Managerial Efficiency and Survivability in Professional Team SportsAuthor(s): Gerald W. ScullyReviewed work(s):Source: Managerial and Decision Economics, Vol. 15, No. 5, Special Issue: The Economics ofSports Enterprises (Sep. - Oct., 1994), pp. 403-411Published by: John Wiley & SonsStable URL: http://www.jstor.org/stable/2487990 .Accessed: 25/05/2012 16:52

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MANAGERIAL AND DECISION ECONOMICS, VOL. 15, 403-411 (1994)

Managerial Efficiency and

Survivability in Professional

Team Sports

Gerald W. Scully School of Management, The University of Texas at Dallas, TX, USA

Students of organizational sociology tend to believe that managerial efficiency has less to do with individual talent than with the environment in which firms operate. Economists and fans know that this is not true in sports. Measures of managerial efficiency are constructed for baseball, basketball and football coaches. Survival analysis is utilized to measure coaching tenure probabilities in these sports and coaching tenure is shown to be related to managerial efficiency.

INTRODUCTION

Organizational sociologists and economists think differently about the role of management in firms. The sociologists believe that individual manage- rial effort matters little to the success of organiza- tions; rather, institutional constraints prede- termine and narrow the range of individual choice. To the extent that individuals seem to matter frequently it is associated with an institutional attribute such as monopoly. Economists believe that individuals are paramount to organizational success. Even in the case of the classical, sole proprietorship firm operating in extremely com- petitive markets, the residual strictly depends on the ability of owner-managers to control shirking within a team production setting (Alchian and Demsetz, 1972; cf. Coase, 1937). Also, managerial competence and malfeasance is a main issue in the market for corporate control (Manne, 1965).

A lack of empirical evidence has made it dif- ficult to sort out the validity of these competing hypotheses. Private firms have no obligation to reveal internal data, other than that required by law. Measures of corporate performance, such as stock prices, may vary for reasons other than managerial performance. Public organizations, such as the military or bureaucracies, produce measurably ambiguous outputs. Also, many orga- nizations are rather complex entities, making it difficult to link managerial quality and firm per- formance directly.

Sports offers a good vehicle for testing some of the issues arising from this controversy. Field managers and coaches are crucial to the perfor- mance of clubs. The constraint set facing them is constant across clubs and is time invariant. The firms are identical in many respects: they produce identical outputs, use the same units of input skills, compete under the same rules, employ the same production function, share a common tech- nology, and so on. They differ in market size and have different owners and managers at any mo- ment of time.

The objective of the manager is to transform a set of relative offensive and defensive playing skills into club victories. That this is done with great variability is illustrated by the high turnover of managers and head coaches throughout the history of sports. In baseball and basketball for all coaches the average tenure has been about three years. Fewer than 10% survive for a decade or more. Tenure is somewhat longer in football, about 4.2 years. In Fig. 1 the distributions of tenure for all coaches with two or more years of tenure, the sample employed in the statistical analysis that follows, is presented. The means, standard deviations, skewnes and kurtosis (in that order) for tenure in each of the sports is as follows: baseball (6.79, 6.15, 2.63, and 14.02), bas- ketball (5.44, 4.58, 1.63, and 5.02), and football (6.39, 5.63, 2.44, and 10.44). Tests of differences in the means reveal that tenure is longer in baseball than in basketball (t = 2.51), but not in

CCC 0143-6570/94/050403-09 ? 1994 by John Wiley & Sons, Ltd.

404 GERALD W. SCULLY

Baseball Basketball

.5- 0 E

Football All Sports c-I IL

0- D 20 40 60 0 20 40 60

Years Figure 1. Histograms by sport.

football (t = 0.68); tenure is longer in football than in basketball (t = 1.60). The skewness of tenure is highest in baseball. The kurtosis of tenure is most pronounced in basketball.

In this paper we develop a simple model of managerial effort or efficiency, construct mea- sures of managerial efficiency and link these mea- sures to tenure using survival analysis. Manage- rial efficiency is found to be a good predictor of managerial survival.

