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# Why Plus/Minus is the Worst Statistic in Hockey

07-05-2014, 02:43 PM
#51
charlie1
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Quote:
 Originally Posted by Ohashi_Jouzu Blocked shots? Is it good to have a bunch, or are they simply the symptoms of poor possession/defensive play? The debate rages on...
It seems to me that standardizing Hits or Blocked Shots for possession might make those stats more useful. For example, Hits / (100-TeamCF%) or BlockedShots / (100-TeamCF%) might be more useful than just hits or block shots. Or even better, normalize the numerator and denominator first, then divide.

Thoughts?

07-06-2014, 01:34 AM
#52
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Quote:
 Originally Posted by number72 +- 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
It is the worst because it A) tells you very, very little useful information and B) it is presented to most people as something more than what it is.

07-06-2014, 03:27 AM
#53
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Quote:
 Originally Posted by DTMAboutHeart It is the worst because it A) tells you very, very little useful information and B) it is presented to most people as something more than what it is.
How is Corsi any better? If your a scoring threat you will start in the other zone a fair bit more, so you will get more shots on goal or at goal then say a guy that starts a lot in his own end. It also says nothing on the quality of shots, it is used to see how much your goalie has to move up and down, yet people treat it as if its the greatest stat ever.

If your a fairly good Dman and you start in your own end a lot to defend... say 58%. and your teams faceoff % is 50% you should be seeing a 58-42 diff in scoring chances against. So you suck? or.... never mind if you stood in the way and blocked 25% of the shots and made them shoot the other 25% wide, your corsi would still look stupid

Last edited by supsens: 07-06-2014 at 03:33 AM.

07-06-2014, 03:51 AM
#54
charlie1
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Quote:
 Originally Posted by supsens How is Corsi any better? If your a scoring threat you will start in the other zone a fair bit more, so you will get more shots on goal or at goal then say a guy that starts a lot in his own end. It also says nothing on the quality of shots, it is used to see how much your goalie has to move up and down, yet people treat it as if its the greatest stat ever. If your a fairly good Dman and you start in your own end a lot to defend... say 58%. and your teams faceoff % is 50% you should be seeing a 58-42 diff in scoring chances against. So you suck? or.... never mind if you stood in the way and blocked 25% of the shots and made them shoot the other 25% wide, your corsi would still look stupid

07-06-2014, 04:10 AM
#55
supsens
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Quote:
 Originally Posted by charlie1 If you're really interested in this, google "zone-start adjusted Corsi."
I know that, but every stat on its own is pointless, but hearing how + - means nothing is getting kind of old, Trotz want's AO to be a even player, he is a great coach and knows a fair bit about hockey and it sure matters to him.

Even save % one guy can face shots from the outside all night and one guy could face break aways and 2 on 1's it does not mean he is a crappy goalie.

It's a team sport, it's hard to judge any part of it based on one stat, unless that stat is wins, and even then one crappy player can look good with a bunch of great players

07-06-2014, 06:58 AM
#56
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This post is not getting nearly enough attention and ties in well with the point made about descriptive and predictive stats.

Quote:
 Originally Posted by treple13 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. 0 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.
I love +/-. It gives me as much information as points, goals, assists, etc do. Do people use past points to predict future points? Sometimes. Are past points a good indicator of future points? Not really. Players get injured, lucky, unlucky, etc. Does this mean that tallying points is useless? No. In some contexts, points accumulated indicate certain things, just as sometimes +/- does.

It just so happens that everyone cares about points more than other statistics. We acknowledge that points don't tell the whole story, but use it because it is easy.

To take it further, imagine a bizarro world where no one tracks points, but instead only tracks +/-. The player with the best +/- wins the Art Ross. Would this be a fundamentally different way to assess the value of the player? Not really, it's just an adjusted form of points. It's points net of opposing player points and adjusted for context (PP, non-PP, etc.).

In that world, a talented player, defined as someone who has a good +/-, would be justified as someone who plays well against the opponents that he faces. He did better against those opponents than his peers. That's not too different on a fundamental level as points. Sometimes Sedins win over Crosby/Ovech in points, but not many people have an issue recognizing that yes, Sedins had more points that particular year but Crosby/Ovech may still have been the better player that year (and every year) because they automatically put the points in context (ie: fewer games, supporting linemates, etc).

