Friday, 29 August 2014

Puckerings archive: Search for Meaning in RTSS (22 Oct 2001)

What follows is a post from my old hockey analysis site (later It is reproduced here for posterity; bear in mind this writing is over a decade old and I may not even agree with it myself anymore. This post was originally published on October 22, 2001 and was updated on April 10, 2002.

The Search for Meaning in RTSS:Hits and Takeaways
Copyright Iain Fyffe, 2002
Many thanks to Marc Foster

In 1997-98, the NHL introduced its Real-Time Scoring System (RTSS). This computerized system allows the tracking of many new official statistics, such as ice time, blocked shots and hits. This has given a wealth of new data to perform statistical analysis with. But there is a serious question: do the new statistics really mean anything?

Ice time is obviously a meaningful stat. The amount of time a player spends on the ice is a direct comment on his value, relative to his teammates. But do stats like hits or takeaways really indicate anything, or are they just numbers? In this essay, I will show that, indeed, hits and takeaways do have value.

If a statistic is to have value, it must indicate something about a player or team. Hits and takeaways would seem to indicate how aggressive a player is, by either making physical contact with the opponent, or by pressuring him and taking the puck away. But is this good thing? The best way to answer this question is to determine if the actions represented by these stats contribute to winning. After all, the point of hockey is to win the game. If hits and takeaways contribute to winning, then they are meaningful stats.

I will examine these statistics by using correlation to team winning percentage. If the stat has a positive coefficient of correlation, we know that as the value of the stat increases, so does the team's winning percentage. The stat would therefore contribute to winning to some degree.
The raw stats of hits (H) and takeaways (TK) themselves have little value. Here are their correlations to winning percentage, as well as the correlation of the sum of hits and takeaways (H+TK):

 97/98  98/99  99/00  00/01  Average
 H  -.04  -.01  -.30  .20  -.04
 TK  n/a  .02  -.04  .19  .06
 H+TK  n/a  .01  -.25  .26  .01

So the raw numbers themselves have absolutely no relationship to winning or losing. By themselves, these stats are just numbers. Faced with this fact, we can try to develop a new stat using these raw data, to see if we can find any meaning.

My thought process for developing this new stat (called the Disciplined Aggression Proxy, or DAP, for reasons which will become apparent) was as follows. Perhaps the reason that hits and takeaways did not correlate highly with winning was because the aggressive play represented by these stats can often lead to taking penalties. Perhaps if a team were able to play in this aggressive manner while taking relatively few penalties, they would be more successful. At first, I used only hits in the formulae, not adding takeaways until it this was suggested by Marc Foster. There are two ways to represent penalties on a team level: penalty minutes (PIM) and times short handed (TSH). TSH is theoretically superior, since it represents actual short-handed situations, but as we will see, there is little difference between the two. The original DAP formulae were as follows:

Version 1: H / PIM
Version 2: H / TSH

I then tested the correlations for these formulae, with the following results:

 97/98  98/99  99/00  00/01  Average
 Version 1  .30  .26  .01  .39  .24
 Version 2  .18  .26  -.02  .47  .22

As you can see, the DAP formulae added much meaning to the stats. The correlations were now out of the range of having no meaning, into a range (.20 and thereabouts) where we cannot simply write the relationship off as a fluke. The 1999/2000 season seems to be a fluke; without it the average correlation would be higher still. To further test the validity of the DAP, I reasoned the following. A team that kills penalties well will suffer less from taking penalties. Therefore, I calculated a new index for each team, to represent both their relative aggression and their relative penalty-killing ability. To do this I took the team's DAP divided by the league DAP, and added the team's penalty-killing percentage (PK), divided by the league average PK. This number is only used as a rough test, as it has no real meaning. The results of this are as follows:

 97/98  98/99  99/00  00/01  Average
 V.1 + PK  .36  .30  .10  .43  .30
 V.2 + PK  .25  .30  .10  .47  .43

The correlations are even higher, which lends more validity to the value of the DAP. Again, note the apparent flukiness of the 1999/2000 season.

But the development of the DAP did not end there. Marc Foster suggested the inclusion of takeaways along with hits to represent aggressive play, and this change is a good one. I therefore defined two new versions of the DAP:

Version 1A: (H + TK) / PIM
Version 2A: (H + TK) / TSH

The correlations for these are as follows:

 97/98  98/99  99/00  00/01  Average
 Version 1A  n/a  .27  .03  .42  .24
 Version 2A  n/a  .26  .02  .50  .26

Note that the averages here is misleading; we should only compare them against averages for the same three-year period. These averages are .22 for Version 1 and .24 for Version 2. The improvement is small, but still there. I also ran correlations including the teams' PK, as before:

 97/98  98/99  99/00  00/01  Average
 V.1A + PK  n/a  .31  .13  .47  .30
 V.2A + PK  n/a  .30  .14  .57  .34

These are the highest correlations we've seen. The averages for Versions 1 and 2 over this period are .28 and .31 respectively.

Therefore, by transforming hits and takeaways into the Disciplined Aggression Proxy, we have found meaning in two of the NHL's new statistics. Now let's apply our new stat.

When applying the DAP to players, I recommend using Version 1A. This is because there is no player-level stat for the number of times shorthanded. The number of minor penalties taken by a player would be a fair approximation, but this data is rarely available. And since Version 1A is only marginally worse than Version 2A, there is no great loss. I will now discuss some players who have the best ranking in DAP (Version 1A) over the past two years. The new stat will shed some new light on the value of some of these players.

1. John Madden
Madden has ranked 2nd in the NHL in DAP each of the past two years. This is remarkable consistency. He is known as perhaps the best checking forward in the game, and this reputation is well-deserved.

2. Curtis Leschyshyn
Due to his pitiful offence, Leschyshyn is not given the respect he deserves. He placed 8th in DAP in 1999/2000, and 4th last year. He is truly an elite player when it comes to aggressive yet disciplined play, and he deserves much more respect than he gets.

3. Ulf Dahlen
Dahlen was 11th two years ago and 7th last year; he's another remarkably consistent performer. He gets credit as good defensive forward, but perhaps not enough.

4. Jeff Nielsen
This defenceman was 15th in 1999/2000, and 8th in 2000/01. He's basically an unknown, but hopefully not for long. His aggressive play deserves respect.

5. Steve Rucchin
He was 18th in 1999/2000, and would have placed very highly last year had he not been injured. He has significant offensive skill to complement his aggressive play.

6. Jay Pandolfo
Pandolfo led the NHL in DAP in 1999/2000, but slipped to 27th the following year. Still, that's a very good ranking, and he deserves kudos for it. With Pandolfo and Madden, the Devils have been loaded with good, aggressive, talent.

7. Sami Kapanen
Another player whose reputation is as a strong two-way forward, Kapanen ranked 13th in 1999/2000 and 16th in 2000/01. He deserves his reputation.

8. Josef Stumpel
The first surprising player on the list, Stumpel is known as a high-skill forward who often does not give his all. But he ranked 10th in DAP in 1999/2000, and 20th last year. You may not notice his aggressive play, but it's there. Don't call this guy a floater anymore.

9. Juha Lind
Lind was in the top 30 in 1999/2000, and rose to 3rd last year. His unfortunate lack of offensive skill has hurt his playing time, but he is a good grinder.

