April 8, 2009
The Plus and Minus of Plus/Minus

by Gabriel Desjardins

Hockey is usually not the sport where statistical or analytical innovation takes place. So it’s ironic that one of the most useful concepts in sports statistics has been an official NHL statistic for over 40 seasons, leading other sports by at least three decades. The statistic in question is Plus/Minus, which is perhaps the biggest subject of debate in hockey right now. Even though it accounts for the two most important actions in hockey, scoring goals and preventing goals, nobody can agree on what’s wrong with it or how to fix it.

Pretty much everyone has their own way of analyzing Plus/Minus: just to name a few, David Staples of the Edmonton Journal counts subjective “errors” to account for a player’s performance on both sides of the puck; Dennis at MC79hockey watches every second of Oilers’ tape to count scoring chances for and against; while Vic Ferrari has popularized the “Corsi” number, which tracks the number of shots directed at night – including goals, shots on goal, missed shots and blocked shots – while a player is on the ice. While no one can claim to have discovered the Grand Unified Statistic of hockey, each method gives us more information to evaluate a player with.

I’d like to introduce my own plus/minus methodology in a few steps. All of the statistics that I’m referring to are available in this rather large chart at behindthenet.ca. First, let’s break plus/minus into Plus and Minus. Here are the NHL’s top offensive producers at 5-on-5 per sixty minutes of ice time:

NAME          PTS/60    NAME         GFON/60    NAME       CORSI+

MALKIN	      3.07	DATSYUK	     4.40	OVECHKIN   73.1
CROSBY	      3.05	B.RYAN	     4.12	GREEN	   72.2
D. SEDIN      3.05	RYDER	     3.91	STAAL	   71.1
KREJCI	      3.04	WHEELER	     3.91	BACKSTROM  70.3
DATSYUK	      3.01	SAVARD	     3.84	GOMEZ	   68.4
PARISE	      2.99	HOSSA	     3.83	MOSS	   68.1
SAVARD	      2.95	KREJCI	     3.80	KOZLOV	   68.0
H.SEDIN	      2.86	PONIKAROVSKY 3.71	HOSSA	   67.4
LANGENBRUNNER 2.80	MALKIN	     3.68	ZETTERBERG 67.0
OVECHKIN      2.79	CROSBY	     3.65	PITKANEN   66.9
					
AVERAGE	      1.43		     2.57	           54.6

So even at the simplest level, looking at points, goals for and shots for, there’s a significant difference between the lists. For example, the Sedins score at a very high rate, but don’t involve their teammates quite as much as Pavel Datsyuk. Perhaps more predictably, several Washington Capitals have been on the ice for the most shots – not surprising given that Alexander Ovechkin is the first player ever to take 500 shots in a single season. Wayne Gretzky took just 369 the year he scored 92 goals.

Let’s look at the other side of the puck:

NAME      GAON/60  NAME CORSI-

YELLE	  1.30	   FRANZEN  40.3
STUART	  1.46	   TOEWS    40.7
MOTTAU	  1.53	   HAVLAT   41.3
BERGLUND  1.54	   BARKER   41.7
LEBDA	  1.58	   METHOT   42.2
BYFUGLIEN 1.61	   CAMPBELL 43.1
RYDER	  1.62	   DATSYUK  43.4
UPSHALL	  1.63	   BROUWER  43.4
KREJCI	  1.65	   LEBDA    43.6
R. BLAKE  1.67	   CHEECHOO 43.6
			
AVERAGE	  2.57		    54.6

Again, not much correspondence between the two lists, though we see a lot of Blackhawks, along with David Krejci and Michael Ryder, who have excelled both at scoring and stopping the other team from scoring, which is a quite rare skill. Let’s combine the two lists to see who’s the top two-way player:

NAME     +-/60  NAME       CORSI+-

RYDER	 2.29	DATSYUK	   23.4
DATSYUK	 2.20	FRANZEN	   23.0
WHEELER	 2.20	HOSSA	   22.2
KREJCI	 2.15	MOSS	   22.2
B. RYAN	 1.74	ZETTERBERG 21.0
BERGLUND 1.70	OVECHKIN   19.3
HOSSA	 1.66	SAMUELSSON 19.1
SAVARD	 1.61	GLENCROSS  18.8
KESSEL	 1.60	KRONWALL   18.6
D. SEDIN 1.53	TOEWS	   18.3

That’s not a very instructive list – it just tells us what we already knew: Detroit and Boston have the best first lines in the league. Let’s make one final adjustment: take a player’s +/- production and subtract from it what happens when he’s not on the ice. In other words, generate a plus/minus relative to his team. This is very similar to what Tom Awad suggested recently:

NAME     RATING  NAME        CORSI RATING

BERGLUND 2.63	 GETZLAF      23.4
DATSYUK	 2.32	 PERRY	      23.0
B. RYAN	 2.16	 BOOTH	      22.2
STREIT	 1.82	 STREIT	      22.2
PERRON	 1.70	 B. RYAN      21.0
WHEELER	 1.67	 M-A.BERGERON 19.3
KREJCI	 1.58	 PENNER       19.1
MONTADOR 1.54	 GOMEZ	      18.8
KLEE	 1.52	 KUNITZ	      18.6
RYDER	 1.52	 PARISE	      18.3

This is a bit more interesting: we still see the top Bruins and Wings, but we also see players who’ve had dominant (and generally unsung) seasons for bad or mediocre teams, like Mark Streit. Perhaps the most interesting player on the Corsi list is the much-maligned Dustin Penner, who has continually failed to live up to expectations in Edmonton despite posting cryptically good numbers on a regular basis.

At any rate, without watching thousands of hours of game tape, +/- relative to teammates is the best single statistic we have to evaluate a player’s performance. However, it doesn’t give a complete picture of a player’s performance. Next time, I’ll build on this player rating to figure out “Quality of Competition” – who plays tough minutes and who gets soft ones.