So why all the hate?

07-06-2014, 02:19 PM
#57
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Quote:
 Originally Posted by supsens I know that, but every stat on its own is pointless, but hearing how + - means nothing is getting kind of old, Trotz want's AO to be a even player, he is a great coach and knows a fair bit about hockey and it sure matters to him. Even save % one guy can face shots from the outside all night and one guy could face break aways and 2 on 1's it does not mean he is a crappy goalie. It's a team sport, it's hard to judge any part of it based on one stat, unless that stat is wins, and even then one crappy player can look good with a bunch of great players
It is a simple proven formula.

A good Corsi% --> a good GoalsFor% --> Wins

Corsi% has been proven to be the best means at predicting future GoalsFor%. Essentially Corsi% tells you if that player is going to help or hurt you when it comes to winning games in the future.

 07-06-2014, 02:41 PM #58 Freudian Clearly deranged     Join Date: Jul 2003 Country: Posts: 39,781 vCash: 50 I always viewed it as line stat more than an individual stat. It has significant weaknesses. It's vulnerable to randomness over a season. I'm not particularly fond of empty net goals and shorthanded goals giving a minus, because of how hard/impossible it is to get a + in those situations. Still, just because it has weaknesses doesn't mean it's useless. I prefer ES GF/GA over +/-. It's a cleaner stat. Last edited by Freudian: 07-06-2014 at 02:57 PM.
07-10-2014, 04:57 PM
#59
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couldn't keep reading after the following:

Quote:
 If we assume that plus/minus is an accurate representation of performance or ability,
THIS is the "problem" with +/- as a stat... people try to make assuptions based on it, try to use it as something that it's not... try to use it as a predictor when it's not.

There was a post early on that said it might be the best stat, and I agree - it has a very clear definition of what it tracks. It's even more accurate than goals, if you consider a scenario what a skater from team A "scores" a goal because he was the last player on his team to touch the puck, and a player from team B puts it in his own net.... by contrast +/- is indisputable, you get a plus when you are on the ice for a goal... and a minus for a goal against.

Calling +/- a bad stat is like saying the number 0 is bad... in that they both tell you 'nothing'. More accurate in my estimation, would be to call anyone that attempts to use +/- as the sole or primary evaluation of a player's performance bad. Thee's nothing wrong with the number, it just IS.

07-24-2014, 11:36 PM
#60
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Quote:
 Originally Posted by DTMAboutHeart It is a simple proven formula. A good Corsi% --> a good GoalsFor% --> Wins Corsi% has been proven to be the best means at predicting future GoalsFor%. Essentially Corsi% tells you if that player is going to help or hurt you when it comes to winning games in the future.
the same analogy can be made for a goal based statistic (like +/-):

good plus/minus = a good GoalsFor% --->wins

The difference is there are many times more corsi events than goal events. You can get the precision from a few games with Corsi that would take a whole season with goal stats. This is particularly important when evaluating different scenarios where there are even less goal scoring events. For this reason Corsi is much more useful. It doesn't mean that plus/minus doesn't mean anything, it's just statistically not as useful.

The author is correct, but I don't think there is a single stat that can be looked at in a vacuum as a true indicator of a player's true contribution to wins/losses.

 07-25-2014, 01:39 AM #61 Rebuilt Registered User     Join Date: Jun 2014 Location: Tampa Country: Posts: 8,802 vCash: 540 The worst stat in hockey is the second assist. Then I would argue its the = -
07-25-2014, 11:04 AM
#62
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Quote:
 Originally Posted by zytz Calling +/- a bad stat is like saying the number 0 is bad... in that they both tell you 'nothing'. More accurate in my estimation, would be to call anyone that attempts to use +/- as the sole or primary evaluation of a player's performance bad. Thee's nothing wrong with the number, it just IS.
I don't think the bolded goes quite far enough.

+/- is a fundamentally flawed metric in regard to player evaluation. Of course, the big problems are:

- Fails to capture qualitative contributions to goals for or against
- Difficult to adjust for team influences
- Prone to arbitrary results due to random timing of line changes

But even if we ignore the big ones, the 4 items below are a major issue for anyone attempting to use +/- in a meaningful way.