10. Sergei Berezin
Another surprise, Berezin is regarded as a skilled, soft player. But he was 6th in 1999/2000, and in the top 30 last year.

Other noteworthy players

Viktor Kozlov, Jody Hull, James Black, Andrew Cassels, Patrick Poulin, Don Sweeney, Robert Kron, Sergei Brylin, Jonas Hoglund and Mike York all deserve credit for their aggressive yet disciplined play over the last two years. Some are already known as two-way players, some are not but probably deserve to be. Also worth noting are two rookies from last year, Stephane Robidas (5th in DAP) and Brent Sopel (6th). Keep an eye on these players. They are solid contributors to their teams.

Friday, 22 August 2014

Puckerings archive: Goal-Scoring and League Talent Level (25 Sep 2001)

What follows is a post from my old hockey analysis site (later It is reproduced here for posterity; bear in mind this writing is over a decade old and I may not even agree with it myself anymore. This post was originally published on September 25, 2001 and was updated on April 10, 2002.

The Relationship Between Goal-Scoring and League Talent Level
Copyright Iain Fyffe, 2002

In this era of an increasingly watered-down NHL and concurrent low levels of scoring, one often wonders about the relationship between the level of scoring and the level of talent in the NHL. This subject was addressed in some detail by Klein and Reif (KR), in "The Klein and Reif Hockey Compendium". However, seeing as KR wrote their piece in 1987, it would be appropriate to re-examine their arguments using the data that we now have available, specifically the 1987-88 to 2000-01 NHL seasons.

KR's argument is this:

"Throughout the history of the game, in those periods when the talent level in a league has risen through the consolidation of franchises or the addition of a large number of skilled players, the level of goal-scoring has consistently fallen. And when the concentration of talent has been diluted by expansion or wartime service, goal-scoring has consistently risen. When rule changes are not a factor and you see the rate of goal-scoring climb, you know something bad is happening, because more goals means bad hockey." (p.15)

KR argue that unless there is a rule change to blame, if scoring has increased, then the quality of play has decreased. If scoring dropped, this means the league talent level has improved. They demonstrate this quite convincingly with their discussion of the ECHA, NHA, and NHL to 1986-87. To recap this discussion, I will examine the 56-year period from 1931-32 to 1986-87. The starting point is selected as it follows the last major rule change, the introduction of forward passing.

During this 56-year period, the change in scoring from one year to the next varied from -15% to +19%. However, for 45 of those years (80% of the years examined), the change fell between -7% and +7% inclusive. So it seems the normal variance for scoring from one year to the next is about 7%. We will thus consider any change of less than 8% from year to year to be normal variation. Therefore any change of greater than 7% is to be considered unusual and needing explanation. These are the interesting years. Let us now examine these years that do not fall within the range of normal variation, to seek possible explanations for the changes.

1932-33: -8% change from prior year
There is no apparent reason for this change. There are no major rule changes, just minor tweaks. However, since it is just slightly greater than the normal change, we can safely assume it is a fluke.

1935-36: -15% change from prior year
1936-37: +14% change from prior year
This is really only one change: the significant drop in 1935-36, which was reversed the following year by a significant increase in scoring. The drop has no easy explanation; there were no rule changes, and the makeup of the league did not change. We may have to write this one off as unexplainable.

1941-42: +18% change from prior year
1942-43: +19% change from prior year
1943-44: +13% change from prior year
1944-45: -10% change from prior year
1945-46: - 9% change from prior year
Here KR's thesis proves very true. The loss of players to wartime commitments wreaked havoc on the level of play in the NHL, and scoring skyrocketed. As players returned from war, scoring began to drop again.

1952-53: -8% change from prior year
Again, there is no apparent explanation for this change. However, the change is only 8%, so it is very close to normal.

1980-81: +9% change from prior year
Once again there is no real explanation here. The WHA had folded two seasons previous; perhaps there was some sort of delayed effect on the NHL? But again, the change is only 9%, so it may be a fluke.

It is also interesting to note anything we might expect would cause a significant change, but did not. For instance, the Great Expansion had no significant effect. This can be explained by the stagnation of the Original Six teams. There had been only six NHL teams for so long that the level of talent in the minor leagues had been building up for a long time. Therefore, the NHL could bear the addition of six new teams without diluting the overall talent level of the league.

The collapse of the WHA also had no apparent effect. This is also explainable; the NHL absorbed only four WHA teams, while all talent from the rival league was now available. Therefore, the effect washed out to some degree.

Now I will examine KR's thesis using the data from the NHL 1987-88 to 2000-01 seasons. Here is said data.

 Year  % change
 1987-88  + 1%
 1988-89  + 1%
 1989-90  - 1%
 1990-91  - 6%
 1991-92  - 3%
 1992-93  + 8%
 1993-94  -11%
 1994-95  - 8%
 1995-96  + 5%
 1996-97  - 7%
 1997-98  - 9%
 1998-99   0%
 1999-2000  + 4%
 2000-01   0%

There are four significant changes in this 14-year period: 1992-93, 1993-94, 1994-95, and 1997-98. I will examine each in turn.

1992-93: +8% change from prior year
This year two franchises were added (Ottawa and Florida), only one year after San Jose joined the NHL. KR's thesis predicts that scoring will increase in such a situation, and so it did.

1993-94: -11% change from prior year
The addition of Anaheim and Tampa this year made five expansion franchises in three years. By KR's thesis, this should have driven scoring upward. But instead it decreased significantly. Why is this? It is likely in part due to the increased number of European players in the NHL, necessitated by the expansion. From 1990-91 to 1993-94, the number of European players in the NHL grew from about 60 to over 130. However, this increase is not even enough to stock the new teams, so at best it would hold scoring steady, not decrease it. It seems KR's thesis is disproved here. However, with one addition that I will detail later, the thesis stands.

1994-95: -8% change from prior year
While my explanation for this is not literally in line with KR, it has the same spirit. This decrease in scoring is likely the result of the strike-shortened schedule. With a shorter schedule, each game was more significant, and therefore (in theory) players pushed themselves more during the season. They also did not need to worry about tiring out during an 80-plus game schedule. Therefore, the drop in scoring is produced by better hockey, and is not surprising.

1997-98: -9% change from prior year
This decrease, coupled with the previous year's 7% decrease, is likely the result of the talent level starting to catch up after the runaway expansion of the early 1990's.
Again, we should also note the things we would expect to have caused a change, but did not. Specifically, I am speaking of the four expansion teams added over three years from 1998-99 to 2000-01. Again, by KR's thesis, this should have caused a noticeable increase in league scoring. It did not; the changes over these three years are 0%, +4%, and 0%. Again, this is contrary to KR, but with the addition I propose (detailed below), it is explainable.

Adding to the thesis

KR's argument is that as the league talent level is diluted, the league scoring level will increase. This is true to a point. It seems, however, there is a limit to this rule. So long as there is an amount of appropriate talent available, dilution will cause scoring to increase. But as the two expansions of the 1990's (nine teams added in 10 years) has demonstrated, there is a breaking point.

The runaway expansion of recent years has led to the extreme dilution of the talent in the NHL. Some players in the NHL today would not have even been above-average players in the AHL in the past. There is a limit to how thin you can spread talent, before you start scraping the bottom of the major-league barrel. When you pass this limit, it begins to drive scoring down, rather than up. The reason for this is twofold.