THE OWNER-MANAGER PROBLEM IN SPORTS

For economists, the problem of separation of ownership from control is that it leads to a possi- ble misalignment of goals of principals and agents in organizations. In a world with information and monitoring costs, managerial shirking, malfea- sance and incompetence may exist. The effect of these agent deficiencies is a reduced residual to the principal. In the context of sports, this is the owner(s)-manager or owner(s)-head coach prob- lem. The effect of a reduced effort by the man-

ager or head coach is fewer games won than would be possible with the playing talent at hand and managed with maximum effort and compe- tence. The link between the win record and profit is well known (Scully, 1989).

Consider a simple production process, as in team sports, in which output (wins), W, is pro- duced with a random productivity parameter, If, that corresponds to some multidimensional mea- sure of team playing talent, and coaching or man- ager effort, e. Increased player productivity, i1, and/or increased coaching effort, E, yield higher levels of the manager's expected performance. In the standard construction of the problem, the principal (owner) and the agent (head coach or manager), both risk neutral, have the same knowledge about the random productivity parameter, but the principal cannot observe the realization of if or the level of agent effort. In the deterministic case W= E+f. The ideal outcome for the owner is that for all realizations of if, the coach expends the efficient level of effort, e*(f). The line segment e*(f) may be thought of as the efficiency frontier or the production frontier for all levels of the productivity parameter if. If the

MANAGERiAL EFFICIENCY AND SURVIVABILITY IN PROFESSIONAL TEAM SPORTS 405

coach shirks or is incompetent and expends effort e1, the principal loses a residual per unit equal to elel* = 01. In fact, the ratio e/e* or 0, which is in the unit interval, is a measure of manager effort or efficiency.

From the owner's perspective, profits are max- imized by extracting the most wins from the ros- ter of playing talent fielded. In the main, the costs of fielding playing talent i1 are incurred at the beginning of the season. The revenues associated with that playing talent are determined by how efficiently the manager transforms playing talent into club victories, 0ti. An increment in manage- rial efficiency by increasing wins increase club profit.

The simple production process may be stochas- tic, rather than deterministic. In this case, W is replaced by its density function and associated cumulative distribution functions: f(WIE,q) and F(WI,E, Ti). Higher levels of coaching effort de- crease the probability that smaller levels of out- put will be realized. That is, F,(W I E, 4i) < 0. In the case of stochastic production, the ratio e/e* only partly measures managerial effort or effi- ciency. Part of the lost output may be due to random factors beyond the agent's control.

This characterization of the principal-agent problem is static - one owner dealing with one agent in a vacuum. In a dynamic setting of the problem, owners learn about the level of manage- rial effort or efficiency. Average ownership tenure in team sports is about eleven years, so most owners will employ about three or four head coaches. Sports is a most data-ridden business. Information is widespread and cheaply obtained. Clubs compete with one another in leagues, more or less playing the same set of competitors on a regularly scheduled basis. Each owner can moni- tor the effort or efficiency of his coach compared to others. Thus, over time, through observation of the performance of his/her club and other clubs and through hiring and firing, owners will learn by experience and distinguish good field manage- ment from bad. As a result, the level of coaching quality will tend to rise over the owner's tenure. Inferred from this argument is that competent managers will tend to survive longer and incom- petent or shirking coaches will be fired more frequently. The length of managerial tenure should be related to the effort level or efficiency of the manager.

More formally, each club owner has to decide

how efficient his or her manager is at any mo- ment of time. The probability of duration in the time interval (t, t + At) is conditional on duration at time t. For any specification of a series of events (continuation or survival versus failure or termination) in terms of a probability distribution, there is a mathematically equivalent specification in terms of a hazard function or a survivor func- tion. If the probability of duration is time inde- pendent and exponential, the hazard rate, A, is the instantaneous probability of the event occur- ring at time t. The probability distribution of duration at time t for the exponential distribution iS

F(t; A) 1 -e-At (1)

The corresponding density function (instanta- neous probability) is:

f(t; A) dF/dt Ae- (2)

The corresponding hazard, H, and survival, S, functions are:

H(t; A) = f(t; A)/[l1-F(t; A)] A (3)

S(t; A) 1 1-F(t; A) e-Akt (4)

