Puck Prospectus - Mucking and Grinding: Plus/Minus

February 25, 2009
Mucking and Grinding
Plus/Minus - A Nonsense Stat?

by Timo Seppa

It sounds like a good idea to begin with. It really does. But the more you look at it, the more you see how Plus/Minus is a nonsense stat.

There are a lot of nonsense stats in sports. They're used because they seem tangible and easy to understand by the mainstream media, by fans, and by old school managers and coaches. Then, they become entrenched and are used out of force of habit. And because nothing better is available.

Our friends at Baseball Prospectus recognize Runs Batted In (RBI) and Pitcher Wins as nonsense stats, stats that are as indicative of opportunities for batters to drive in runs, and of offensive support and defensive support for pitchers, as they are of individual skill.

In football, a pet peeve of mine is the 300 yard passing game, a common milestone that is applauded weekly. Unfortunately, this benchmark often negatively correlates with a team's success, as the most common reason for throwing the ball a ton is when you’re spending most of the afternoon playing catch up.

But don’t get me wrong. Plus/Minus was born out of good intentions. It would be an elegant concept if it wasn’t problematic, as I’ll detail in a moment.

The Plus/Minus rating was first used by the Montreal Canadiens in the 1950’s. A skater was given a plus every time he was on the ice when an Even Strength or Short Handed Goal was scored by his team and was given a minus every time he was on the ice when an Even Strength or Short Handed goal was scored against his team. By 1968, the NHL began to officially track the statistic. The all time highest Plus/Minus for a season was a dizzying +124 posted by Bobby Orr of the Boston Bruins in 1970-1971, while the all time low was -82 by Bill Mikkelson of the hapless expansion Washington Capitals in 1974-1975. In comparison, last season’s Plus/Minus leader was Pavel Datsyuk of the Detroit Red Wings at +41, while the low of -31 was achieved by Radek Bonk of the Nashville Predators.

What is commendable about Plus/Minus is that it is a simple stat. It’s an attempt to give an overall value to performance. It’s an attempt to give value to defensive contribution, while essentially all other skaters’ stats focus on offense. Further, Plus/Minus correctly recognizes that Power Play Goals are much easier to come by than Even Strength Goals and Short Handed Goals and therefore it does not skew the statistic by rewarding for them.

Basketball and soccer do not have a similar stat in common use, and they certainly could. Hockey is to be applauded for making the attempt.

Plus/Minus has its proponents, even among our staff. Our scouting expert Leslie Treff has pointed out that "plus/minus at the junior level is extremely important in predicting who will do well in the NHL. Not for the potential superstars (or obviously goalies) but for everyone else, it, combined with points per game, is the gold standard." Her conclusion is the result of looking at the junior careers of more than 1300 players drafted into the CHL over a five-year period. The full results will be published within the next few months.

Regardless of the obvious problems that I see with Plus/Minus in the NHL, I recognize Leslie’s expertise and would therefore surmise that some of these problems may be significantly diminished when dealing with perhaps a more homogenous set of players on the junior level. Ideally, a better metric –with the same good intentions as Plus/Minus– would provide an enhanced measure of current and future performance at all levels, from juniors through the NHL.

But enough of making apologies for Plus/Minus. Now let’s take it apart and see why it’s nonsense. Here are six ways that Plus/Minus is fatally flawed:

Location, location, location. What is true in real estate is true for Plus/Minus. A significant factor in a player’s Plus/Minus rating is the team he is playing on. Clearly, there will not be an even playing field comparing players on the Red Wings, Bruins, and Sharks to players on the Islanders, Senators, and Thrashers. We can't make blind statements about the overall contribution or ability of Dany Heatley of Ottawa based on this season’s Plus/Minus, as he is on pace for a -8 in 2008-2009 compared to +29, +31, and +33 in the past three seasons. Did he forget how to play all of a sudden? Is he over the hill at age 27? Is he just plain lazy this year? Of course not. Clearly, the quality of a player's team has much more of an impact on an individual's Plus/Minus than his personal contribution. Conversely, if you took Valtteri Filppula off the Wings and put him on the Islanders, is he really going to be +11?