Offence is more a function of natural skill than is defence. The players NHL teams have to resort to now have so little offensive talent that they lower the amount of offence in the league. The extension of this is a natural change in strategy. If you have a limited amount of offence on your team, it is natural to emphasize defence (think Minnesota Wild) in order to maximize your chances of winning. More teams have to rely on this sort of defensive play now than ever before, and this also results in less scoring.


Diluting the talent level only drives up scoring to a certain extent. Extreme dilution of talent, such as what we have seen over the past decade, actually drives down scoring. So we can add to KR's original thesis. If dilution occurs and scoring does not increase, and there are no rule changes to explain it, then you know that the well of legitimate, major-league talent has run dry.
We can only hope that the NHL realizes this, and that we do not see any further expansion for a long time.


Klein, J. and K.-E. Reif. The Klein and Reif Hockey Compendium. Toronto: McClelland and Stewart, 1987.

Thursday, 21 August 2014

Was Rugby a Significant Influence on Early Hockey?

In discussions of early hockey in Montreal, starting in the 1870s, you'll often see claims that rugby football was a significant influence on the early versions of the game. Take this article as an example, in which many comparisons are made between 1870s ice hockey and rugby. To be fair to author Adam Gopnik, not all of the comparisons he makes are of the direct kind, some are simply the similar physical natures of the two sports; however, I suspect this point is overstated when made in reference to the 1870s version of hockey, which was not as physical as the version of the game we know now. The author's application of modern impressions of hockey is indicated when he refers to  "...its combination of being the most flashily brilliant and speedy of games and at the same time the most brutal of contact sports..." Hockey in the 1870s did not feature nearly the speed that it does now; it could not, both because of the equipment used by the players, and the fact that they had to play every minute of the game, forcing the players to pace themselves.

But the idea of significant rugby influence is well-ingrained in stories about early Montreal hockey. Once again, the article above claims that "...what [James] Creighton was trying to create when he first codified the rules of hockey in 1873 was a form of rugby on ice, played according to rules inflected by lacrosse." Now, since we don't have any writing from Creighton himself on the topic, we must ask what the source of this information is. The most likely candidates are the tales told by a number of old-time Montreal hockeyists, some time after the fact.

Some of these claims are discussed here, in an article penned by E.M Orlick on the origins of ice hockey. Richard Smith claimed (in 1908, some thirty years after the alleged fact) that he had been involved with writing the first set of hockey rules, and used both field hockey and rugby as inspiration. Orlick rightly points out the problems with details in Smith's story, in that the dates do not line up and there is no evidence that Smith was actually a player in the very first recorded matches of hockey in Montreal; he showed up a few years later. Orlick then discusses the claims of William "Chick" Murray, who relayed his tale in 1936 (about 60 years after the alleged fact). Murray stated that it was his idea to pattern the rules on rugby, but to add lacrosse posts as goals. So it seems quite likely that Gopnik's impression of the origin of ice hockey rules were informed by Murray's claims. Again Orlick rightly points out the inconsistencies in Murray's story, and feels justified in rejecting it. I cannot disagree.

A later article by Orlick discusses Henry Joseph, who has a decided advantage over Smith and Murray in that we know he was a player in the first two organized ice hockey matches played in Montreal in 1875. This was written in 1943, and refers to events allegedly occurring as early as 1873, so we're now dealing with statements made 70 years after the fact. Joseph appears to be Gopnik's source that ice hockey was first played in 1873, two years before the first recorded match on March 3, 1875. It is, of course, eminently plausible that ice hockey, specifically the version played in the Victoria rink in Montreal, was played for some time before the first recorded game. Joseph goes on to say that James Creighton suggested a shinny-like game to be played on skates, noting that in Montreal at the time, shinny was played on ice, but not with skates. Finally Joseph claims that this shinny-like game had its rules patterned on rugby.

So these stories do seem to be the source of the idea that rugby was a significant influence on the first hockey matches in Montreal, perhaps enhanced by the fact that so much of early hockey was connected to McGill University, a stronghold of rugby. If the influence was so great, surely we should be able to detect it in the historical record. So let's have a look at early ice hockey and rugby, and compare their similarities to those between ice hockey and field hockey, a game that, at least superficially, seems to bear a more immediate resemblance.


As discussed at some length in my book On His Own Side of the Puck, the early Montreal hockey code was based directly on English field hockey association rules (which in turn were based on association football [soccer] rules). Here is a comparison of the offside rules from various rule sets.

1877 Montreal offside rule
Rule 2: When a player hits the ball, any one of the same side who at such moment of hitting is nearer to the opponents’ goal line is out of play, and may not touch the ball himself, or in any way whatever prevent any other player from doing so, until the ball has been played. A player must always be on his own side of the ball.

1875 Hockey Association offside rule
Rule 6: When a player hits the ball, and one of the same side who at such moment of hitting is nearer to the opponents' goal-line is out of play, and may not touch the ball himself, not in any way whatever prevent any other player from doing so, until the ball has been played, unless there are at least three of his opponents nearer their own goal-line; but no player is out of play when the ball is hit from the goal-line.

1863 Association Football offside rule
Rule 6: When a player has kicked the ball, any one of the same side who is nearer to the opponent's goal line is out of play, and may not touch the ball himself, nor in any way whatever prevent any other player from doing so, until he is in play; but no player is out of play when the ball is kicked off from behind the goal line.

1871 Rugby Football offside rules
Rule 22: Every player is on side but is put off side if he enters a scrummage from his opponents' side or being in a scrummage gets in front of the Ball, or when the ball has been kicked, touched or is being run with by any of his own side behind him (ie between himself and his own goal line).
Rule 23: Every player when offside is out of the game and shall not touch the ball in any case whatever, either in or out of touch or goal, or in any way interrupt or obstruct any player, until he is again on side.
Rule 24: A player being offside is put on side when the ball has been run five yards with or kicked by or has touched the dress or person of any player of the opposite side or when one of his own side has run in front of him.
Rule 25: When a player has the Ball none of his opponents who at the time are offside may commence or attempt to run, tackle or otherwise interrupt such player until he has run five yards.
Rule 26: Throwing back. It is lawful for any player who has the Ball to throw it back towards his own goal, or to pass it back to any player of his own side who is at the time behind him in accordance with the rules of on side.

You will note that although both ice hockey and rugby had an offside rule, they were different offside rules. Early ice hockey is sometimes called a "backwards game" in the sense that rugby is; that is, the object of play can be passed backward to teammates, but cannot move ahead (see rugby rule 26). This was not the case in hockey. The puck itself could move forward, so long as the pass recipient was not ahead of the puck at the time the pass was made. So you could pass the puck ahead of your winger, who could skate up to meet it. Indeed, in his 1899 book Hockey: Canada' Royal Winter Game, Art Farrell explained that this was the ideal method for making a pass; note that the offside rule had not changed at all by 1899.

If you go rule-by-rule, it's absolutely clear that field hockey played a much larger part in the rules of early ice hockey. I would go so far as to say that there is no reason to believe rugby had any influence at all on the rules, if you actually look at the rules. Even the sort-of-similar rules (such as offsides) are handled differently. Joseph claimed that rugby used one referee and two umpires, as we know that early ice hockey did. But the 1871 rugby rules make no mention of either, instead specifying that the team captains are the sole arbiters of infractions. However, lacrosse did use one referee and two umpires.


