Team Rankings and Playoff Probabilities

The first chart shows how each team in the league has fared thus far in terms of adjusted winning percentage. Adjusted winning percentage is essentially each team’s Pythagorean Expectation, with the exception that, instead of goals for and goals against, I use adjusted goals for and adjusted goals against. In computing each team’s adjusted GF and adjusted GA, I simply take each team’s actual GF and GA, subtract shootout goals and empty netters, and then make a second order correction for schedule difficulty. In determining schedule difficulty, oppositional strength is determined through the goal differential of the opponent, the location of the game (i.e. whether it’s a home or away game), and the circumstances of the game – namely, whether or not it’s the second half of a back-to-back for the road team.

If you compare these rankings to the actual standings, most teams are similarly positioned. There is, however, one notable outlier.

The Rangers are currently 9^th in the league in points per game, yet 26^th by this metric. Not surprisingly, they’ve had a ton of success in the shootout so far (record: 9-4), which is basically equivalent to sheer luck. While some may point to the Rangers shot differential, especially at EV, as evidence of them being not that bad of a team, I’m inclined to disagree. Reason being: they're in the red in terms of expected goals, which suggests that they’ve been below average in terms of shot quality for, shot quality against, or both.

Of course, there are a few teams who can be labeled as either lucky or unlucky in general – notwithstanding the fact that that these rankings aren’t too different from the standings. In other words, teams who are either better or worse than these rankings would suggest.

In terms of teams that probably aren’t as good as their adjusted winning percentage would indicate, I’m thinking of BOS, FLA, and PHI. These teams have all been greatly aided by the percentages this year. I think that the success that each of these teams has experienced thus far is unlikely to continue during the remainder of the regular season and the playoffs. Granted, the Flyers outperformed their underlying numbers last season as well. As the sample size in games played increases, it becomes increasingly difficult for one to point to randomness in an attempt to account for success with the percentages. On the other hand, I find it very difficult to look at a team that’s scored 15 shorthanded goals and conceded none and say that they haven’t been at least somewhat fortunate. I just don’t think that they're an inherently good hockey team.

And for teams in which the opposite is true, I’m thinking of OTT, LAK, COL, and TOR. These teams have all been – for lack of a better term – utterly screwed by the percentages this season, to the point where none of them have a realistic shot at making the playoffs. This is unfortunate in the sense that, if you were to compare this group of teams with the three listed above, I don’t think that there’s much to choose between them. Hell, I think that one could make a reasonable argument for the Kings being the best team of the seven – at least, looking at it in terms of which team is most likely to experience success from this point forward.

Anyway, here the playoff probabilities for all 30 teams (updated on 02/19/09). The left hand column contains seeds 1-15 in each conference, with the corresponding column for each team showing the probability of finishing the season in that position, expressed as a percentage. So, for example, the Blackhawks have an (approximately) 1% chance of finishing in 1st place in the West. The final two rows contains each team's probability of making the playoffs (in the second last row) and each team's probability of winning the division (in the last row). Future game probabilities are based on the respective adjusted winning percentages of the involved teams, game location, and whether or not the game is the second half of a back-to-back for the road team.

Coming off a Win/Loss: The effect of Prior Results

I’ve often wondered if the outcome of a team’s previous game has any affect on the result of that team’s subsequent game. Intuitively, I wouldn’t expect there to be much of an effect. The outcome of any given game is determined by many different factors, some of which are known to have a large effect.

While the result of the previous game could conceivably be one of these factors, it would probably rank pretty far down the list in terms of importance. In other words, if there is such an effect, I would expect it’s magnitude to be small.

That said, I’ve heard it argued before that the previous game does in fact have an effect on a team’s performance in the following game, so it’s something worth examining, I think.

On the one hand, some have suggested that the momentum of winning the previous game carries over to the next game, thus enhancing a team’s chance of success. According to this line of reasoning, the average team should do slightly better when coming off a win than when coming off a loss.

Conversely, others have suggested that winning breeds complacency, with losing having the opposite effect. This approach predicts that teams should do better when coming off a loss, on average.

