I've been a big proponent of evaluating teams statistically, and particularly through the use of goal differential. In discussions about this, invariably a person who's new to the discussion finds it to be a bit like voodoo. Those of us who are comfortable with the concepts and who've been kicking them around for a few years get tired of rehashing it and why we like it which makes it difficult to bring converts to the cause. This article takes a look at the evidence as to why outscoring is so important and what I see as being the implications of this.

In seeking to evaluate how strong a team is, it's important to know whether or not their record fairly represents their abilities. It's generally accepted that a puck can hit a goalpost and stay out costing a team a win, or hit a goalpost and go in, giving a team a win. It appears to be generally assumed that the breaks even out, and that a team's record is a fair indicator of their strength. This is not so.

In many cases, a team will have a winning percentage that either outperforms or underperforms what could be expected given their goal differential. An examination of the historical record of hockey teams shows that goal differential is a powerful predictor of the record we can expect a team to achieve. If a team differs greatly from their expected record, the decisions that management makes in the off-season should be informed by the knowledge that the team is stronger/weaker than it appeared.

This article will look first at two different questions and then draw a number of conclusions from the results. First, I will show that teams will generally earn a number of points corresponding to their goal differential. Second, that there is no ability to consistently outperform or under perform an expected record. If points generally correspond to goal differential, and there is no ability to change that relationship, it would be foolish for a GM (or fan) to evaluate his team based on record as opposed to goal differential. While goal differential itself can be affected by luck-sometimes the puck hits the post and stays out, other times it hits the post and goes in-that goal differential should still correspond with a given number of points.

All data used in this article was collected from www.hockeydb.com. For ease of analysis, the points awarded to overtime losers were discarded, and those games were treated as wins under the old system, with only two points being awarded.

1.  Does goal differential correspond to winning percentage?

There have been 1115 team seasons since the 1917-1918 season, the first of NHL play. I have looked for linear relationships by checking the correlation of GF, GA and goal differential to winning percentage. A correlation of +1.00 indicates a positive perfectly linear relationship, while a correlation of -1.00 indicates a negative perfectly linear relationship. Correlations between these two extremes indicate a lesser linear relationship between the sets of numbers being compared.

During the history of the NHL, there has been a weak correlation between GF and winning percentage (.317) and between GA and winning percentage (-0.37). Strong defence or a strong offence will not suffice alone to guarantee a strong winning percentage. The key is goal differential. The correlation between goal differential and winning percentage since 1917-1918 is 0.93.

Knowing that there is a relationship between goal differential and winning percentage would lead one to think that one should be able to predict winning percentage based on knowing a team's goal differential. This is true. A year or so ago, when I was first becoming interested in this, a poster on an internet message board noted that the relationship between the two was similar to a poisson distribution. That is to say, that if one assumes that teams have a certain ability to score goals and a certain ability to prevent goals, those goals will occur more or less randomly over the course of a season.

If the poisson method is applied to the 1115 team seasons that have occurred, we see a very strong relationship between the poisson winning percentage and the actual winning percentage, as there is a correlation of .96. As with the relationship between goal differential and winning percentage, this is a very strong relationship. If you'd like to see the actual winning percentage and predicted winning percentage for every team in history using this method, one is available here.

Variation	Teams	%
+ 0.100	3	0.3%
+ 0.090	5	0.4%
+ 0.080	4	0.4%
+ 0.070	5	0.4%
+ 0.060	15	1.3%
+ 0.050	20	1.8%
+ 0.040	43	3.9%
+ 0.030	74	6.6%
+ 0.020	99	8.9%
+ 0.010	128	11.5%
+ 0.000	155	13.9%
- 0.010	140	12.6%
- 0.020	139	12.5%
- 0.030	98	8.8%
- 0.040	85	7.6%
- 0.050	44	3.9%
- 0.060	29	2.6%
- 0.070	14	1.3%
- 0.080	4	0.4%
- 0.090	8	0.7%
- 0.100	0	0.0%
- 0.110	1	0.1%
- 0.120	3	0.3%

A table is available here that predicts the winning percentage of a team playing an 82 game season based on goal differential using the poisson method. The numbers in the vertical column represent a team's GF, while those in the horizontal row are GA. As should become clear from looking at the table, an average goal is worth about .002 winning percentage. This means that for an average team, that is one with a goal differential of 0, a goal is worth about .328 points. Thus, for every 6.1 goal differential that a player creates during the course of a season, he earns the average team a win.

How does this look in practice? The table below sets out the variation between actual and expected winning percentage for the 1115 team seasons that have occurred. Variation represents actual winning percentage minus expected winning percentage. To offer an example of this, the 1989-90 Edmonton Oilers had an actual winning percentage of 0.563 (90 pts divided by 160 possible points). Their goal differential was +32, which would lead us to expect them to post 89 points, for an expected winning percentage of 0.556. Thus, their variation was +.007.

Just to explain the interpretation of this chart, 3 teams were 0.100 better than their expected winning percentage. 5 teams fell between 0.090 better and 0.100 better. For the negative numbers, 140 teams fell between -0.010 and -0.001 and so forth.

It should become quickly evident that the vast majority of teams over the course of history fall very close to their expected winning percentage. Many of the extreme teams come from the early days of the NHL-the top 6 teams in terms of outperforming expected winning percentage and the bottom five teams in this regard all played before the end of WWII.

In light of this, it seems evident that there is a strong relationship between goal differential and points.