The earliest reference to positions in early Montreal ice hockey we have is from 1876, which identified players in a match as forwards, half-backs, backs and goaltenders. Goaltenders were referred to in 1875, but this was the first time other positions were named. Some of the rugby influence claims state that rugby positions were used (except, of course, for the curious addition of a goalkeeper). Neither modern rugby (nor modern field hockey) positions bear much apparent resemblance to this set-up. However, if we do look at groups of players rather than individual positions, in rugby today players will be referred to as forwards, half-backs and backs. No goaltender, of course.

However, this does not seem to be terminology contemporary to early ice hockey. Here, for example, we see that rugby in the 1870s featured forwards, half-backs, three-quarter-backs, and full-backs. Which is still quite close to the early ice hockey setup. However, we must also consider field hockey in this equation.

Hockey: Historical and Practical is a volume on English (field) hockey, written by J. Nicholson Smith and Philip A. Robson and published in 1899. As the title suggests, it discusses both the history of field hockey, and how it was played. When detailing the positions on the field, Smith and Robson break the players into four categories: the forwards, the half-backs, the backs and the goal-keeper. These are precisely the positions that were used in 1870s hockey in Montreal. So it seems that even if rugby used such nomenclature, it was not unique to that sport. And indeed this would make field hockey a better fit, since rugby does not use a goaltender.


It should be plainly obvious that the equipment used in early ice hockey was much more similar to that of field hockey than to rugby. Rugby has no sticks, and the ball is much too large to be used for hockey. The goal markers were much different as well. Ice hockey added skates of course, but you cannot credit that idea to rugby, clearly.


We have already noted that the difference in the offside rules produce a significant effect on the game play of these sports. In rugby, the ball could only move backward. In field hockey and ice hockey, it could move forward so long as the players involved were onside.

The objects of rugby are quite different than ice hockey. You scored goals by kicking the ball over the crossbar and between the posts, and of course you could score touch downs, which have no equivalent in ice hockey or field hockey. In terms of the object of the game, it's clearly field hockey that is more similar.

Rugby, then as now, involved scrummages (which have no equivalent in ice hockey), and allowed tackling, which ice hockey did not. You were not permitted to take hold of a hockey player and drag him down, even if he did have the puck. In rugby, players could pick up the ball and catch it out of the air before beginning a run while holding on to the ball. There was nothing like this in hockey.

So all we're left with in terms of game play is the vague sense of physicality mentioned by Gopnik. Now, I believe that the physicality in the early version of Montreal hockey can easily be overstated, if it is thought of in modern terms. In its earliest days, ice hockey certainly allowed contact, but it was not the constant body-checking we see in the game today. Indeed it could not have been, since players expending their energy on such endeavours would not have lasted the 60 minutes they were required to play each match. However, there was certainly some rough and physical play, whereas in field hockey there was a rule in place that was designed to prevent body contact (playing right to left).

If you want to see this is as a rugby influence on early ice hockey, I'm not going to stop you. Indeed many of the players involved in the early Montreal matches were rugby football players. But it seems fairly clear that it was field hockey one ice, perhaps sprinkled with a taste of rugby. The level of physicality in early ice hockey was not equal to that in rugby; it was certainly more than field hockey, but it was also certainly less than rugby.


Going through this process, I cannot see how rugby can be said to have been a significant influence on early Montreal ice hockey. There are several claims of this, however they were all made at least three decades after the fact, and are part of stories that tend to have rather large inconsistencies with history in them. In all of the ways discussed above, with one possible exception, field hockey is a clearer source of inspiration for early Montreal hockey than rugby. When you couple this with the fact that claims of rugby influence were all made well after the fact and rely solely on fallible human memory, you reach the conclusion that there is no particular reason to believe rugby played a role.

Since McGill was such a rugby stronghold, perhaps these McGillers (Smith, Murray, Joseph) just associated everything with rugby, when in fact there were other sports much closer in nature. But whatever the reason, it appears that their claims do not stand up to scrutiny.

Tuesday, 19 August 2014

Hall of Fame Standards for the Major-League Era (Part Two)

This year's new edition of the Hockey Abstract includes a lengthy chapter on the Inductinator, which is a system I devised to determine implicit standards for the Hall of Fame, trying to figure out why each Hall of Fame player was selected as such. It may not be that the best or most deserving players are inducted according to your personal standards or indeed mine, but the Inductinator proceeds with the assumption that the Hall of Fame Selection Committee acts in a reasonably rational manner, and has a reason for each of its selections, even if the justification for using such a reason might be weak.

Last time we had a look at goaltenders and defencemen who played in what I call the Major-League Era, specifically the years 1912 to 1929 when the Stanley Cup became the domain of only a top few hockey leagues. Today we'll be looking at the forwards from this era. Remember that the system is designed so that every player with an Inductinator score of 100 or more meets the implicit Hall of Fame standards.

For most players, the criteria are pretty straightforward. If we look at the top man as an example, Newsy Lalonde. He earns 22 points for the senior-level hockey games he played in excess of 200, and another 42 points for the points he scored in excess of that number. He earns 67 points for his senior career points-per-game average; anyone in excess of 0.95 gets points for this, up to a maximum of 70. Lalonde receives 43 points for his 19 seasons of senior hockey; 14 is the minimum number to earn any points in this category. Newsy earns a ridiculous number of points for his top-four finishes in major-league scoring. He led a major league in scoring three times, was second once, third once and fourth four time, resulting in 112 points. Only Joe Malone (with four) and Fred Taylor (with five) led a major league in scoring more often during this period. Lalonde also served as a player-coach in the major leagues for nine seasons, and earns 60 points for that, giving him a total of 346. He was also head coach in the NHL for seven seasons after his playing career was over, but only those players with at least nine such seasons earn any points for it. It may seem odd to reward a player for something that happened after his playing career, but without this category there would be no way to explain Jack Adams' induction into the player category in 1959.

This isn't the only post-career accomplishment that has to be considered in this era to explain some player selections. You might notice Conn Smythe on the list below, with 60 points on the scale despite playing literally only a handful of senior games. All of these points come from the fact that he was the coach of a Canadian Olympic hockey team (in 1928). Without this massive amount of points, you could not explain Frank Rankin's induction; he was the coach of the 1924 team. Ranking was quite a good player, but had a very short career. His high career points-per-game gives him 47 points, and the other 60 come from the Olympics. It's even worse in the case of Steamer Maxwell, who is recognized as the coach of the 1920 Olympic team, and receives 100 points on the Inductinator scale for this. You can explain the extra 40 points either because he was the first Olympic coach, or because he had a longer senior career than Rankin or Smythe. Once again, Maxwell was a good player in his day, though he never played professionally. He was an extremely fast rover, but he used his speed largely in defence, and never scored very much. He's nowhere near the Hall of Fame purely as a player.

There are some other kludgy work-arounds needed in this era, awarding a large amount of points to a player for an accomplishment that would not seem to be worth that much at first glance. Shorty Green is probably the best example. Based on his playing career alone, his Inductinator score would be precisely zero. He was a decent player, but nothing special. There are two things for which he might be renowned, both of which arise from his captaincy of the 1924/25 Hamilton Tigers. This was the first (and to date, only) NHL club that went from worst to first in the span of a single season. Green was also the leader of the Hamilton player strike before the 1925 playoffs, which earned them a good deal of fame. So we can assign arbitrary values to these events, and give Short Green 50 points for each of them to get to the Hall. It's not terribly satisfying, but it works.