I don’t think that either of these arguments have much merit. Both are based on the idea that psychological factors have a measurable effect on game outcomes, a premise with which I personally disagree. While casual fans often resort to folk psychology when discussing success and failure at the NHL level, its relevance has never, to my knowledge, been demonstrated through actual evidence.

In any event, I attempted to determine if the preceding game has any effect on following game results. My methodology was pretty straightforward. The sample included all regular season games played during the seasons of 2005-06, 2006-07 and 2007-08. Each game played was classified as a win, a loss, or a tie for both of the involved teams. For the sake of simplicity, any game that went past regulation was considered to be a tie. I then looked at whether that team won, lost or tied in its next game. Here are the results for 2007-08. The teams that had a better record when coming off a win compared to coming off a loss are shaded green. Teams for which the opposite was true are shaded orange.

Below is a chart of the average winning percentages of all 30 teams in each situation (coming off a win, coming off a loss, and coming off a tie) for all three seasons. The left hand column shows the average winning percentage for all 30 teams in games played after a win. The middle and right hand columns do the same, only for games where the team was coming off a loss and tie, respectively. It’s necessary to look at the average winning percentages rather than the aggregate winning percentages for one simple reason: better teams, by virtue of winning more games, tend to play a higher percentage of their games when coming off a win. For example, the Thrashers played a mere 18 games coming off a win last season; Detroit played 46. It needn’t be explained as to how this could confound the results.

Also included is a chart that breaks down the number of teams that had a better record after winning vis-à-vis their record after losing, and vice-versa.

The results are pretty consistent with my expectation in that the effect of the preceding game appears to be fairly small. In the 90 ‘team-seasons’ analyzed, 41 teams had a better record after winning, whereas the other 49 had a better record after losing. The average winning percentage for teams coming off a win was slightly less than 0.49. For teams coming off a loss, that figure was approximately 0.505. Therefore, it can be said that teams have, since the lockout, done slightly better after losing their previous game than they have when coming off a win. Of course, the margin is quite small and well within the potential range of random variance. Even supposing that the results are statistically significant, the influence of a team’s preceding game upon the outcome of its following game appears to be limited.

Even Strength Shooting Percentage

To what extent is team-to-team variation in even strength shooting percentage the product of random variation? I'm not sure what the answer is, but I suspect that the contribution is substantial. I've included several graphs below in order to illustrate this. The table below the first graph contains the data upon which each distribution is based.



The first graph. The yellow line is the actual spread in EV ( note: 5 on 5 only) shooting percentage that exists among NHL teams at this point in the 2008-09 NHL season.

The X-axis contains the percentage 'categories' in which the figure listed is the midpoint value of the category.

They Y-axis is the relative frequency of each individual percentage 'category'.

As an example, 6 teams in the NHL this year currently have an EV shooting percentage that is between 0.08 and 0.085. As there are 30 teams in the league, the relative frequency is 0.2 ( as 6/30 = 0.2). The midpoint value for this category is 0.0825. Therefore, the relative frequency of the '0.0825' category is 0.2.

The pink line shows the predicted spread in EV shooting percentage if each team had the exact same underlying shooting percentage at ~0.085 ( i.e. the league average 5-on-5 shooting percentage). This was determined through the following.

1000 "seasons" were simulated.
For each "season", each team has an artificial shooting percentage.
This percentage is the number of goals that a team scores over x number of trials.
The number of trials is equivalent to the number of EV shots that the team has taken through this point in the season.
The probability of "scoring" in each individual trial is the same for every team at 0.085.
Therefore, any team-to-team variation will be the product of randomness.

A specific example will hopefully make this clear.

Philadelphia has taken 984 shots at EV at this point in the 2008-09 season. Therefore, Philadelphia has 984 trials. The probability of scoring in each individual trial for Philadelphia is the league average EV shooting percentage at ~0.085. In Philadelphia's first "season", they scored 107 times. As 107 / 984= ~0.109, Philadelphia's EV shooting percentage for their 1st "season" is 0.109. I then did this for every team and repeated the process 100 times (i.e. simulated 100 seasons). Here's how the first 48 or so shaped out:




Even though the probability of a goal on any given "shot" is 0.085, the artificial shooting percentage will necessarily differ from 0.085 due to insufficient sample size. While it goes without saying, as the sample size (number of trials) increases, any given team's artificial shooting percentage will more closely approximate 0.085. Therefore, for teams that have taken more shots through this point in the 2008-09 season will have more "trials". The spread in shooting percentage for these teams will be lower due to them having a greater number of trials. For example, the standard deviation for Detroit's 100 seasons is ~0.007. By comparison, the same value for Pittsburgh is ~0.009.