- Arbitrarily punishes players for spending time on the PP
- Arbitrarily rewards players for spending time on the PK
- Arbitrarily rewards players for being on offense while down a goal
- Arbitrarily rewards players for being on defense while up a goal

^ Unlike the first three, this second group creates a systemic bias against players who are asked to carry the mail offensively for their teams; and a corresponding bias in favor of defensive specialists.

So it's not enough to say that +/- should never be used as the primary evaluation of performance. It shouldn't even be used as a secondary factor, or mixed into a formula, or otherwise employed in comparisons -- because the results are known to be flawed, and introduce a systemic bias into whatever larger picture you're trying to paint.

 07-25-2014, 12:39 PM #63 Thenameless Registered User   Join Date: Apr 2014 Posts: 664 vCash: 500 That was a nice article exposing some of the weaknesses of the plus/minus stat. However, when a player like Bobby Orr has the best +/- for a season, and a player like Larry Robinson has the best +/- over a career, the stat can't be dismissed as completely meaningless. It's fairly argued that good teammates and bad teammates can greatly influence one's numbers, but the players themselves still have some control over what happens while they're on the ice. It's one of those things that you should take with a grain of salt.
07-25-2014, 10:22 PM
#64
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Quote:
 Originally Posted by Mike Farkas 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.
That's exactly what the evolution of advanced statistics is though. If you take baseball... that's exactly what happened. Teams were using things that had literally no bearing on predictive results and it wasn't until the advanced stats continued to grow that it finally became apparent that some things were relatively meaningless.

07-26-2014, 12:21 AM
#65
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Quote:
 Originally Posted by BillDineen 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 isn't accurate. Look at hartnell on other lines too. He actually brought up other player's corsi rels as well. He was a very good possession player no matter what line he was on.

07-29-2014, 10:46 PM
#66
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Quote:
 Originally Posted by Mortgage Broker The worst stat in hockey is the second assist. Then I would argue its the = -
A lot of plays are actually something like this:

-player A has the puck, finds player B, who's open
-player B shoots
-player C gets a goal either from a deflection or rebound

So yeah, give a secondary assist to player A, no problem.

But then again, it's true that some secondary assists are really worthless. It's just that you can't which one is which in advance.

07-31-2014, 10:35 AM
#67
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Quote:
 Originally Posted by Noob616 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?
It looks like you are missing one series from your numbers. It should be a total of 105 series since 2008.

I quickly went through the same series using team plus/minus from NHL.com

The team with the higher team plus/minus won 66 series and lost 39. Depending how the missing series worked out for fenwick close, it was better by 5 or 6 series over 7 seasons. I guess that is not bad for a useless stat.

 07-31-2014, 11:06 AM #68 Bear of Bad News Mod Supervisor     Join Date: Sep 2005 Location: Windsor Posts: 5,035 vCash: 663 I'd expect plus-minus to be a good predictor at the team level, since it's a proxy for even strength goal differential. But at the individual level? It ascribes "good" and "bad" at too coarse of a level for my tastes.
08-01-2014, 11:25 AM
#69
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Quote:
 Originally Posted by Isbrant It looks like you are missing one series from your numbers. It should be a total of 105 series since 2008. I quickly went through the same series using team plus/minus from NHL.com The team with the higher team plus/minus won 66 series and lost 39. Depending how the missing series worked out for fenwick close, it was better by 5 or 6 series over 7 seasons. I guess that is not bad for a useless stat.
Ovechkin being a -35 doesn't tell us very much about him as a player. The Sabres being a -93 as a team tells us a lot about them.

This thread is mostly about using it as a stat for individual players. For a team stat +/- is essentially just goal differential which is valuable. The caveat in a small sample like a playoff series is that goal differential doesn't tell us whether the better team won, it tells us who had a better goal differential but that can be misleading in small samples. That's the essence of why possession metrics are used, possession drives goal scoring in the long run (on both an individual and team level, most goal scorers are high volume shooters rather than high percentage shooters), while in the short run goals/goal differential can be driven by shooting or save percentages that aren't likely to continue.