Rusty Crawford is another one. Based purely on his career numbers, despite his very long career Crawford would score only a 50. The only thing that sticks out about him at all, that other players cannot match, is the range of his major-league career. He is the only player from this, so far as I can tell, to have played for a major-league team in every Canadian province that had such a team (British Columbia, Alberta, Saskatchewan, Ontario and Québec). He played for the Vancouver Maroons, Calgary Tigers, Saskatoon Crescents, Toronto Arenas, Ottawa Senators and Quebec Bulldogs in his career. I can't find anyone else who meets this criteria. Newsy Lalonde missed out Alrberta and Tommy Dunderdale didn't play in Ontario. They're Hall of Famers nonetheless. Art Gagne and Eddie Oatman both also hit four provinces, but not five; Gagne missed BC and Oatman, Saskatchewan. So if we give Crawford 50 points for this feat, his induction makes sense.

Rewinding a bit, there are a number of things that Newsy Lalonde missed out on for Inductinator points. Players who won at least three Stanley Cup championships earn points for the feat, while Lalonde had only one. Captaining a Stanley Cup championship, and scoring a Cup-winning goal also garner points. Playing and scoring goals in the Olympics are also rewarded, as are Allan Cup accomplishments. The Hart and Byng awards are also valuable, though they arrived relatively late in this time period.

As you can see from the table below, there are a number of players who could just as easily be Hall-of-Famers as not. Bernie Morris, Corb Denneny, Harry Smith and Dubbie Kerr are all only a few points off of the 100 threshold. Personally I would have put each of these men in before Rusty Crawford among others, but the Inductinator is not about merit, about who should be in the Hall of Fame. It's about explaining who is in the Hall. It's an attempt to shed some light on history, not to call down the efforts of the selection committee.

We'll finish up our look at the Inductinator next week, when we examine the Hall-of-Fame players from the Challenge Era, up to 1911.

Newsy Lalondeyes34634444394537806
Joe Maloneyes27727834573418221
Fred Tayloryes242206218110328219
Frank Nighboryes231438255119374324
Didier Pitreyes23134431379392457
Cy Dennenyyes17739831090400450
Dick Irvinyes16032436793460409
Ernie Russellyes15110017616192299
Duke Keatsyes150301234117351764
Frank Fredricksonyes145366246112358499
Harry Broadbentyes14138522463287829
Frank Foystonyes14036725582337206
Tommy Dunderdaleyes14030226074334609
Mickey MacKayyes138422274118392334
Jack Walkeryes13844426299361129
Hobey Bakeryes130416533982
Billy Burchyes12741216673239255
Jimmy Gardneryes1201699029119431
Frank Rankinyes10721630630
Scotty Davidsonyes10749521870150
Harry Watsonyes1066094201142
Gord Robertsyes10617120744251325
Tommy Smithyes10521336533398359
Jack Darraghyes10425820873281355
George Hayyes102410208118326145
Jack Adamsyes10229724956305518
Babe Dyeyes10128121648264221
Moose Goheenyes1011436515800
Barney Stanleyyes10126519094284257
Steamer Maxwellyes1003720123263
Shorty Greenyes100126751893183
Rusty Crawfordyes10030316569234435
Harry Hylandyes10015519234226398
Bernie Morrisno9923720283285139
Corb Dennenyno9835022572297365
Harry Smithno921122468254229
Dubbie Kerrno9116619145236340
Eddie Oatmanno85320198101299456
Tony Conroyno8418654146880
Art Gagneno8239517990269434
Louis Berlinguetteno803469257149304
Odie Cleghornno7729923165296444
Herb Druryno72294591675205
Cully Wilsonno6535520485289814
Fred Harrisno6128217581256449
Conn Smytheno6052020
Bert McCaffreyno5232110349152202
Jack McDonaldno3424419559254179
Carson Cooperno333412157428997
Ty Arbourno3137013769206184
Don Smithno2718918927216359
Billy Boucherno2525211641157442
Sibby Nicholsno219910227129150
Harry Meekingno1727410641147330
Charley Tobinno1420115439193139
Jimmy Herbertno112388933122255
Ken Mallenno1018218227209277
Harry Scottno91231787185182
Alf Skinnerno925711732149432
Carl Kendallno86733195252
Skene Ronanno513810825133244

Monday, 18 August 2014

On His Own Side of the Puck - New Formats

Earlier this year I published On His Own Side of the Puck, the first book discussing the origin of the rules of ice hockey. I'm happy to announce that it is now available in a wider variety of formats.

You can get the paperback or Kindle edition from Amazon here, or you can download a PDF copy here.

Friday, 15 August 2014

Puckerings archive: Effect of Rest of NHL Team Performance (10 Sep 2001)

What follows is a post from my old hockey analysis site (later It is reproduced here for posterity; bear in mind this writing is over a decade old and I may not even agree with it myself anymore. This post was originally published on September 10, 2001 and was updated on November 12, 2002.

The Effect of Rest on NHL Team Performance
Copyright Iain Fyffe, 2002

What effect does the amount of rest an NHL team has before a game have on the outcome of the game? We would probably expect that the more rest a team has, the better they will do. However, there is the possibility of too much rest leading to teams being “rusty”, and not performing as well. This simple study examines this question.

Using data from 1998/99 and 1999/2000, I compiled the records of all NHL teams based upon the number of days off since their last game. For comparability’s sake, I ignored the “1 point for an OT loss” rule that came into effect in 1999. Here are the results:

 Tot  Tot  98/99  98/99  99/00  99/00
 Days rest  GP  Pct  GP  Pct  GP  Pct
 0  850  .450  410  .456  440  .444
 0  850  .450  410  .456  440  .444
 1  2130  .503  1041  .500  1089  .506
 2  899  .526  463  .531  436  .521
 3  378  .525  180  .492  198  .556
 4  130  .519  60  .575  70  .471
 5 or more  70  .600  33  .530  37  .662

The results match our expectations quite well. Teams perform the worst when they played the night before, having no time off. There is some suggestion that too much time off may not be good, since at four days off there is a drop in winning percentage. It is a small drop, and is probably not statistically significant. But remember, we would actually expect an increase in percentage, so it seems the benefits of additional rest are offset by the effect of rust, shall we say.

There is one more interesting thing to note in this study. The average NHL team had 108.3 days of rest between their first game of the season and their last game. This average is identical in 1998/99 and 1999/2000. However, the range of days off among teams went from (103,112) in 1998/99 to (104,111) in 1999/2000, and the standard deviation dropped from 1.8 to 1.4 days. Therefore, the NHL schedule got a little fairer in 1999/2000, with teams having more similar amounts of days off.

Tuesday, 12 August 2014

In-Depth Review: L'histoire du hockey au Québec, Part 5

We're up to part five of my in-depth review of Donald Guay's 1990 book L'histoire du hockey au Québec: Origine et développement d'un phénomène culturel avant 1917 ("The History of Hockey in Quebec: The origin and development of a cultural phenomenon before 1917"). We're still working through the quite extensive third chapter; after this post we'll about one-third of the way through the book.

