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CHAPTER III THEORY The purpose of this chapter is to discuss the theory of NHL team production. The chapter will begin by summarizing the most common measures of production and will then apply a production function to the NHL. The chapter will theoretically examine the possible variables that might have an effect on team success and will construct a production model that will be further explained and tested in chapter 4.

**The Basic Production Function **

Ultimately, any type of production function expresses the relationship between a firm’s inputs and outputs.

1 Production is simply the conversion of resources into finished products, and, more specifically, a production function will explain what quantity of output can be obtained from various combinations of inputs.

2 These inputs, otherwise known as factors of production 3 can be any type of resource, labor, or material used to create the desired output. An underlying theory here is that a profit maximizing firm will 1 Robert S. Pindyck and Daniel L. Rubinfeld,

*Microeconomics*

, Sixth Edition, New Jersey: Pearson Education Inc., 2005: 188. 2 Ibid, 189. 3 Ibid, 188. 22

23 produce a given level of output using the minimum amounts of inputs at the least cost.

4 However, in this assessment of the NHL, this will not be the focus. In this study, profit is not discussed in the production models proposed, but rather profits are implied through increased attendance. As Hansen and Gauthier’s previous study has shown that better NHL teams draw more fans, 5 these teams should make more money. Therefore, simply determining how professional hockey teams win games will be the main endeavor.

**The Production Function and the NHL**

One attractive quality of the production function is that it can be applied to almost any entity. It can be applied to an individual, a single firm, an industry, or even an entire nation. Thus, a production function can be easily applied to the NHL as we can use numerous individual and team statistics as factors of production. As such, it will be helpful to review the ways of measuring production in professional sports. As a review of the past literature dealing with this topic has shown, there are a variety of ways to measure production. As numerous studies have used wins to measure production in professional sports, 6 other authors have used win percentage.

7 In addition, Bradbury uses Earned Run Average (ERA) in his assessment of Baseball, 8 and 4 Robert S. Pindyck and Daniel L. Rubinfeld,

*Microeconomics*

, Sixth Edition, New Jersey: Pearson Education Inc., 2005: 265-266. 5 Hansen and Gauthier, “Factors Affecting Attendance at Professional Sporting Events,”

*Journal of Sport Management, *

Vol. 15, No. 1, 1989: 15-32. 6 Berri (1999) and Hofler and Payne (1997). 7 Scully (1974), Depken (2000), Jewell and Molina (2004), Frick Prinz, and Winkelmann (2003), Onwuegbuzie (2000). 8 John Bradbury, “Sorting Out the Joint Production of Defense in Baseball,”

*Working Paper, *

2005.

24 Yilmaz and Chatterjee employ points per game, points allowed per game, rebounds per game, and assists per game as measures of production in their assessment of Basketball.

9 In contrast to these measures of production, a different measure will be used for this study of the NHL. As wins and win percentage have often been employed, the NHL does not base their rankings on either of these measures. In contrast, rankings in the NHL are determined by Team Points, where each team receives two points for a win and one point for a tie after regulation. If a team then wins in overtime, another point is awarded, and the losing team walks away with one point.

10 In addition, because previous studies measuring production in the NHL have merely dealt with individuals, 11 Team Points will be a great overall measure of an entire team’s performance. Essentially, this statistic of Team Points will be used as the measure of production in the NHL, because it is what ultimately determines the ranking and fate of a team at the end of a season. Although wins are a great measure of success in any sport, overtime appearances also play a large role in the NHL, and thus a team’s season points will be used. In addition though, a separate production model accounting for Goals Allowed will also be included as a further measure of a team’s defensive production. As Team Points will be used as an overall measure of an NHL team’s success, Goals Allowed will give a deeper insight into defensive contributions to team production. 9 Mustafa Yilmaz and Sangit Chatterjee, “Patterns of NBA Team Performance from 1950-1998,”

*Journal of Applied Statistics*

, Vol. 27, No. 5, 2000: 555-566. 10 NHL Rulebook, “Rule 89; Tied Game,” available from http://www.nhl.com/rules/rule89.html, visited 12/12/05. 11 Lavoie, Grenier, and Coulombe (1987) and Jones, Nadeau, and Walsh (1999).