Teams don't get flukey with possession, good possession teams continue being good possession teams in the playoffs (unless they run into someone better) and consistently through multiple seasons they can be above average. Shooting percentage and save percentage can fluctuate wildly, and that can significantly influence a team's goal differential. When a team with a better +/- wins a playoff series, we don't know at a glance whether that's because they outplayed the other team, or if it's because they had a goalie or shooter play significantly above their heads. If a team is posting a 55% fenwick close, we know that in the absence of a mitigating factor (New Jersey's chronically low shooting percentage) they're the better team in the long run.

Same thing here at the individual level, the sample is just too small and filled with variance that's essentially outside a player's control for Ovechkin's -35 to be meaningful in a vacuum.

Last edited by Noob616: 08-01-2014 at 11:35 AM.

08-02-2014, 07:39 PM
#70
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Quote:
 Originally Posted by Noob616 Ovechkin being a -35 doesn't tell us very much about him as a player. The Sabres being a -93 as a team tells us a lot about them. Same thing here at the individual level, the sample is just too small and filled with variance that's essentially outside a player's control for Ovechkin's -35 to be meaningful in a vacuum.
There is a great Gabe Desjardins observation on the matter. Historically, unless your talking about players on expansion franchises, the guy with the lowest plus/minus in the league is typically somebody you'd really want to have on your team next season.

Which is to say, if your coach was willing to give you enough ice time to really rack up those - events, chances are you aren't a bad player but a good player trapped in a bad situation.

08-02-2014, 09:44 PM
#71
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Quote:
 Originally Posted by Brainiac A lot of plays are actually something like this: -player A has the puck, finds player B, who's open -player B shoots -player C gets a goal either from a deflection or rebound So yeah, give a secondary assist to player A, no problem. But then again, it's true that some secondary assists are really worthless. It's just that you can't which one is which in advance.
I get what you're saying but even a high % of first assists aren't really from pretty passing plays. The way I see it, if a see a player with alot of assists the first thing that comes to my mind is mainly that his team scores alot of goals when he is on the ice, not necessarily that he's a great playmaker. That doesn't mean that he is the one driving it but it's usefull hint.

Quote:
 Originally Posted by Talks to Goalposts There is a great Gabe Desjardins observation on the matter. Historically, unless your talking about players on expansion franchises, the guy with the lowest plus/minus in the league is typically somebody you'd really want to have on your team next season. Which is to say, if your coach was willing to give you enough ice time to really rack up those - events, chances are you aren't a bad player but a good player trapped in a bad situation.
Yep. Kinda like how, ranking high on the list of players with the most giveaways on NHL.com is seen as a bad thing, even though, realistically, the list is mostly a bunch good players who are good enough to play high minutes and have the puck alot.

08-05-2014, 03:14 PM
#72
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Quote:
 Originally Posted by Noob616 Ovechkin being a -35 doesn't tell us very much about him as a player. The Sabres being a -93 as a team tells us a lot about them. This thread is mostly about using it as a stat for individual players. For a team stat +/- is essentially just goal differential which is valuable. The caveat in a small sample like a playoff series is that goal differential doesn't tell us whether the better team won, it tells us who had a better goal differential but that can be misleading in small samples. That's the essence of why possession metrics are used, possession drives goal scoring in the long run (on both an individual and team level, most goal scorers are high volume shooters rather than high percentage shooters), while in the short run goals/goal differential can be driven by shooting or save percentages that aren't likely to continue. Teams don't get flukey with possession, good possession teams continue being good possession teams in the playoffs (unless they run into someone better) and consistently through multiple seasons they can be above average. Shooting percentage and save percentage can fluctuate wildly, and that can significantly influence a team's goal differential. When a team with a better +/- wins a playoff series, we don't know at a glance whether that's because they outplayed the other team, or if it's because they had a goalie or shooter play significantly above their heads. If a team is posting a 55% fenwick close, we know that in the absence of a mitigating factor (New Jersey's chronically low shooting percentage) they're the better team in the long run. Same thing here at the individual level, the sample is just too small and filled with variance that's essentially outside a player's control for Ovechkin's -35 to be meaningful in a vacuum.
This thread was about individual +/- and then you brought up team fenwick close. I was just trying to compare apples to apples. Assuming your numbers were correct, team fenwick close was a better predictor for the playoff series than team +/-, but not as large as you made it seam. There is also the small sample size issue for fenwick close over a 4 to 7 game series, but the sample size will be larger for fenwick than it is for team +/-.