Today I'm going to look at Guay's discussion of the development of the major eastern senior hockey leagues from 1886 to 1917. On page 77 he gives us a nifty graphic representation of the subject matter, which I cannot provide a scan of without ruining my copy of the book. So instead, I re-created it below.
The Amateur Hockey Association of Canada (AHAC), which was formed in 1886, went along fairly swimmingly for the first decade of its existence. In 1897, the executive of the league passed a fateful resolution, but one that made a good deal of sense. With this resolution, the champion team of the AHAC intermediate section for a year could apply for admission into the senior ranks the following season, subject to the majority vote of all AHAC clubs (senior, intermediate and junior).

The Ottawa Capitals had, the season before, applied for admission into the senior AHAC. The Capitals were the champions of the Central Canada Hockey Association (CCHA), but as the AHAC did not recognize that league as a senior one, the Capitals instead joined the AHAC intermediate division for 1897/98. They were intermediate champions in 1898, and that's when the fun began.

As was their right, the Capitals applied to join the senior ranks of Canada's greatest hockey league. Guay notes that after a long debate and appeals to fair play, the team was admitted by a vote of 23 to 11. All of the intermediate and junior clubs were in favour of the motion, as were the senior Shamrocks. The older clubs - Ottawa, Québec, AAA and Victorias - were all vigorously opposed. So, they exhibited the very best in amateur sportsmanship, and took their pucks and went home. These four clubs withdrew from the AHAC, and formed the Canadian Amateur Hockey League (CAHL).  The Shamrocks eventually joined them, which was really their only option, and Guay notes that when drafting the CAHL constitution, the new executive made sure that it would require a unanimous vote to admit a new club to the senior level.

Guay states that after this split, the AHAC ceased operations entirely, but this not accurate. Michel Vigneault's dissertation on the history of hockey in Montreal makes it clear that the AHAC continued to operate at the intermediate and junior levels for several seasons, meaning that it should not be included at all in the illustration above since they were not senior. Guay's illustration is also inaccurate since it shows the Capitals splitting off to play in a league with Brockville and Cornwall. But this is a reversal of history; these three teams made up the CCHA before the Capitals joined the AHAC. At the senior level, there was no split; the senior AHAC became the CAHL.

Guay then discusses the Federal league, and notes that le National de Montréal were the first senior-level French-Canadian hockey club. When this club transferred to the CAHL in 1905, they were replaced by the Montagnards. The author suggests that the battle between the CAHL and FAHL that ensued in the mid-nineteen-oughts is the reason that the French teams became accepted in senior hockey. The Nationals had been rebuffed by senior hockey before, but with a rival league to battle, establishing a French-Canadian fanbase was important. I certainly cannot argue against Guay's conclusion here, and it's a very interesting observation.

The author proceeds with the development of the CAHL into the Eastern Canada league, but his illustration does not take note of the cross-pollination that occurred between the CAHL and FAHL, as Ottawa defected from the CAHL to the FAHL, and then went back, taking the Wanderers with them. Guay does correctly describe that the Eastern Canada league did not undertake a smooth transition to the NHA. In fact, arguably, the direct line of descent of AHAC to CAHL to ECAHA to ECHA ends with the Canadian Hockey Association, which began the 1909/10 hockey season but did not complete it, being absorbed by the National Hockey Association mid-season.

Guay's direct line between the Federal league and the NHA is really also invalid. Only one team from the 1908/09 FHL season actually played in the NHA in 1909/10. The Wanderers came over from the ECHA, and the Canadiens were an entirely new team. The greatest representation in the inaugural NHA season was actually from the Temiskaming Professional Hockey League (Cobalt and Haileybury), thanks to J. Ambrose O'Brien's money. The NHA was not a continuation of any league when it first started, it was assembled from bits and pieces, but Guay's direct line from the Federal league to this one would suggest otherwise. With the NHA and CHA merged into one, senior hockey in Canada was well in the hands of the professional leagues.

Overall, Guay gets quite a lot of the details wrong in the development of senior hockey in eastern Canada into the professional game in the 1910s. I can't give him a failing grade, but I can't say that I'm impressed:

Monday, 11 August 2014

Hall of Fame Standards for the Major-League Era (Part One)

Any longtime fan of hockey knows that the identity of the players in the Hockey Hall of Fame, and of the players who have not been inducted, can be a source of great debate among the faithful. Almost everyone has a favoured played they really feel deserve the honour, and can name several players already in the Hall that probably shouldn't be there, especially not ahead of their preferred hockeyist. These disagreements arise not only because of the selection committee's opaqueness when it comes to the selection process, but also because there are obviously no objective standards as to who should be a Hall-of-Famer and who should not. You cannot look at a player's career, add up all his awards and accomplishments, compare the total to a chart, and arrive at a “yes” or “no” answer. It's just not that simple.

However, even though there are no objective standards, we can try to figure out whether the Hall of Fame selection committee has any implicit standards; that is, standards that can be determined based on who has been inducted into the Hall of Fame, and just as importantly who has not, in a sort of reverse engineering of the selection standards. Such a system could be used to discuss past selections, but perhaps more interestingly it could also be used to predict future inductees based on the career records of active or recently-retired players. So, can we examine the career statistical records of Hall-of-Famers and non-Hall-of-Famers, and come up with a formula that represents the basis the selection committee apparently used to select the players for the honour?

As it turns out, we can derive these standards, and we call the resulting system the Inductinator. The Inductinator calculates a score for every hockey player, and any player who achieves a score of 100 or more meets the implicit standards of the Hall of Fame selection committee. It's important to remember that this system is not concerned with who should or should not be in the Hockey Hall of Fame, but rather to determine whether there are any set of standards that the selection committee could have used for the honourees. It's descriptive rather than prescriptive; it does not deal with what should be, but what is.

The Inductinator results for players whose careers were primarily after 1930 make up the bulk of my contribution to Hockey Abstract 2014, available now. Here at Hockey Historysis, I'm going to take it back even further, and today we're going to look at the Inductinator for players whose careers primarily spanned 1912 to 1929, which I refer to the as the "major-league era" here, since it was the first time that competition for the the Stanley Cup was restricted to the major professional league or leagues (NHA, NHL, PCHA, WCHL and WHL).

Like later eras, the system addresses forwards, defencemen and goaltenders separately. Later eras are generally easier, because of greater consistency in the statistics (since top players only played in one league for the most part) and because of the existence of annual individual awards. So while I was able to arrive at implicit standards that perfectly discriminate between Hall-of-Famers and non-Hall-of-Famers for 1930 and beyond, it's to be expected that earlier eras are more difficult. And indeed, there are some players from this era that I am not able to statistically make a Hall-of-Famer without also elevating dozens of other players who have not been honoured to the minimum score of 100. But it's actually only three players that I cannot account for, although a couple of others require something of a cheat to get them in, as we'll see. Just like in the Hockey Abstract, I'm going to go position-by-position, starting in goal.

Hall of Fame Standards for Major-League Era Goaltenders
As it turns out, the goaltenders for this era are really, really easy to develop implicit standards for. So easy, in fact, that there is an almost limitless number of ways in which you could do it. Also, you could do it with a single one of a number of statistics.