Notice how much better Ryan Kesler is playing now that he is paired with Pavol Demitra and Mats Sundin? Corollary to the above: More specifically than the quality of his team, the success of a player is influenced by the quality of the other skaters the coach chooses to play him with and by the skill level of the specific opposing players that he lines up against.

Frequently, coaches match up their 1st line against their opponent's 1st line. In such cases, it would be reasonable to think that the benefit of playing with more skilled teammates would be more or less a wash with the increased difficulty of playing against more skilled opponents. But checking lines are often matched against the opposing 1st lines. So to get a fair indication of a player's offensive and defensive contributions, the abilities of linemates and opposition should be known. Otherwise, those checking line players –likely excellent defenders– will ironically end up with less than ideal Plus/Minus ratings.

Think of an extreme example. The Oilers’ dynasty keeps sending players to the Hall of Fame. Do they all belong? Who rode the coattails of their linemates? Would Glenn Anderson be a Hall of Famer if he had played his career somewhere else?

Time On Ice is not taken into account. All things being equal, a player with a +10 rating averaging 10:00 TOI would be equivalent to a player with a +20 rating averaging 20:00. A rate statistic wouldn’t allow better players to double dip both time and ability to seem even better in comparison than they are.

Plus/Minus doesn’t differentiate offensive contribution from defensive contribution. Is a player that is +30 for a season –even if the +30 was somehow mostly indicative of his own skill– an outstanding offensive player, an outstanding defensive player, or some of both? By splitting out offensive and defensive contributions –as we’ll do in the examples below– it will be easier to see extreme levels of Plus or Minus that are likely to be unsustainable in the future.

Plus/Minus gives the illusion of being a comprehensive measure of a player’s performance. Important facets of a player’s game are not included in Plus/Minus - Primarily, the effects of taking and drawing penalties, and power play and penalty killing contributions.

The scale is out of whack. For an even strength goal, the five skaters on the scoring team get +1 each and five skaters on the scored upon team get -1 each. That’s one Goal For and one Goal Against, but five plusses and five minuses. This makes it easy to be misled into thinking that a +20 player was individually good for 20 more GF than GA for the season. But of course, they were only good for a fifth of that, 4 more GF than GA for the season, since they only contributed one fifth of the effort towards each of those 20 Goals. It wouldn’t be as elegant looking, but if each skater was given +0.2 for their share of each 1 GF that they created instead of +1, perceptions of what the Plus/Minus rating meant would be closer to reality. +4 would mean that the skater himself was worth 4 Goals to his team.

Let’s take a look at some concrete examples of how the top Plus/Minus performers from last season are doing now to see some of these factors in practice:

2007-2008 Plus/Minus leaders for Forwards – Performance in 2008-2009


                         2007-2008         2008-2009*         Difference 

Name           Team    +/- Plus Minus   +/- Plus Minus      +/- Plus Minus 

Pavel Datsyuk  DET     +41   84    43   +36   76    40      -5    -8    -3

Dany Heatley   OTT     +33   88    55   -8    56    64      -41   -32   +9

Ryan Getzlaf   ANA     +32   72    40   +10   65    55      -22   -7    +15

H. Zetterberg  DET     +30   72    42   +16   54    38      -14   -18   -4

Alex Ovechkin  WAS     +28   94    66   +23   87    64       -5   -7    -2

Viktor Kozlov  WAS     +28   71    43   -5    58    63      -33   -13   +20

Jarome Iginla  CAL     +27   86    59   -1    71    72      -28   -15   +13

Jason Spezza   OTT     +26   86    60   -13   56    69      -39   -30   +9

Patrick Sharp  CHI     +23   70    47   +1    47    46      -22   -23   -1

*2008-2009 stats through 2/17/2009, prorated through year end

Looking at the top Forwards of 2007-2008, the decline in Plus/Minus is by no means limited to the Senators’ train wreck of a season. True, the aforementioned Heatley is on pace to lose a whopping 41 points of Plus/Minus, while teammate Jason Spezza is on his way to an equally whopping 39 point loss, but highly regarded players such as Jarome Iginla and Ryan Getzlaf are pretty much in the same boat, on pace to decline by 28 and 22 as well.