The same rules regarding the x and y axes that apply to the yellow (actual) distribution also apply to the pink (random) distribution. The relative frequency for the pink distribution is the proportional representation of each artificial shooting percentage category. As an example, as there were 100 "seasons" and 30 teams, the entire sample consisted of 3000 artificial shooting percentages. 601 artificial percentages fell between 0.08 and 0.085. The relative frequency for the '0.0825' category is therefore ~0.2, as 601/3000 = ~0.2.


As many will note, the spread between the worst ( NYI at 0.069) and best ( BOS at 0.108) teams appears to be sizable, as is indicated by the breadth of the yellow distribution.

However, the pink distribution is itself fairly broad. In fact, it very closely resembles the yellow distribution. As would be anticipated, the yellow distribution is slightly broader than than its counterpart, but the difference is not large. This suggests that much of the inter-team variation in EV shooting percentage is the result of randomness.


The second graph, shown above, contains a 'smoothed' version of the actual distribution, which is represented by the dark line. The average shooting percentage in the league is currently ~0.085, as has been mentioned. The standard deviation is currently ~0.01. The dark graph is simply a normal distribution (bell curve) with a mean of 0.085 and standard deviation of 0.01.

The light line is merely the pink distribution reproduced. Again, the two distributions are very similar to one another.

The fact that the actual distribution is somewhat broader than the expected distribution shows that teams do indeed differ in their underlying shooting percentage at EV. Nonetheless, this variation is only very slightly larger than what would be predicted by chance alone. The underlying differences appear to be minimal.

Vic Ferrari has done a lot of excellent, excellent work over at his site that is similar to this. Much of his work has examined the ability of individual players to influence shooting and save percentage while on the ice. His findings are comparable in that the vast majority of inter-individual variation seems to be due to random variation.

EDIT: I've included some supplementary data tables for the purposes of clarity.

I should mention that the data I used for this post was obtained at behindthenet -- an awesome site that I highly recommend. Without it, this post wouldn't have been possible.

The Bruins

The Bruins have been one of the surprise teams this year, what with them having the best record in the league at the halfway point (few would have predicted this to be so). They also have the best goal differential, so it's not as if they've been lucky in the conventional sense by winning a lot of close games. However, just because a team's record is proportional to its goal differential doesn't necessarily mean that it hasn't been lucky.


This is a chart showing how the Bruins have fared in various game situations so far this season. The numbers are as of 01/07/08. A couple things can be said about these numbers:

1. The Bruins success appears to largely be a product of the percentages. They have the best shooting percentage in the league, as well as the best save percentage. This also holds true at even strength.

2. For a team with such a good record and goal differential, the Bruins are anomalous in that they're pretty average with respect to shot differential. In fact, they get outshot on average.

The Percentages

The problem for Boston is that there isn't a great deal of repeatability in terms of the percentages, particularly at even strength. This post by Tyler at mc79hockey demonstrates how the sum of a team's even strength shooting percentage and its even strength save percentage tends to regress to 100 as the season progresses. The Bruins currently sit at ~105. If I was a betting man, I'd place money on that figure significantly decreasing by April.

Are Boston's percentages at all sustainable?

We know from past posts that, while fluctuations in the percentages do indeed have little sustain in the future, a team is able to reliably influence its shooting/save through shot quality. Shot quality is moderately correlated with the percentages and is substantially reliable. Thus, over a sufficiently large sample of games, there would still likely be team-to-team variation in the percentages, with this effect being mediated by shot quality.

In past seasons, the team that leads the league in shot quality for typically has a shot quality index of roughly 1.1. That is, that team takes shots that, on average, are 10% more likely to result in a goal than the average team.

