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Why Plus/Minus is the Worst Statistic in Hockey

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Old
06-05-2014, 10:51 AM
  #1
truck
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Why Plus/Minus is the Worst Statistic in Hockey

A fun little stats piece that I will be pointing to for years to come...

Plus minus is horrible:

http://www.arcticicehockey.com/2014/...stic-in-hockey

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06-05-2014, 11:35 AM
  #2
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Wow. I'd say it is one of, if not, THE best stat in hockey

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06-05-2014, 11:42 AM
  #3
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Originally Posted by JB51Hockey View Post
Wow. I'd say it is one of, if not, THE best stat in hockey
It really isn't though. It is horrible and all but meaningless.

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06-05-2014, 12:22 PM
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This article's a nice synopsis.

I couldn't get it to open initially, and was going to respond to that effect but note that plus-minus needs to be adjusted for a lot of things in order for it to have good meaning. Happily, you've done that.

Plus-minus is very good as a descriptive statistic - it's well-defined, and it does exactly that. If a player is +2 in a game, then you know with 100% certainty that he was on the ice for two more (non power play) goals for than goals against.

As a predictive statistic, or as a value statistic, it suffers. People expect more from it than it can reasonably deliver, and that's not the fault of plus-minus of course.

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06-05-2014, 12:33 PM
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Quote:
Originally Posted by Chalupa Batman View Post
This article's a nice synopsis.

I couldn't get it to open initially, and was going to respond to that effect but note that plus-minus needs to be adjusted for a lot of things in order for it to have good meaning. Happily, you've done that.

Plus-minus is very good as a descriptive statistic - it's well-defined, and it does exactly that. If a player is +2 in a game, then you know with 100% certainty that he was on the ice for two more (non power play) goals for than goals against.

As a predictive statistic, or as a value statistic, it suffers. People expect more from it than it can reasonably deliver, and that's not the fault of plus-minus of course.
...and even has flaws in the descriptive framework. Going +2 or -2 doesn't mean a player had a good or bad game. Players can pick up a plus or a minus on plays they have nothing to do with. They can also get credit / blame for goalie error at either end.

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06-05-2014, 12:37 PM
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Originally Posted by truck View Post
...and even has flaws in the descriptive framework. Going +2 or -2 doesn't mean a player had a good or bad game. Players can pick up a plus or a minus on plays they have nothing to do with. They can also get credit / blame for goalie error at either end.
Well, no - plus-minus describes what happened very well. It's a perfect descriptive statistic, just as (for instance) "goals" is. If you see that a player scored two goals in a game, then they scored two goals, plain and simple.

But a player can be +2 and have a bad game, and I suppose that a player could score two goals and have a bad game, too.

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06-05-2014, 12:54 PM
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Originally Posted by Chalupa Batman View Post
Well, no - plus-minus describes what happened very well. It's a perfect descriptive statistic, just as (for instance) "goals" is. If you see that a player scored two goals in a game, then they scored two goals, plain and simple.

But a player can be +2 and have a bad game, and I suppose that a player could score two goals and have a bad game, too.
Yes. In that regard it tells you what happened, just saying even on the game to game level +/- doesn't tell us whether or not a player played well.

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06-05-2014, 01:20 PM
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Great article. Not perfect, since players will not be the exact same, but still a great article.

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06-05-2014, 02:29 PM
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I think +/- is awful and wish it didn't exist. I agree with OP that its probably the worst stat in hockey.

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06-05-2014, 03:25 PM
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Originally Posted by ColdWaterCowboy View Post
Great article. Not perfect, since players will not be the exact same, but still a great article.
Players surely won't be the same, but even if they were +/- would vary wildly. That is what Dan was getting at.

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06-07-2014, 12:41 PM
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One of the previous "advanced stats" that debuted some years ago after being kept in some form by coaches prior to it being made public. Have to wonder how many of the "advanced stats" we have now will be looked back on in 10, 15, 20 years as a terrible idea. You can't help but wonder in 20 years if we're looking back and going "can you believe they used to count every shot as equal meaning?"