25 One of the most commonly used production functions used today is the Cobb Douglas production function set up by Charles W. Cobb and Paul H. Douglas in 1928.

12 This is a multiplicative function usually based off of two inputs: labor and capital. The Cobb-Douglas function is set up as follows: Q = f ( K, L ) Q = A K a L b * E e Where: Q = Output (3.1) K = Capital L = Labor A, a, & b = Positive constants determined by empirical data E e = Error term Because all of the constants (A, a, & b) are positive in the Cobb-Douglas function, this implies that as any input is increased, output will also increase. In addition, one large advantage of the Cobb-Douglas model is that it is linear in logarithms. Therefore, through a relatively easy derivation, the Cobb-Douglas model can be transformed into an additive production function. The derivation follows below. Q = A K a L b * E e Taking the log of the Cobb-Douglas production function yields: (3.2) 12 Charles W. Cobb and Paul H. Douglas, “A Theory of Production,”

*The American Economic *

Review, Vol. 18, No. 1, 1928: 139-165.

26 log Q = log A + a*log K + b*log L + e*log E and substituting variables in for log A, log K, etc… yields: Q = A + a K + b L + e E (3.4) (3.3) Thus, an additive function can be easily produced by taking the logarithm of the Cobb-Douglas production function. In addition, this additive model seems to leave more room for experimentation with the data set proposed, and as such, it should be more forgiving and more appropriate for work outside a classical firm where labor and capital are less strictly defined. For the purposes of this study, we can replace the various measures of inputs and output and can increase the number of independent variables to account for the numerous individual and team statistics that contribute to NHL team production. As such, the basic production function employed for the NHL will look as follows: Q = A + a K + b L + c M + d N ...... + e E (3.5) Where: Q = Team Points or Goals Allowed K , L , M , N etc.. = Various individual and team statistics such as Goals, Assists, Shooting Percentage, Saves, Goals Allowed and other statistics accounting for offensive

27 and defensive contributions to NHL team success. A, a, b, c, d = Positive constants determined by empirical data e E = Error term As this additive model will be applied to the NHL, it is also helpful to discuss some properties of production functions in the context of professional hockey. One implication of production functions is the concept of returns to scale. Returns to scale simply refer to how much the changes in inputs affect output; it is a property determined by varying all factors of production simultaneously.

13 For example, if there are constant returns to scale and an NHL team doubles all of their input statistics, then Team Points would double as well. Conversely, if there are increasing returns to scale, Team Points would more than double, and for decreasing returns to scale, Team Points would not double. However, another property of production functions is that of diminishing marginal returns. Ultimately, the law of diminishing marginal returns asserts that as one more unit of input is added into the production process, ceteris paribus (holding all else constant,) output will increase by smaller and smaller increments.

14 For example, if one more goal is added for an NHL team (keeping all other input statistics the same,) originally Team Points may increase by 2 units. However, Team Points may only 13 Robert S. Pindyck and Daniel L. Rubinfeld,

*Microeconomics*

, Sixth Edition, New Jersey: Pearson Education Inc., 2005: 207. 14 Ibid, 194.

28 increase by 1 unit the next time a goal is added, and then only by ¾ of a unit, ½ of a unit and so forth. Essentially, this explains the decreasing slope in the production function. While the production frontier originally slopes upward, it will eventually plateau. Therefore, as inputs are added that might contribute to team wins in professional hockey, it is implied that wins will increase at a decreasing rate. Now that these properties have been explained, the various variables that will contribute to NHL team production will be examined. First, the variables affecting Team Points will be discussed, and then those affecting Goals Allowed are analyzed. As there are many factors within the game of hockey that contribute to a team’s success, the variables included will cover nearly every aspect of the game. Statistics accounting for offensive, defensive, and goaltender contributions are incorporated. Figure 3.1 is a representation of the factors affecting production of Team Points in the NHL, and figure 3.2, which will appear later, is a representation of the factors contributing to Goals Allowed.