All of these players can look at an overall downturn in their teams’ production as the biggest reason for their poor performance in this “individual statistic”. Of course, part of the issue here is simply regression to the mean, as we statistics eggheads say. Extreme performances are very likely to fall back down to earth. But clearly, Plus/Minus is likely to experience much more variability year to year than other statistics such as Goals scored.

Unlike those Forwards, Patrick Sharp’s drop-off is troublesome on a young Blackhawks team otherwise in the ascendant. The only Forwards more or less treading water are Alex Ovechkin -arguably the best player in the game- and Pavel Datsyuk and Henrik Zetterberg of the always competitive Red Wings.

By breaking out Plus/Minus into its Plus and Minus components, you can see how the ground has mainly been lost on the Plus side for this set of Forwards. Heatley and Spezza, for instance, are on a pace for only an increased Minus rating of 9 in 2008-2009. On the other hand, their Plus rating is on a pace to decline by thirty-odd goals. Those are the sort of results that get coaches fired. Whoops, that already happened. But the consensus here among the Puck Prospectus staff pegged the major losses of offensively oriented Defensemen as the key breakdown affecting all of Ottawa’s offensive output. If the coaching change does not turn the tide, that’s the sort of thing that gets general managers fired.

2007-2008 Plus/Minus leaders for Defensemen – Performance in 2008-2009

                         2007-2008         2008-2009*         Difference 

Name             Team  +/- Plus Minus     +/- Plus Minus      +/- Plus Minus 

Nicklas Lidstrom DET   +40   84    44     +33   85    52      -7   +1    +8

Duncan Keith     CHI   +30   82    52     +49  101    52      +19  +19    +0

Johnny Oduya     NJD   +27   56    29     +22   76    54      -5  +20   +25

Brian Rafalski   DET   +27   67    40     +19   81    62      -8  +14   +22

Niklas Kronwall  DET   +25   56    31     -12   57    69      -8  +14   +22

Matt Niskanen    DAL   +22   68    46     -11   70    81      -33   +2   +35

M. Schneider     MON** +22   49    27     -19   67    86      -41  +18   +59

J. Cullimore     FLA   +21   48    27     -16   34    50      -37  -14   +23

*2008-2009 stats through 2/17/2009, prorated through year end

**ANA/ATL/MON

Looking at the top Defensemen of 2007-2008, Red Wings’ perennial stalwarts Nicklas Lidstrom and Brian Rafalski match teammates Datsyuk and Zetterberg in more or less staving off regression to the mean and staying at similar high levels to last year – Mainly due to Detroit’s continuing exceptional play. Even more impressively, Duncan Keith has completely bucked that regression trend to significantly improve from an already great last season.

Breaking it down into Plus and Minus components, it is apparent that extremely low Minus ratings are hard to sustain. Performances such as Oduya’s 29 Minus rating, Kronwall’s 31 Minus rating, and Cullimore’s 27 Minus rating are very unlikely to be repeatable. This season, those blueliners are on pace for a 25, 38, and 23 worse performance in Minus rating, though Oduya’s increase of 20 Plus almost negates the difference for him. Notably, many of the top Defensemen improved in Plus rating, while all inevitably losing ground in Minus rating.

Mathieu Schneider, traded to Montreal as of February 16th, may be the best proof that Plus/Minus has little to do with individual performance. His projected drop of 41 Plus/Minus –at least if he were to have continued with Atlanta– includes an immense increase in Minus from 27 to 86 in one season! Clearly, the primarily cause for this difference was his offseason departure from the Ducks and his free agent signing by the lowly Thrashers, rather than by a falloff in individual performance.

What’s the takeaway from all of this? Stop the nonsense! Like the RBI in baseball has started to slowly fade in importance as the media, management, and fans have begun to embrace better stats like OPS (On base percentage Plus Slugging percentage), hopefully Plus/Minus has seen its heyday and will soon be replaced by metrics that are more indicative of comprehensive individual contribution to a team.

Special thanks to Thomas Awad and Frederick Reynolds for their assistance.

Timo Seppa is an author of Puck Prospectus. You can contact Timo by clicking here or click here to see Timo's other articles.