For example, as you can see below, for goaltenders who played primarily in this era, there are only five netminders who played at least 333 top-level games, and they're all in the Hall of Fame. So you could say that any goalie who played at least 11 major-league seasons is a Hall-of-Famer. You could even say that any goalie who won a Stanley Cup as a starter is a Hall-of-Famer. There are other goalies who won a Cup in the years 1912 to 1929, however their careers were primarily after this era, and so are not included in this group.

Of course I did not want to use any of these simplistic ideas for the Inductinator, so I put together something that seemed reasonable, considering not only the Hall-of-Famers but other goalies as well. I'll use Georges Vezina to illustrate. Vezina played 15 seasons of top-level hockey; he gets seven points for each of those seasons beyond the eighth, for 49 points. He gets 40 points for winning at least one Stanley Cup as a starter, and since he had at least one win for every two games played, he earned points there as well. He receives one point for each .001 that his winning percentage (wins divided by games played) exceeds .460, for 67 points. He died tragically in mid-career, and the Hall of Fame loves that kind of thing, so he gets 40 points for that as well. He also gets the maximum 30 points for his career games played. This brings his total to 226, well above the 100 minimum and more than any other netminder of the era. Note that for career statistics, for seasons before 1926/27 we consider professional stats, and after that season NHL stats only.

The only thing Vezina misses out on is points for his GAA relative to league average. He had a career GAA of 3.40, which the league average for the seasons in which he played was 3.41. He would have received points if his GAA was .90 of the league average or less. Alec Connell, for instance, meets the Inductinator standard with his GAA alone, earning 114 points that way. It should be noted that while Percy LeSueur and especially Paddy Moran look bad by GAA, they played largely in earlier times than the others, when scoring was much higher. For the first half of Moran's career, he played in leagues that featured more than six goals per game.

Georges Vezinayes2263281733.41
Alec Connellyes2054171931.91
Clint Benedictyes2034402392.44
Hugh Lehmanyes1814222203.29
Percy LeSueuryes178170984.31
Hap Holmesyes1404091982.81
Paddy Moranyes107206985.24
Hal Winklerno832031002.28
Bert Lindsayno64150665.37
Jake Forbesno26210852.76
Charles Stewartno1877302.45
Hec Fowlerno17186833.64
Bill Lairdno1053302.96

Hall of Fame Standards for Major-League Era Defencemen
Defencemen are a much more varied group than the goaltenders when it comes to Hall-of-Famers. There are 15 honoured defenders from this era, compared to five goaltenders. It is worth noting that  players are included in this era if they had even one full season after 1911. This is the only way we can make sense of the inclusion or exclusion of certain players.

Defencemen receive points from many things for their Inductinator score. Games played (adjusted to consider any seasons missed due to military service), points scored and points per game are all important. The number of senior seasons played, and the number played at the highest level are also considered. Stanley Cups won, and being the captain of a Stanley Cup champion are also very important. The number of years that the defenceman was a player-coach is included, and if he had a very long career as a coach after his playing days were over, he received some points for that. Players whose careers were ended early by injury or death have an adjustment for this fact.

Since Québec-born Francophone players and US-trained players were fairly rare in this time period, such players receive a bonus to their Inductinator scores. Without this adjustment, it would be extremely difficult to see how Jack Laviolette had a Hall-of-Fame career.

One player from this era that you might have wondered about is Gordon "Phat" Wilson, the great senior player for Port Arthur. Wilson never played professionally, and never played in the best senior leagues either. What he did do, and what it seems the Hall of Fame selection committee wished to reward, is be in the Allan Cup playdowns year in and year out. His teams qualified for the Allan Cup eight times and won the championship three times, and Wilson played 41 Allan Cup matches, scoring 29 points as a defenceman. No one else from this era can match these accomplishments, and as such it seems clear that Allan Cup play is what earned Phat Wilson his place in the Hall.

The only one that I simply cannot explain with any kind of implicit standards is George McNamara. Although he was a very famous player in his day, especially in conjunction with his brother Howard with whom he shared the moniker "Dynamite Twins" due to their powerful body-checking, there is nothing remarkable about his career. If anything, his brother Howard had the more impressive career, and yet it is George who is in the Hall of Fame. Here he scores a big fat zero on the Inductinator as a player, and I cannot provide any reason for him to have been inducted based on his days as a player.

The only thing that makes him stand out from his brother is that after his career, he was the coach of an Allan-Cup winning team, with Sault Ste. Marie in 1924. For some early players, the selection committee clearly did consider post-playing career accomplishments, as we will see. But it would be incredible to say that an Allan Cup championship as a coach for a former player would be worth, by itself, selection to the Hall of Fame. This was during probably the toughest era for the Allan Cup, since it was after a formal playoff system was instituted for the Allan Cup, and before the establishment of minor-league hockey which siphoned off so many quality senior players. Moreover, Eddie Carpenter, who scores at nine on the Inductinator for his playing career, was the coach of Port Arthur as they won two Allan Cups in 1925 and 1926. So if McNamara were to be enshrined for this accomplishment, surely Carpenter would have been as well. This strongly suggests tells us that this was not the implicit standard that McNamara benefited from. I gave both McNamara and Carpenter 20 points for this accomplishment, but that only puts George up to 20, though it does move him ahead of his brother who scores 17 based on his playing career.

McNamara's score of zero as a player led me to a deep search for anything that made him stand out. I decided to check newspaper reports from the time that he was selected for the Hall of Fame, and made what could turn out to be a rather startling discovery. I checked several different Canadian newspapers from April 28, 1958, and they all say the same thing when discussing the newly-elected members of the Hall of Fame for that year. Here is an example from the Regina Leader-Post:


Those added were:

Builders. Senator Donat Raymond, Montreal; the late George McNamara, Toronto; George Dudley, Midland, Ont.; the late Jim Norris Sr., Detroit; Conn Smythe, Toronto; Al Pickard, Regina; and Lloyd Turner, Calgary.

Players with the teams they were most closely identified with. Frank Boucher, New York; Frank (King) Clancy, Ottawa and Toronto..."
George McNamara was listed as a builder, not as a player. Now, it remains entirely possible that the media was given erroneous information, and that McNamara was in fact supposed to be listed as a player. Indeed the Hockey Hall of Fame itself lists him as an Honoured Player. Frankly, his selection would make a great deal more sense in the builder category. A SIHR member related to me that McNamara contributed a substantial amount of cash toward the construction of the International Hockey Hall of Fame in Kingston, and that he was generally quite philanthropic after his playing career was done, so it would make a great deal more sense as a basis for his induction than what he did on the ice.

However, it seems that this is ultimately a red herring, that the player category is where McNamara was inducted. This was confirmed by a SIHR member via a contact at the Hall of Fame. But yet another SIHR member, Andrew Ross, actually blogged about the McNamara induction a few years ago. He noted that in a letter, Frank Selke Sr. (who was a member of the Hall of Fame selection committee) wrote that "when George was admitted [to the Hall] Howard's wife told a friend of mine that George could not carry Howard's skates. I asked [Art] Ross and Lester [Patrick] about this and they said, which one was Howard?"

So perhaps it was supposed to be Howard. He would certainly have been a better choice based on his playing career, but the Inductinator still would not have been able to justify it. The McNamaras were a bit larger than life, and perhaps their reputation was all that was needed. Regardless, the selection of George McNamara is surrounded by quite a bit of confusion.

Next time we will look at the forwards from this era.