The evolution of the game creates an ever-growing and -evolving need to adjust at an analytical level as well.

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06-08-2014, 02:11 AM
  #12
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Quote:
Originally Posted by Chalupa Batman View Post
This article's a nice synopsis.

I couldn't get it to open initially, and was going to respond to that effect but note that plus-minus needs to be adjusted for a lot of things in order for it to have good meaning. Happily, you've done that.

Plus-minus is very good as a descriptive statistic - it's well-defined, and it does exactly that. If a player is +2 in a game, then you know with 100% certainty that he was on the ice for two more (non power play) goals for than goals against.

As a predictive statistic, or as a value statistic, it suffers. People expect more from it than it can reasonably deliver, and that's not the fault of plus-minus of course.
I really liked your write up. You said it all.

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06-08-2014, 07:27 AM
  #13
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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.

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06-13-2014, 09:38 AM
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Quote:
Originally Posted by Chalupa Batman View Post
Well, no - plus-minus describes what happened very well. It's a perfect descriptive statistic, just as (for instance) "goals" is. If you see that a player scored two goals in a game, then they scored two goals, plain and simple.

But a player can be +2 and have a bad game, and I suppose that a player could score two goals and have a bad game, too.
Let's look at it this way...

Player A dumps in puck and changes
Player B retrieves puck behind opponent net and scores on a wrap around
Player C gets on ice just as Player B retrieved the puck

Player C gets a plus for this despite not being involved in any way shape or form in the play.

on the flip side...

Player A tries to dump puck in and changes, but he doesn't get it in deep.
Player B on opposition takes puck and passes up to his forward who scores on a rush up the ice
Player C jumps on ice just as opposition forward enters the zone

Player C in this case picks up a minus despite once again having nothing to do with the play and Player A actually avoids a minus despite making the turnover that lead to the goal.


Last edited by Fish on The Sand: 06-13-2014 at 09:49 AM.
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06-13-2014, 10:50 AM
  #15
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Its kind of fashionable to sneer at plus/minus due to its imperfections. Terrible is, IMO, hyperbolic. Most observers who consider it a useful stat consider its imperfections. To me, a consistent high negative, suggests caution when evaluating otherwise impressive stats. And vice versa, a consistent high plus should lend a cautionary note to downgrading a certain player too much due to underwhelming surface stats - goals, points, etc. It should be viewed as a handy sub strata indicator to help further weigh surface stats.

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06-13-2014, 10:56 AM
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Quote:
Originally Posted by Fish on The Sand View Post
Let's look at it this way...

Player A dumps in puck and changes
Player B retrieves puck behind opponent net and scores on a wrap around
Player C gets on ice just as Player B retrieved the puck

Player C gets a plus for this despite not being involved in any way shape or form in the play.

on the flip side...

Player A tries to dump puck in and changes, but he doesn't get it in deep.
Player B on opposition takes puck and passes up to his forward who scores on a rush up the ice
Player C jumps on ice just as opposition forward enters the zone

Player C in this case picks up a minus despite once again having nothing to do with the play and Player A actually avoids a minus despite making the turnover that lead to the goal.
Please go back and read what I wrote (the post that you quoted).

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06-13-2014, 03:03 PM
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Quote:
Originally Posted by Chalupa Batman View Post
Please go back and read what I wrote (the post that you quoted).
What do you mean by "descriptive"? I think his objection is that +/- is well-defined, in that players get pluses and minuses for being on the ice when a goal is scored, but it's not descriptive of much of anything besides being on the ice.

Quote:
Originally Posted by Czech Your Math View Post
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.
1) Not necessarily. It could just mean that the coach has an unreasonable man-crush or hate-on for a particular player. That's not even getting into more details of usage like zone starts and QoT/QoC, which affect #2-3 too.

2) I vaguely recall reading that on-ice sv% between seasons for the same player are practically uncorrelated and random. Unless you can show that good defense players have predictable and repeatable effects on on-ice sv%, this point is moot. Furthermore, I doubt forwards could possibly have as much of an effect as defensemen do.