Conversely, the team that leads in the league in shot quality against typically has a shot quality index of roughly 0.9. That is, that team allows shots that, on average, are 10% less likely to result in a goal against than the average team.

If we make the very conservative assumption that Boston currently leads the league in both shot quality for and shot quality against, then we can estimate the Bruins' expected shooting percentage based on these adjustments.

Expected shooting percentage = shot quality for index * league average shooting percentage
Expected save percentage = 1- ( shot quality against index * league average shooting percentage)

League average shooting%: 0.0917

Boston's expected shooting percentage: 1.1*0.0917 = 0.10
Boston's expected save percentage: 1-(0.9*0.0917)= 0.917

Boston's actual shooting percentage: 0.118
Boston's actual save percentage: 0.93

Therefore, even if we assume that Boston currently leads the league in both shot quality for and shot quality against, the Bruins' have still outperformed their expected shooting percentage and expected save percentage. While far from constituting definitive proof of good luck, it is suggestive of it.

In actuality, the Bruins have not been leading the league in either shot quality for or in shot quality against. Hockeynumbers tabulates data on shot quality that is periodically updated throughout the season. While the data is only available for specific game situations (EV, PP, SH), figures for overall shot quality can be obtained by dividing each team's expected goals for/goals against by their corresponding shots for/shots against total, and then expressing the resulting figure relative to the league average.

In addition to having a negative shot differential, the Bruins are below average in both shot quality for and shot quality against, thus making it even less likely that they'll replicate their impressive shooting/save percentage in second half. Indeed, Boston is in the red in terms of its expected goal differential, as is nicely illustrated here

Boston's 'true' even strength shooting/save percentage

As displayed in the table at the beginning of the post, the fact that Boston has managed to lead to the league in both shooting and save percentage is largely tied to even strength play -- that is, the overall percentages are largely being driven by the exceptional even strength percentages. Therefore, the sustainability of Boston's overall percentages is critically contingent upon sustaining its high percentages at even strength. Boston's shooting/save percentage at even strength will likely fall to something more reasonable by the time the season has ended. At the same time, however, it's unlikely that its EV shooting/save percentage is merely average.

To illustrate this, assume that Boston's true underlying even strength shooting percentage is exactly league average (~0.084), with the same holding true for its even strength save percentage (~0.916). The Bruins have taken 890 shots at even strength so far this season, while allowing 920. If a team with a true EV shooting percentage of 0.084 takes 890 shots, the probability of shooting 0.109 or better by chance alone is remote (about 4 times per thousand). Likewise, if a team with a true EV save percentage of 0.916 has 920 shots against, the probability of having a save percentage better than or equal to 0.939 by chance is equally minuscule (about 5-6 times per thousand). Thus, Boston's underlying EV shooting/save percentage -- while almost certainly lower than what they've attained thus far -- is probably above average. Therefore, a complete regression to the mean is unlikely.

The First Goal

In hockey, scoring the first goal is important. Last season, every single team in the league had a better record in games where they scored first compared to games where they did not.

However, one has to wonder: is scoring the first goal as important it's made out to be? For example, hockey media types love to harp on the importance of scoring first, invariably citing team A's record when managing to do, or how team B's losing streak is explicable through its tendency to surrender the lead early in the game. Not only does this emphasis conflate cause and effect, but it's insufferably repetitive and trite. One would intuitively expect the team that scores first to have a higher probability of winning, and it's fairly obvious that such a relationship exists. In fact, I suspect that the probability of winning when scoring first is not significantly different than what would otherwise be expected on a mathematical basis.

Moreover, scoring in general is important, whether it be the first goal of the game or the last one. Any given goal is more or less significant and potentially determinative of the game's outcome. To make the distinction between the first goal and any other goal scored during the game just smacks of arbitrariness. Scoring first is probably more correlated with winning than, say, scoring second, but I'd be surprised if the difference was large, and shocked if it was large enough to warrant the special attention.

Thus, this post seeks to answer two questions:

1. When a team scores scores first,what percentage of the time does it win the game? Is this value any different from what probability theory predicts it to be?