Eddie Gerardyes24925017076246325
George Boucheryes21849615191242927
Sprague Cleghornyes209377174105279849
Lester Patrickyes20622716971240187
Harry Cameronyes18035022095315490
Reg Nobleyes173541195109304982
Art Rossyes1641859834132563
Joe Hallyes14124015940199913
Moose Johnsonyes10925712250172505
Herb Gardineryes1092777647123147
Jack Lavioletteyes1022359834132489
Joe Simpsonyes10039712776203274
Si Griffisyes1001498343126181
Phat Wilsonyes100117562480148
Bobby Roweno9929112356179567
Goldie Prodgerno9123411540155262
Frank Patrickno8812410538143106
Clem Loughlinno803838044124342
Art Duncanno803829669165406
Lloyd Cookno7423111459173210
Walter Smaillno6814010135136231
Hamby Shoreno6718912131152566
Bert Corbeauno603418355128939
Billy Coutuno57300452167532
Percy Traubno51318323466551
Leo Reiseno503298054134276
Duke Dukowskino423566648114424
Muzz Murrayno421264445269
Gord Fraserno30279633194495
Eddie Carpenterno29192521264330
Bobby Trappno28257474592264
Harry Mummeryno27239623294602
George McNamarayes20139371754291
Slim Haldersonno192186244106318
Howard McNamarano17152542074456

Friday, 8 August 2014

Puckerings archive: Isolating Team Defence (01 Aug 2001)

What follows is a post from my old hockey analysis site (later It is reproduced here for posterity; bear in mind this writing is over a decade old and I may not even agree with it myself anymore. This post was originally published on August 1, 2001 and was updated on April 10, 2002.

Isolating Team Defence
Copyright Iain Fyffe, 2002

Probably the most difficult aspect of hockey to quantify is defence. Among official stats, we basically only have goals-against average (team) and plus-minus (individual). I will not discuss plus-minus, as my emphasis here is on team defence. Another way of looking at defence is by using marginal goal analysis, which forms the basis for the Point Allocation system. This essay details another way of examining team defence, Defensive Winning Percentage.

Goals-against average is not sufficient for the evaluation of team defence, for two reasons. First, it varies with the level of goal-scoring in general, making direct comparisons across years difficult. Second, and most important, goals-against average is made up of two things: team defence and goaltending. What we need is a method for separating the two.

The DWP method stems from the Neutral Winning Percentage system for goaltenders. In that essay, we arrive at a winning percentage for goaltenders that is (for the most part) attributable only to the goaltender, not to the team he plays for. And since offence is relatively easy to quantify, that leaves only one facet of the game not measured: defence.

What we need now is a formula that combines all of the following elements: team winning percentage, offence, defence, and goaltending. No such formula exists, but we can adapt one for our use. Bill James developed a Pythagorean Winning Percentage formula for baseball, which uses offence and defence together to calculate an expected winning percentage. It works quite well. Marc Foster of the HRA adapted this concept to hockey, and the formula (for modern times) looks something like this:

TWP = GF^2 / (GF^2 + GA^2)

Where TWP is the team’s (expected) winning percentage, GF is goals for and GA is goals against. The exponent is more accurately set at 2.03, but for our purposes, we will use the simpler exponent of 2.

Goals against are determined by two things: defence and goaltending. For our purposes (creating a measure of team defence), we will make an assumption on how to separate the two. Since at any time there are (usually) five players on the ice who are responsible for defence, and only one for goaltending, we will assume that defence is five times more important than goaltending in determining goals against.

To keep the presentation constant, we will work only with winning percentages. This has the additional benefit of making numbers from one year directly comparable with numbers from another. We have team winning percentage (TWP) and goaltender (neutral) winning percentage (GWP) so far. In order to calculate defensive winning percentage (DWP), we will first need to calculate offensive winning percentage (OWP).

To calculate OWP, we use a method similar to the one used in calculating GWP. First, we compile the records of all teams in the league for each level of goals scored (0, 1, 2, 3, etc.). This gives us a winning percentage determined by the number of goals you score, independent of how many goals you allow. Thus, it measures only offence.

Second, we compile the number of times each team scores each number of goals. However, since we want this to be free of any bias created by the opponent’s defence, we must make an adjustment. For each opponent, we calculate a multiplier based on their goals-against average relative to the league goals-against average. Thus, if a team allows 3.00 goals per game, and the league average is 2.50, this team will have a multiplier of 0.83 (2.50/3.00), reflecting the relative ease with which you can score on this opponent. So if you score 5 goals against this opponent, you get credit for only 4.15 (5 x 0.83), which is rounded off to 4.

Now, using the winning percentages for each number of goals and the number of times each team scores each number of goals, we can calculate a weighted-average winning percentage. This is the OWP, and it (in theory) reflects only the quality of team offence.

Now, we can express the Pythagorean Formula as follows, bearing in mind the assumptions we have made thus far:

TWP = OWP^2 / {OWP^2 + [1- (5/6 x DWP + 1/6 x GWP)]^2}

With some simple algebraic manipulation, the formula for DWP is:

DWP = 1.2 - .2 x GWP - 1.2 x OWP x (1/TWP - 1)^.5

One of the nice things about using the Pythagorean Formula is that it captures the synergies that exist in hockey. Winning is not linear; the results of above-average goaltending, offence, and defence is greater that the sum of the individual parts. With this method, having a .500 OWP, GWP and DWP will produce a .500 TWP. However, if several of these factors are above-average, the TWP will not increase linearly. Results for 2000/01 are included at the end of this essay; examine them to see what I mean.

DWP is really only a rough measure. When examining it, please remember the following points:

(a) it absorbs all the error present in the Pythagorean Formula,
(b) it assumes defence is fives times as important as goaltending in preventing goals,
(c) it assumes the GWP and OWP calculations are accurate, and
(d) it indicates only how defence was played, not the potential for defence; it can be influenced by strategy.

2000/01 NHL Results
 Anaheim  .372  .404  .487  .473
 Atlanta  .354  .446  .485  .380
 Boston  .488  .498  .467  .494
 Buffalo  .591  .483  .585  .600
 Calgary  .421  .445  .492  .475
 Carolina  .518  .451  .512  .576
 Chicago  .402  .461  .459  .433
 Colorado  .650  .609  .536  .557
 Columbus  .396  .406  .523  .494
 Dallas  .634  .535  .559  .600
 Detroit  .652  .566  .531  .598
 Edmonton  .549  .554  .484  .501
 Florida  .348  .436  .526  .379
 Los Angeles  .543  .557  .507  .485
 Minnesota  .384  .375  .563  .517
 Montreal  .390  .465  .499  .402
 Nashville  .470  .418  .579  .552
 New Jersey  .659  .610  .517  .570
 NY Islanders  .299  .394  .438  .388
 NY Rangers  .433  .555  .435  .351
 Ottawa  .640  .595  .536  .557
 Philadelphia  .591  .521  .521  .576
 Phoenix  .530  .458  .561  .570
 Pittsburgh  .567  .591  .491  .482
 St.Louis  .598  .564  .519  .541
 San Jose  .561  .474  .586  .580
 Tampa Bay  .329  .428  .495  .368
 Toronto  .518  .490  .503  .532
 Vancouver  .506  .531  .429  .485
 Washington  .561  .508  .552  .550
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