FIGURE 3.1 Determinants of Team Point Production in the NHL Goals Penalties Shooting % 29 NHL Team Points Face-offs Plus/Minus Goaltending Assists

**Determinants of NHL Team Points **

All of the variables in figure 3.1 should affect the production of Team Points in the NHL. Because statistics are so readily available for the NHL, this makes many

30 variables easy to incorporate into a production model. For the production of Team Points, almost all aspects of the game are covered. This production model will incorporate offensive, defensive, and goaltending variables. These variables, and additional statistics, will be discussed in detail according to the categories of figure 3.1.

**Goals **

Obviously, Goals are going to play a large part in any team’s ability to win games. Thus, in the NHL, Goals are expected to have a significant and positive effect on the production of Team Points. Even-strength Goals, Power-play Goals, and Short handed Goals will all be included in this model. All are expected to have a positive effect on Team Points.

**Assists **

As hockey is a team sport, player cooperation is an integral part of the game. Kahane and Idson (2000) have confirmed this fact through their study done on co-worker productivity in the NHL. Their results show that team attributes do in fact have an impact on individuals’ salaries, and that, essentially, teammates seem to work as complements in the NHL.

15 Thus, some aspects of teamwork should be included in the production model. One of these statistics is Assists. As Goals are expected to play a large role in my analysis, other factors that helped these Goals happen, such as Assists, should be included. Assists are expected to have a positive effect on Team Points. 15 Todd Idson and Leo Kahane, “Team Effects on Compensation: An Application to Salary Determination in the National Hockey League,”

*Economic Enquiry, *

Vol. 38, No. 2, 2000: 345-357.

31

**Shooting Percentage **

Goals cannot be scored in hockey unless you shoot the puck. Thus, some sort of variable accounting for shots must be included in this study. The more shots a team takes, the more chances they have of scoring goals, and the better chance they have of winning games. Therefore, a vital statistic in the game of hockey is Shooting Percentage. How well a team shoots the puck definitely plays a role in a team’s success, and thus, Shooting Percentage is included as an independent variable. If a team is making good use of their shots on net and scoring more goals as a result, they are going to have a better chance at coming out ahead over the opposing team. Shooting Percentage is expected to have a positive effect on Team Points.

**Plus/Minus **

Another variable that should have an effect on Team Points is the statistic of Plus/Minus. This statistic is kept for each individual player and shows whether a player has contributed more to goals, or has been scored on more while he is on the ice. If a player is on the ice while his team scores a goal, a player receives a “plus.” If he is on the ice while the opposing team scores, the player receives a “minus.” These “plusses” and “minuses” are then tallied throughout the season to assess how well a player plays both offensively and defensively. A high, positive Plus/Minus statistic is one sign of a good player. Ultimately, this Plus/Minus variable should have a positive effect on Team Points. If a team has a high cumulative Plus/Minus, this generally asserts that they have scored

32 more goals than their opponents throughout a season. Therefore, if a team is scoring more goals than their opponents, they should win a higher percentage of their games.

**Face-offs **

Face-offs are also a big part of the game of hockey. Each time there is a stoppage of play in hockey, the puck is dropped between two opposing players, and they battle for control of the puck. If a player is able to win a lot of face-offs, this helps his team control the puck, gives them more chances to score goals, and a better shot at winning games. In contrast, if a player is not able to win a lot of face-offs, this gives the opposing team an advantage. Two statistics dealing with face-offs will be included in this model of NHL team production. Total Face-offs Won is expected to affect Team Points positively, and Total Face-offs Lost is expected to affect Team Points negatively.