2.  Can teams consistently outperform their poisson winning percentage?

If teams can consistently outperform or under perform their expected poisson winning percentage, this tool becomes much less valuable. Wins and losses are what matters, not some equation that manages to offer a guess. Were teams able to consistently outperform or under perform their expected poisson winning percentage, fans and GM's would be justified in ignoring it-clearly there would be other more significant factors at play.

As it stands however, teams do not appear to be able to do so. Differences between actual winning percentage and expected winning percentage are not sustainable from year to year. The correlation between difference year over year is incredibly weak-it's 0.08, which means that there is essentially no relationship.

Edmonton Oilers
Season	Actual Win%	Predicted Win%	Difference
2003-2004	0.512	0.527	-0.015
2002-2003	0.506	0.502	0.004
2001-2002	0.537	0.550	-0.013
2000-2001	0.549	0.542	0.007
1999-2000	0.488	0.529	-0.041
1998-1999	0.476	0.508	-0.032
1997-1998	0.488	0.482	0.006
1996-1997	0.494	0.510	-0.016
1995-1996	0.415	0.383	0.032
1994-1995	0.396	0.354	0.041
1993-1994	0.381	0.421	-0.041
1992-1993	0.357	0.336	0.021
1991-1992	0.513	0.496	0.016
1990-1991	0.500	0.500	0.000
1989-1990	0.563	0.557	0.005
1988-1989	0.525	0.533	-0.008
1987-1988	0.619	0.627	-0.008
1986-1987	0.663	0.648	0.015
1985-1986	0.744	0.682	0.062
1984-1985	0.681	0.666	0.015
1983-1984	0.744	0.702	0.042
1982-1983	0.663	0.671	-0.009
1981-1982	0.694	0.693	0.000
1980-1981	0.463	0.502	-0.039
1979-1980	0.431	0.463	-0.032

As an example, here's the Edmonton Oilers since their debut in 1979-1980. The team fluctuates massively from year to year. It's particularly interesting to look at the years between 1981-82 and 1987-88. The actual winning percentage ranges from a high of 0.744 to a low of 0.619. The expected winning percentage is much more consistent, ranging from 0.702 to 0.627. Some years you get the breaks, some years you don't, some years Steve Smith makes a bad pass…that's hockey.

If you look at the cumulative value by which the Oilers have exceeded their expected winning percentage over the past 25 years, it's .012%. That works out to an average of 1.91 points per season by which they've exceeded that which we would expect with this method.

This point is important. If goalies could dramatically improve their play at key moments, or if they tended to dose off when the game didn't really matter, or if skaters really could bear down when it mattered most, we'd expect those teams staffed with those players with this special skill to consistently exceed their expected winning percentage. Those teams would be able to consistently win one goal games, and could be expected to put up 100 point seasons with goal differentials of 0, all because they mailed it in the snoozers and lost by 5, while they made up for that with 5 one goal wins. The evidence is that the game doesn't work this way.

For all the commentary about how we should excuse Grant Fuhr's low save percentage and lousy all around numbers because he turned it on when it counted, the Oilers were significantly worse during their four Cup years with Fuhr as the main starter when they played a close game than they were in blowouts. In games decided by 3 or more goals, the team won at an .853 clip. If the game was decided by two goals or fewer, they won at a .762 clip. Did they win so many close games because Fuhr closed the door, or did they win so many close games because the team was loaded? Given that we know team's cannot sustain a winning percentage far above what poisson would project, and that the Oilers were significantly worse in those games, it seems reasonable to suggest that maybe it wasn't Grant Fuhr stepping up his game, but rather the fact that they were the better team, and although chance might send a pass off the back of Fuhr's leg into the net, it was a heck of a lot more likely that Gretzky would hit Kurri for the winner.

In light of the above, two key implications become evident. This discussion contains reference to specific players, and EV+ EV- numbers. These numbers have had empty net goals removed, so as to minimize the distortion of goals that don't actually indicate much ability.

1.  The value of a player corresponds to his impact on goal differential.

A player like Henrik Sedin (EV+ 47 EV-21 in 2003-04) may be as valuable or more valuable than someone like Brendan Morrison (EV+58 EV-41). Brendan Morrison is seen as a potential candidate for Team Canada, while Henrik Sedin is seen as something as of a bust. While there are other factors to consider (linemates and quality of opposition in the case of team mates, add in goaltending with non-team mates), traditional hockey statistics like goals, assists and points do not tell us what impact a player has had in the defensive zone. All other things being equal (ice time, level of opposition, quality of teammate and impact on results), Player A who scores 60 points with an EV+ 50 and an EV- 60 is not as valuable as Player B who scores 40 points with an EV+ 40 and an EV- 30. Player A will certainly get paid more though.

This goes for goalies as well. When evaluating a player, the question is: how much of the goal differential that occurred when this player was on the ice can be attributed to him? This is not necessarily an easy question to answer-indeed, it's very difficult-but it's the question that has to be answered in order to understand what type of players will contribute to building a winning hockey club. I'll explore this in a later article, but for goalies, it seems logical to assume that the majority of their impact comes from their ability to stop the puck.

2.  Clutch is not all that significant.

If clutch were significant, we'd expect teams with clutch players to be able to outperform. Leaving aside the various issues of how we know who's clutch, this simply doesn't happen. Teams laden with Stanley Cup veterans under perform their expected winning percentage one year and outperform it the next. There's no rhyme or reason to it-it just happens. Even if clutch is playing a role that we can't detect, it's swamped by plain old fashioned ability-a team that outscores like the Oilers of the 80's doesn't need to be particularly clutch-they won't be looking for a goal late in a game down by one very often, whether it's regular season or playoffs.