Individual +/- is one way to identify outliers for in depth review. Ovechkin's -34 this year was significantly lower than his average. He would normally play against top competition so something else changed. This would be a starting point to identify if the chage was due to him or external factors.

While individual +/- can be affected by external factors, it can also be affected by the individual. If the player never comes back inside their own zone, their +/- should be lower even if their counting stats are high. The low +/- could be attributed to that player while the +/- of their line mates would not be due to them.

All I am trying to say is don't compare team stats to individual stats and any stat can be useful when used in the proper context.

 08-05-2014, 03:52 PM #73 OCSportsfan Registered User   Join Date: Sep 2011 Posts: 959 vCash: 500 Could it be that the team with the better players ends up having a better +/- Corsi, Fenwick, etc., not that high corsi players create the better team? I guess it is chicken and egg. I don't buy into that shooting the puck makes a team better, or that each shot is the same (from the defense at the point or 15ft from the goal with Stamkos). There is value in every stat, but not one stat can be a predictor of future success. I do agree that if a team is shooting more they should generally be playing in the offensive zone more of the time, but unless that is turning into goals, I am not sure if it shows anything more than that. If you use the same principal in basketball. Team A has 100 shots and Team B has 90 shots. If 80% of Team A's shots were long distance (20ft), at 30% success, would they be as good as Team B who had 80% of the shots inside 10 feet at 60%.success. Sorry to get to the thread topic, +/- has its place, but it is not any worse than assists, goals, corsi, etc. as a predictor of future events. As a stat is shows EXACTLY what it is supposed to. One could argue they are getting offensive rebounds and keeping the possession, but it eventually comes down to getting the ball in the net.
08-06-2014, 10:36 AM
#74
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Quote:
 Originally Posted by OCSportsfan Could it be that the team with the better players ends up having a better +/- Corsi, Fenwick, etc., not that high corsi players create the better team? I guess it is chicken and egg. I don't buy into that shooting the puck makes a team better, or that each shot is the same (from the defense at the point or 15ft from the goal with Stamkos). There is value in every stat, but not one stat can be a predictor of future success. I do agree that if a team is shooting more they should generally be playing in the offensive zone more of the time, but unless that is turning into goals, I am not sure if it shows anything more than that. If you use the same principal in basketball. Team A has 100 shots and Team B has 90 shots. If 80% of Team A's shots were long distance (20ft), at 30% success, would they be as good as Team B who had 80% of the shots inside 10 feet at 60%.success. Sorry to get to the thread topic, +/- has its place, but it is not any worse than assists, goals, corsi, etc. as a predictor of future events. As a stat is shows EXACTLY what it is supposed to. One could argue they are getting offensive rebounds and keeping the possession, but it eventually comes down to getting the ball in the net.
+/- has essentially zero predictive power from season to season, that's a lot worse than goals and points which correlate fairly well year to year. The funny thing is that you can make it a fair bit more predictive if you ditch the plus/minus model and look at percentage of goals for and against 5 on 5. One of the biggest problems is that the stupid statistical noise baked into the +/- formula (special teams, empty net goals etc.) is enough to ruin quite a bit of the signal strength of the numbers.

The problem with your example on shot distance is not that what you are suggesting is a bad model to talk about hockey with, its that if you go and observe how things work statistically in the NHL, it doesn't turn out to be what happens. Its not like its a bad hypothesis, its entirely plausible, its just one that doesn't explain observable evidence, so its a bad theory. (Not that shooting percentage talent doesn't exist, its just not a dominant factor on observable skater performance the way shot control is).

 08-06-2014, 09:17 PM #75 aleshemsky83 Registered User     Join Date: Apr 2008 Posts: 14,913 vCash: 500 Has there ever been an advanced stats guy that took plus minus and tried to adjust it for quality of competition. Wouldn't it be useful in that case. It's done all the time for other advanced stats.

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