2. How much more important is the first goal than the second goal?

The first question can be answered through application of the poisson distribution. As Alan Ryder explains in this paper, goal scoring in hockey is essentially a poisson process. Ryder has determined that a team's probability of winning by z goals in regulation at any particular point during the game can be found through application of the following formula in Microsoft excel.

Pr(Win by z) = EXP(-(mt+vt)) * (mt/vt)^(z/2) * BESSELI(2*SQRT(mt*vt),ABS(z))

where:

m = that team's average goals for per game*
v = that team's average goals against per game*
t = the time remaining in regulation divided by 60
z = the margin of victory

* - Adjusted goals ought to be used here as they provide the best measure of a team's true ability to score and prevent goals.

Through use of this formula, the theoretical probability of winning in regulation for a team that scores first can be determined.

In the 2007-08, there were 1222 games that had at least one goal scored in regulation. On average, the first goal was scored just prior to the 12 minute mark of the 1st period. Thus, our value for t is 0.803.

The m and v values are, for the purposes of the formula, 2.639 and 2.545. These figures are adjusted to reflect the following:

1. That the team that scores first is, on average, slightly better than the average team.
2. That the team that gives up the first goal is, on average, slightly worse than the average team.
3. That the home team is more likely to score the first goal.

For determining the probability of winning, the z value ranges from 0 to sufficiently high n (~10), as the team that scores first must only maintain the existing margin -- or increase it -- in order to win. For the probability of losing, z is -2 to sufficiently low n (~-10), as the trailing team must outscore the opposition by 2 or more goals in order to win. For the probability of a tie, z is -1, as this will restore the original margin of zero.

Thus, all of the necessary input variables having been determined, the theoretical probability of winning when scoring first can be computed. Below is a comparison of the theoretical probability against the actual probability.



As can be seen, the actual and theoretical probabilities more or less mirror one another, save for the fact that probability theory predicts ties to occur less frequently than they actually do. This reflects the fact that teams do, to some degree, play to the score, particularly as the end of regulation nears. The upshot of there being more ties in reality is that the first goal is somewhat more valuable than what the values expressed in the chart would otherwise indicate. For example, while the actual probability of winning is nominally lower than its theoretical counterpart (0.599 vs 0.615), if one examines only those games resolved in regulation, the actual probability of winning is slightly higher than the theoretical probability (0.764 vs 0.744). Nonetheless, the important part is that the theoretical and actual values are essentially equivalent to one another. If the actual probability of winning was substantially higher than the theoretical probability, the large amount of emphasis placed on scoring first may be justifiable. However,the fact that they are virtually the same means that the advantage conferred by scoring first is neither surprising nor contrary to expectation, thus making it unworthy of mention.

What about the importance of the second goal vis-a-vis the first goal?



Scoring second is very nearly as highly correlated with winning as scoring first. And yet, it is the latter that -- rather unfairly -- receives all of the attention. In this sense, the emphasis that's placed on scoring first seems more than a little arbitrary. It's simply not very accurate to accord the first goal special status when, in actual fact,the vast majority of goals scored throughout the course of a hockey game are significant.

Worst post-67 Cup Winning Team?

The columns in the above list show, from left to right,  the season,  the cup winning team during that season, that team's adjusted winning percentage (AW%) during the regular season, and how that team ranked in the league in terms of AW% during that season.   The teams that I've highlighted are teams that I feel are arguably the worst post-67 teams to win the cup,  or teams that are generally included in that discussion by others.

A few general comments:

1.  Those Hab teams of the late 1970s were very,  very good.
2.  The Oilers dynasty teams,  despite putting up some gaudy offensive totals,  don't appear to be much better than the average cup winning team.
4.  The 89' Flames were probably the best non-dynasty team of all time.

Now, the analysis:

The 91' and 92' Penguins

 While their AW% is pretty unspectacular for a team that managed to win the cup two consecutive years,  a lot of this probably has to do with the fact that Lemieux only managed to play 90 regular season games in total during those two seasons.    That probably explains the regular season success/playoff success discrepancy.    With a healthy Lemieux,  neither of those teams are close to being the worst post-67 to win it all.   Not even remotely.