**Penalties **

In addition to losing face-offs, penalties can also hurt an NHL team’s chances at winning games. Playing short-handed, or with fewer men on the ice than the opposing team, is a huge disadvantage. The opposing team has a much better chance at scoring goals with more men on the ice, and therefore, all of the statistics dealing with penalties should affect Team Points negatively. However, one variable’s outcome in this category is less obvious. The two statistics accounting for penalties in this study are Penalties In Minutes and Major Penalties. And, although Penalties In Minutes should definitely have a

33 negative effect on Team Points, the effect that Major Penalties will have is a bit uncertain. A minor penalty is the most common type of penalty assessed to a player in the NHL. When a player has committed a minor penalty, he must stay off the ice, in the penalty-box, and his team must play short-handed for two minutes, or until the opposing team scores. In addition to minor penalties though, Major Penalties are also called in professional hockey. A Major Penalty is a five minute penalty, and the team assessed must play short-handed for all five minutes, regardless if the opposing team scores. Thus, Major Penalties can be a more severe detriment to a team. On the other hand, most Major Penalties that are called are assessed as a result of fighting. In this case, both teams are almost always penalized, which results in no power-plays for either team. Thus, as neither team gains a man-up advantage here, Major Penalties may not necessarily have a negative effect on Team Points. In addition, fighting can also be used as a tool in the NHL. As Stewart, Ferguson, and Jones have shown that violence attracts fans to NHL games, 16 Jones, Nadeau, and Walsh have also shown that violence is a significant determinant in a player’s employment and salary.

17 Therefore, bigger and more physical players are in fact hired and paid for their brutish style of play. Following, NHL teams often have a player that will initiate fights in order to motivate his team and spark some enthusiasm and better play from his teammates. Because momentum is a big part of the game of hockey, 16 K.G. Stewart, Donald Ferguson, and J.C. Jones, “On Violence in Professional Team Sport as the Endogenous Result of Profit Maximization,”

*Atlantic Economic Journal,*

Vol. 20, No. 4, 1992: 55-65. 17 J.C. Jones, S. Nadeau, and W. D. Walsh, "The Wages of Sin: Employment and Salary Effects of Violence in the National Hockey League,"

*Atlantic Economic Journal*

25, No. 2, 1997: 191-206.

34 fighting is often used to regain momentum for the instigating team. Therefore, as fighting can help elicit stronger play from an NHL squad, and doesn’t always imply a team being short-handed, Major Penalties’ impact on Team Points is undecided.

**Goaltending **

Goaltending is another huge aspect of hockey. A team’s goaltender has an enormous impact on a team’s success due to the fact that he can single-handedly keep the opposing team from scoring goals. Therefore, statistics accounting for goaltender contributions are definitely included in this model dealing with Team Points. The two variables included in this category are Saves and Goals Allowed. A Save is recorded any time there is a shot on net from the opposing team and the goaltender keeps the puck from going into the net. Thus, as a Save is preventing the opponent from scoring, Saves are expected to affect Team Points positively. In contrast, the Goals Allowed variable is expected to affect Team Points negatively. Obviously, as goals are going to help a team win games, Goals Allowed should have the opposite effect. In substituting these NHL variables into a production function, the basic equation will look as follows:

35 Team Points = α 0 +α 1 Even-strength Goals + α 2 Power-play Goals +α 3 Short-handed Goals + α 4 Assists + α 5 Shooting Percentage + α 6 Plus/Minus + α 7 Total Face-offs Won + α 8 Total Face-offs Lost + α 9 Penalties In Minutes + α 10 Major Penalties + α 11 Saves + α 12 Goals Allowed +

*e*

(3.6) This equation will be further explained and tested in the following chapters. Figure 3.2, using NHL Goals Allowed as a measure of defensive performance, will now be presented and its determinants will be discussed.

36 FIGURE 3.2 Determinants of Goals Allowed in the NHL

**Determinants of NHL Goals Allowed **

As all of the variables in figure in 3.1 affect NHL Team Points, all of the categories in figure 3.2 should affect NHL Goals Allowed. Here, a different combination of variables will be tested, most of which are defensive statistics. As NHL Team Points is a measure of overall team production, NHL Goals Allowed will be used as a stronger measure of defensive success. Although many of the same variables will be used in both

37 equations, those that are expected to have a positive effect on Team Points should have a negative effect on Goals Allowed.