3) More or less the same point applies here, and especially for defensemen, who can only do so much to improve on-ice sh%. If they're on with 3rd and 4th lines against top lines, what can they possibly do? And again, you'd have to actually show that good playmakers can repeatably boost their teammates' sh%, or that Alex Ovechkin's on-ice sh% is low because he's a greedy puck hog or something.

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06-13-2014, 03:07 PM
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Originally Posted by Cap'n Flavour View Post
What do you mean by "descriptive"? I think his objection is that +/- is well-defined, in that players get pluses and minuses for being on the ice when a goal is scored, but it's not descriptive of much of anything besides being on the ice.
Descriptive means that it measures something well (what it is intended to measure).

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06-13-2014, 05:39 PM
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Originally Posted by Chalupa Batman View Post
Descriptive means that it measures something well (what it is intended to measure).
What statistic do we keep track of that is not 'descriptive' in this sense? Seems a rather obvious statement to make...

Just because something can be accurately quantified does not mean it has any inherent value.

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06-13-2014, 06:02 PM
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Originally Posted by hockeyfreak7 View Post
What statistic do we keep track of that is not 'descriptive' in this sense? Seems a rather obvious statement to make...

Just because something can be accurately quantified does not mean it has any inherent value.
What he's getting at is the difference between +/- as a stat and Hits, Giveaways or Takeaway

Plus minus is near perfect in that it almost perfectly describes what it intends too. It's pretty rare to have a phantom +/- attributed to a player. Whether than holds any predictive value is another issue.

Hits, Giveaways and Takeaways are more subjective, and subject to recorder bias. The data collected often doesn't accurately describe what it intended to. Whether it would have provided any predictive value if we had a more accurate version again is another issue.

I don't think he's trying to suggest that plus minus is a valuable stat at the NHL level (I've read that there are scouts that do value it at the junior level though, apparently it holds more predictive value there due to the disparity in talent levels).

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06-13-2014, 06:07 PM
  #21
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Quote:
Originally Posted by hockeyfreak7 View Post
What statistic do we keep track of that is not 'descriptive' in this sense? Seems a rather obvious statement to make...

Just because something can be accurately quantified does not mean it has any inherent value.
I never said that it had particular value.

Do me a favor. Go back to the start of the thread, and read each post in order. Then my comments should make sense in the proper context.

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06-14-2014, 10:43 PM
  #22
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Originally Posted by Nothing Is New View Post
Its kind of fashionable to sneer at plus/minus due to its imperfections. Terrible is, IMO, hyperbolic. Most observers who consider it a useful stat consider its imperfections. To me, a consistent high negative, suggests caution when evaluating otherwise impressive stats. And vice versa, a consistent high plus should lend a cautionary note to downgrading a certain player too much due to underwhelming surface stats - goals, points, etc. It should be viewed as a handy sub strata indicator to help further weigh surface stats.
This is how I look at it. To view +/- on its own as a stat is somewhat useless. But once used against other information such as; Team +/-, or Linemate +/- it can at times be very telling.

But to those that use it as a single stat to define a player are simply wrong IMO.

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06-20-2014, 11:09 AM
  #23
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I mean, sure it describes exactly what it intended to. But that description isn't useful at all. It doesn't say anything about a player's accomplishments, just that he was on the ice when a (non-pp) goal happened. And it has no predictive value whatsoever because of sample size issues. Even an entire team over the course of a season is looking at ~ 750 events at the high end. So yes, academically it's quite nice since it's exactly what it's meant to be and not subject to bias, but it has zero practical application IMO.

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06-20-2014, 11:36 PM
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I don't find a +\- stat useful at all and would love to here why that stat even serves a purpose. Coaches can obviously observe how well a player performs just by watching them play. You could say that about all stats but at least goals and assists and things like shooting percentage and GAA or save percentage are worth following. Plus minus doesn't measure a players defensive ability. +\- is an important stat to a players agent when his guy is looking for a big contract, plays defense as a stay at home guy, and doesn't score a whole lot. Of course the stat means little


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06-22-2014, 01:19 AM
  #25
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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.


Last edited by Ryker: 06-22-2014 at 02:05 AM.
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