The 86' Canadiens

Contrary to popular belief,  the 86' Canadiens were not a mediocre team that Roy carried to the cup.   Despite receiving average goaltending for the majority of the regular season (sv%=0.873),  they had the third best AW% in the league.   Considering that they,  rather fortuitously,  managed to avoid playing both the Oilers and the Flyers during their road to the cup,  it's not really surprising that they managed to win.    Not the worst post-67 team to win the cup.

The 95' Devils

Admittedly,  their regular season numbers were pretty underwhelming,  finishing 10th in a 26 team league in AW%.   However,  a lot of this,  I think,  had to do with bad luck.   They were averaging 30.1 SF/G and 25 SA/G during the regular season and, despite playing tight defensive hockey,  had a team save percentage of only .901.   Presumably,  they just weren't getting the bounces.   All of this was to change in the playoffs,  though.   They went 16-4,  scored 67 GF while allowing 33,  averaged 30.4 SF and 23.2 SA,  all the while starting every series on the road against tough competition (DET, PHI, PIT, BOS).   Highly impressive.

The 93' Canadiens

Like the 86' team,  the 93' Habs benefited from not having to play the truly elite teams during their cup run (PIT, DET, CAL, BOS).   The difference is that the 93' team was much more reliant on goaltending and luck (12-1 in one goal games) to do it.    Also,  their regular season was fairly mediocre by cup-winning standards.    Still,  they only managed to lose 4 games en route to winning.    Probably not the worst post-67 cup winner,  but we're getting warmer.

The 90' Oilers

I don't know too much about this team,  but the fact that Ranford won the Conn Smythe suggests that they,  like the 93' Canadiens,  were pretty dependent on goaltending.   However,  they were still the 5th best team that year and were only one year removed from their dynasty.    Not the best post-1967 cup winner by any stretch of the imagination, but not the worst ceither.

The 04' Lightning

The 04' Lightning were one of the best teams in the league during the regular season.   While one might point out that they played in the league's worst division that year,  AW% takes schedule difficulty into consideration.   They were the 4th best team despite regularly playing the likes of FLA,  ATL,  WAS,  and CAR.    Their shot differential was impressive too (30 SF/G, 25.3 SA/G),  so it's not as if their success was being driven by the percentages.   Why,  then,  have I chosen to include them in the discussion?    Well,  that team was extraordinarily fortunate on the injury front that year.   They only lost some 35 man games to injury that year,  the majority of which belonged to Andre Roy.    It can be safely assumed that this had a lot to do with their success that season,  and the fact that they were fairly average in both the following and preceding seasons lends support to this.   Still,  they're not the worst.

The 06' Hurricanes

It's no secret that the Hurricanes were the recipients of tremendous good fortune in terms of their opponents sustaining bizarre and debilitating injuries to key players all throughout the postseason.   Injuries to Koivu,  Roloson,  and virtually the entire Sabres defence contributed more to that victory than any single Hurricane player.   What will surprise most,  though,  is how ordinary Carolina was during the regular season that year.    While their 112 points might give the impressive that they were an elite team,  this was largely the product of: a) playing one of the easiest schedules in the league b) doing well in the shootout and c) outperforming their goal differential by winning close games.   Their AW% was 13th in the league --  barely above average.   This was,  without question,  the worst post-expansion team to win the cup.


EDIT: As requested,  here are the Top 50 post-expansion teams according to AW%.

Parity

Since the 2005-06 season,   there’s been a lot of talk in the media about the amount of parity that currently exists in the NHL. While I’m inclined to agree with this,   I have a feeling that people are simply looking at the (presumably diminished) spread in point totals and making their conclusions on that basis.    This is,   of course,  completely misguided and incorrect.

Points totals themselves are not necessarily indicative of reduced parity.    For in order to measure parity,   you first have to measure team strength,   and point totals do not adequately measure team strength.

To be sure,   point totals are correlated with team strength.    Hockey would be a very strange game if this were not true.    However,  there are certain problems with point totals that preclude its use as a proxy for team quality.