**Goaltending **

The variables expected to have the largest effect on NHL Goals Allowed are those accounting for goaltender contributions. Goalies are an enormous part of any team, and they can make a huge difference in an NHL team’s success. As it is their job to keep the puck out of their net, a goalie plays a very important and influential position in the game of hockey. If a goaltender can keep the opposing team from scoring by making numerous Saves, then his team is going to have a much better chance at winning games. Save Percentage will be used as the ultimate measure of goaltender contributions to NHL Goals Allowed. As this statistic measures the amount of Saves made in ratio to the total number of shots faced by a team’s goaltender(s), this should be a very comprehensive measure of a goaltender’s role in defensive production. Save Percentage is expected to affect Goals Allowed negatively, as it implies that Saves are being made.

**Penalties **

As the Penalties In Minutes variable is expected to have a negative impact on NHL Team Points, it is expected to have the opposite effect on Goals Allowed. By giving the opposing team numerous power-play opportunities within a game, they are bound to score a goal at some point, and thus, the variable Penalties In Minutes is expected to affect Goals Allowed positively.

38 On the other hand, just as with Team Points, the effect that Major Penalties will have on Goals Allowed is undecided. Because most Majors are called as a result of fighting, this does not imply that a team is going to play short-handed. In addition, fights are often instigated in the hopes of regaining momentum of the game. Thus, Major Penalties’ effect on Goals Allowed is undetermined.

**Face-offs **

Variables accounting for face-offs will also be included in the model accounting for Goals Allowed. As winning face-offs is expected to affect NHL Team Points positively, it should have a negative impact on Goals Allowed. Face-offs are a large part of the game of hockey in that they imply a team’s control of the puck. Thus, Total Face-offs Won should affect Goals Allowed negatively. In contrast, if a team is losing face-offs, this is going to give the opposing team more chances to control the puck, more chances to shoot the puck, and more chances to score goals. Therefore, Total Face-offs Lost is expected to have a positive effect on Goals Allowed.

**Goals **

As all of the variables accounting for goals scored by a team are expected to have a positive effect on a team’s season points, the variable of Goals For is expected to have a negative effect on Goals Allowed. One key to a good defense, and keeping the other team from scoring, is a good offense and scoring goals yourself. If a team can keep scoring

39 goals and keep the momentum going their way, then they are likely to keep outplaying the other team and should be able to keep them from scoring. On the other hand, some teams might respond positively to being scored on. Where one team is better at playing with the momentum, some teams might need something to kick them into action. This could be a goal scored by the opposing team. If a team has just been scored on, then possibly, they could realize their downfall and begin to play harder and smarter. Thus, although Goals For is expected to have a negative impact on Goals Allowed, it is still a bit uncertain.

**Shots **

And finally, in addition to Goals For, Shots will also be included as a determinant of NHL Goals Allowed.

As Shooting Percentage is included in the model accounting for Team Points, the variable Shots will be included in the model accounting for Goals Allowed. Because a team cannot score without shooting the puck, this is an important statistic to include. In addition, because Shots imply that a team has control of the puck (almost always in the opposing team’s zone,) this variable can count as some measure of momentum in this model. Because Shots taken by a team imply that the puck is nowhere near their own goaltender, Shots is expected to have a negative effect on Goals Allowed. A production function using the NHL variables contributing to Goals Allowed is presented on the following page in Equation 3.7.

40 Goals Allowed = α 0 + α 1 Save Percentage + α 2 Penalties In Minutes + α 3 Major Penalties + α 4 Total Face-offs Won + α 5 Total face-offs Lost + α 6 Goals For + α 7 Shots +

*e*

(3.7) This equation will be further explained and tested in the following chapters.

**Conclusion **

This chapter has summarized the theory behind production functions and behind the models that will be tested in the chapters to come. Hypotheses as to the effects of numerous variables are asserted, and basic production models are proposed to be utilized in the following chapter. Essentially, all of the statistics expected to affect NHL Team Points positively are expected to have a negative effect on NHL Goals Allowed. Both of these regression equations will be run for each individual team (for a number of seasons), to test the hypotheses established. This concludes the discussion of the theory and implications behind a production model for the NHL. The following chapter will give a detailed description of the data set employed, including its sources. In addition, the regression models utilized will be discussed in further detail, and an overview of the methods employed for this study will be given.