2008
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Ok. What does it mean?

It could mean that you were on the ice for double the amount of ice time.
Hi Hank, you'll be happy to hear NHL posts information on players' time on ice per game, including a breakdown into time on the ice while the teams are at even strength, on powerplay or on a penalty kill. You just go to NHL.com -> Stats -> Individuals -> Time on Ice.

It could mean that you created or gave up the same amount/quality of shots, but your goalie allowed double the amount of goals, or the opposing goaltender happened to allow double the amount of goals.
I love your use of "happened" here :nod: Acting as if goalies' random flops and whiffs raising/dropping a single player's +/- to a significant degree over a sustained period of time is any more likely than an asteroid hitting you in the face tomorrow morning 7.50 AM MST. Cute.
 

Hank Chinaski

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Hi Hank, you'll be happy to hear NHL posts information on players' time on ice per game, including a breakdown into time on the ice while the teams are at even strength, on powerplay or on a penalty kill. You just go to NHL.com -> Stats -> Individuals -> Time on Ice.

:help:

Of course you can easily verify a player's ES TOI to put his +/- into context, that's the whole point. The raw +/- stat is perfectly descriptive, but gives you very little meaningful information about how and why player A is doubly worse in +/- than player B.

I love your use of "happened" here :nod: Acting as if goalies' random flops and whiffs raising/dropping a single player's +/- to a significant degree over a sustained period of time is any more likely than an asteroid hitting you in the face tomorrow morning 7.50 AM MST. Cute.

Umm, what? I have no clue what you're trying to argue here. Who said anything about random flops and whiffs?

Truth be told, there is evidence that some defenders may very well influence save percentage in a sustainable way, in the same way there are a few players that likely influence shooting percentage in a sustainable way. However, the effect on plus/minus is very small in most cases:

http://hockeyanalysis.com/2012/02/09/defenders-effect-on-save/

In real terms, what does it matter? Well, there are 13 defensemen (9.1%) who (with the help of their linemates) save 5+ goals per season when they are on the ice in 5v5 situations solely due to their higher than expected on-ice save percentage and 22 defensemen (15.6%) who save 4+ goals. Nick Lidstrom (and his linemates) save % boost saved his team 9.8 goals per season while Jack Johnson (and his linemates) save % suppression cost his team 11 goals per season, just at 5v5.

Also, we don't know how much control these individual players exert on that higher than expected save percentage. This is why the eye test will always be useful.
 

Ryker

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Oct 3, 2008
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:help:

Of course you can easily verify a player's ES TOI to put his +/- into context, that's the whole point. The raw +/- stat is perfectly descriptive, but gives you very little meaningful information about how and why player A is doubly worse in +/- than player B.
What do you mean "that's the whole point"? Whoever said +/- is useful on its own and out of context? If you're going against that (as the article is), then you're going against a strawman, that was the point. There is no statistic that gives you meaningful information on its own. Having to put +/- into context for it to start making sense and giving value isn't really a knock on it.

Again, those of us saying the article is ******** aren't saying +/- is useful on its own. Or at least I'm not saying that and I don't think Ohashi_Jouzu was, either.

Umm, what? I have no clue what you're trying to argue here. Who said anything about random flops and whiffs?
The original article (that me and Ohashi_Jouzu critiqued) did, so I assumed you were going with its flow. If not, then my bad, and disregard what I wrote.

Truth be told, there is evidence that some defenders may very well influence save percentage in a sustainable way, in the same way there are a few players that likely influence shooting percentage in a sustainable way. However, the effect on plus/minus is very small in most cases:

http://hockeyanalysis.com/2012/02/09/defenders-effect-on-save/
Alright, I'll take a look at the article when I have more time.

Also, we don't know how much control these individual players exert on that higher than expected save percentage. This is why the eye test will always be useful.
I agree. I am a proponent of taking into account both the eye test and the statistical data. Relying too heavily or exclusively on one or the other isn't the way to go, in my opinion.
 

Hank Chinaski

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What do you mean "that's the whole point"? Whoever said +/- is useful on its own and out of context? If you're going against that (as the article is), then you're going against a strawman, that was the point. There is no statistic that gives you meaningful information on its own. Having to put +/- into context for it to start making sense and giving value isn't really a knock on it.

Again, those of us saying the article is ******** aren't saying +/- is useful on its own. Or at least I'm not saying that and I don't think Ohashi_Jouzu was, either.

Ohashi_Jouzu said:

It means something to be almost doubly minus the next "worse" player on your team whether it happens repeatedly/reliably in the past or not.

And to that I asked what? What does it mean? I guess you could say it's no more or less meaningful than any other stat, but when you're talking about goals, assists, shots, PIM, etc., you're talking about events that the player has a great deal of control over relative to +/-.

I was more interested to hear what he had to say about that, because he seemed to be trashing the article without actually refuting anything that it said.
 

Ryker

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Oct 3, 2008
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Ohashi_Jouzu said:

And to that I asked what? What does it mean? I guess you could say it's no more or less meaningful than any other stat, but when you're talking about goals, assists, shots, PIM, etc., you're talking about events that the player has a great deal of control over relative to +/-.

I was more interested to hear what he had to say about that, because he seemed to be trashing the article without actually refuting anything that it said.
OK, I won't belabor the point then (you can see my reply in this thread, which addresses this already), so I'll let him respond if he wants.
 

Ohashi_Jouzu*

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Ok. What does it mean?

It could mean that you were on the ice for double the amount of ice time. It could mean that you created or gave up the same amount/quality of shots, but your goalie allowed double the amount of goals, or the opposing goaltender happened to allow double the amount of goals.

You haven't really refuted anything in that article.

Yeah, it could, but we have the ice time numbers, we've watched the games, and Ovechkin wasn't on the ice for double the time of those who were only half as "bad" as him for +/-, so... I don't think Ovechkin's +/-, relative to his teammates, just "happened", lol.
 

Captain Bowie

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Jan 18, 2012
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The only problem with +/- is that people expect it to be accurate as to good/bad games and good/bad players. Like others have said it's a perfect descriptive stat. I know having a "be all and end all" stat as to good/bad players would make all of our lives easier, but there isn't one. Some are better than others, and +/- is at the bottom of the list.

Just like PIM, it tells you what happened, not that it had a positive or negative impact on the game. A player may have had 4 PIM in a game, and he could have saved a couple goals by taking guys down, or he could have taken 2 lazy holding penalties in the offensive zone. That is not the purpose of the stat.
 

number72

Registered User
Oct 9, 2011
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+- is not the "worst" statistic. It is a # that tells you something. So long as you have a hockey mind and can understand that a statistic does not tell the complete story and use it in that fashion it can be helpful
 

Mc5RingsAndABeer

5-14-6-1
May 25, 2011
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Patrice Bergeron and Alexander Ovechkin are great examples of why +/- is a horrendous statistic (look at their career numbers).

When a statistic changes to dramatically between season with a seemingly minimal change in the player's ability, you have to wonder what it's really representing.
 

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