For one,   points totals are influenced by overtime and shootout success,   and I would argue that overtime and shootout success have very little to do with how strong a team is.    When I use the term ‘team quality’,   I’m referring to how good a team is at actually playing hockey.    And when I use the term ‘actually playing hockey’,  I’m basically referring to how good a team is at winning in regulation.    The distinction between regulation and extra-regulation results might seem arbitrary at first,   but there's good reason for it.    For one,  overtime and shootout success has almost nothing to do with regulation success.    Observe:



Moreover,  extra-regulation results are not very repeatable across seasons, especially compared to regulation results.



The fact that extra-regulation results have virtually nothing to do with regulation results and have little to no repeatability suggests that they are largely the product of randomness.    If something is largely random,   then it cannot be thought of as an underlying ability.    And if something cannot be thought of as an underlying ability,  then it ought not to be part of a metric that ostensibly measures team strength.    And yet,   shootout and overtime success does have a sizable affect on point totals. Hence,  my reluctance to use point totals as a metric for team strength.

However,   the inadequacy of point totals goes much deeper than this.   Even before the advent of 4-on-4 overtime and the shootout, points were not the best metric for team strength.    The reason for this is that point totals only reflect wins and losses while completely ignoring the margin of victory.    If there are two teams with similar point totals, one of them tending to win convincingly and lose narrowly,   the other tending to win narrowly and lose convincingly,   then the former team is,   in almost all cases,   the better team.    The concept is an intuitive one.    If you disagree with the assertion that a team’s goal differential better conveys its ability relative to its point total or place in the standings,  then you’re probably at the wrong site.

Granted,  goal differential per se,   while better than points,   is not the best available metric.    Several corrections need to be made to it for this to be true.    Firstly,   shootout and empty net goals should be excluded from the totals,   as they provide no useful information.   Secondly,  raw goal differential is problematic in that not all teams play identical schedules.   Some teams,   usually by virtue of playing in a stronger division or conference,   are burdened with a more difficult schedule than average.    If you thought that the 2005-06 Phoenix Coyotes and the 2005-06 Carolina Hurricanes had equally difficult schedules,  then you would be mistaken.    Thus, some attempt should be made to correct for schedule difficulty.   Finally,  it is not so much a team’s absolute goal differential that is important,   but its GF-GA ratio.    A team that scores 200 goals and concedes 100 is better than one that scores 400 and gives up 300.    Furthermore,  simple goal differential is too sensitive to scoring context for it to provide any useful information on league parity,   as it would lead to the spurious conclusion that there was less parity in higher scoring seasons.    These two problems are avoidable by using each team’s Pythagorean expectation instead–  essentially,  its theoretical winning percentage determined through the following calculation:

(Adjusted goals for)^2 / [(adjusted goals for)^2 + (adjusted goals against)^2]

The resulting metric can be termed adjusted winning percentage.

AW% is important as provides us with a suitable metric for assessing team strength.   By computing the standard deviation in AW% in any particular season,  we’re essentially measuring parity.

What,  then,  does AW% tell us about the amount of parity in the NHL over the last ten years?


A few comments.    Firstly,  parity in the pre-lockout NHL was pretty invariant on a year to year basis (mean: 0.094, ST DEV: 0.008).    Only 1996-97 is anomalous,   with all of the remaining values falling between 0.092 and 0.101.    Secondly,   there is clearly more parity (read: the standard deviation in AW% is smaller) in the post-lockout NHL relative to the pre-lockout NHL.    The difference may not seem like much,   but the 2005-06 and 2006-07 values are separated by one SD from the pre-lockout mean.    The value for 2007-08 is 4 SD(!) from the pre-lockout mean.    That's a fairly significant difference.

Parity in the new NHL seems to be more reality than fiction.    Teams really are less separated in ability now compared to five or ten years ago.    I find this interesting as the purpose of having the shootout and three point games seems,  to me,  like a ploy designed by the NHL with the intention of creating the illusion of parity.   However,  the fact that the new NHL is characterized by genuine parity has in some sense obviated this purpose.    That considered,   perhaps the NHL should do away with three point games and the shootout.   I certainly wouldn't complain.