The exponential distribution may be an inade- quate representation, when the sample contains both long and short durations. In this case, the Weibull distribution may be a better representa- tion. If the probability of duration is time inde- pendent and Weibull, the hazard rate is Ap(At)P- 1. The probability distribution of dura- tion at time t for the Weibull distribution is

F(t; A) 1 1-exp(-Akt)p (l a)

The corresponding density function (instanta- neous probability) is:

f(t; A) dF Fd t Ap (At)P exp(-AktP) (2a)

The corresponding hazard, H, and survival, S, functions are:

H(t; A) = kp( kt)pl (3a)

S(t; A) exp(-AktP ) (4a)

Largely, the question of the shape of the dis- tribution is an empirical matter. This empirical issue will be discussed below.

406 GERALD W. SCULLY

THE EMPIRICAL MEASUREMENT OF MANAGERIAL EFFICIENCY

By definition, a game is won when the team outscores its opponent. Scoring (runs in baseball, points in basketball and football) is determined by a vector of players' offensive skills relative to opponent players' defensive skills: s =f(Xi), where X is the ith offensive skill relative to its defensive counterpart. Opponent scoring is de- termined by a vector of players' defensive skills relative to opponent players' offensive skills: os =

g(Yi), where Y is the ith defensive skill relative to its offensive counterpart.

In baseball, offensive skills mainly are hitting. But once a player is on base the object is to advance the man: steal, hit and run, pinch hit, etc.). Bases advanced yield runs scored. Defensive skills mainly are pitching and fielding. Consider- able scouting resources are employed in de- termining the opponent hitters' weaknesses (types or position of pitches and portion of field hits are likely to occur). In basketball, offensive skills are mainly measured by shooting percentages (field goal and free throw), offensive rebounds, assists and turnovers. Defensive skills are mainly mea- sured by blocked shots, steals, defensive rebounds and fouls. But coaching inputs seem higher in basketball (and in football) than in baseball. Teams appear to develop certain playing strate- gies (e.g. fast break or a more deliberate pace of play, set offensive plays and defensive strategies, etc.) that are not equally viable for all opponents. Particularly, in the last quarter of a close game head coaches make near-continuous playing ad- justments and play-calls. In football, offensive skills are mainly measured by offensive blocking, quarterback pass completion rates and yards per pass, receiver completions and yards per pass, running back yards per carry, and kicker three- point field goals and conversions. Defensive skills are measured by defensive blocking, tackles, quarterback sacks, interceptions, fumble recover- ies, etc. As with basketball, football teams de- velop certain styles of play, both offensively and defensively. The ability of such teams to adjust their offense and defense at halftime partly mea- sures head coaching ability.

Each team plays 162 games in baseball, 82 in basketball, and 16 in football, during a regular season. The total regular season scoring (S) and opponent scoring (OS) are, by definition: S = Es

= Ef(Xi) and OS = Eos = Eg(Yi). Then the team win per cent for the regular season, W, is functio- nally related to scoring relative to opponent scoring.

W= F(S/OS)

= F[Ef(Xi)/Eg(Yi)] (5)

In the form for statistical estimation the model for the win per cent is:1

InW= a +,8 ln(S/OS) + e (6)

This formulation has certain attractive statisti- cal properties. The win percentage is bound between 0 and 1 and, since one team's victory is another's loss, definitionally has a constant mean (0.5). With the large number of contests over a season and through time, the variance is constant across time subsamples. Definitionally, across teams, as with the win per cent, runs or points scored during a regular season must equal oppo- nent runs scored. S/OS has a constant mean of 1 (a mean of zero, if the specification is S - OS). While scoring has not been constant in professio- nal sports due to rule change and innovation (movement of the pitcher's mound to 60'6" from 50', the introduction of the lively ball, the forward pass and the field goal in football, the jump shot and 24-second clock in basketball, etc.), whatever change increases scoring also increases opponent scoring. With the specification of the independent variable in relative rather than absolute form the variance is constant. The expectation then is that the error term is normally distributed, with con- stant variance across time.2 With this formulation it is possible to measure managerial performance through time and across sports.

The objective of a manager or head coach is to win as many games as possible with the relative offensive and defensive playing skills at hand. The goal is achieved by maximizing scoring, minimiz- ing opponent scoring and transforming that rela- tive scoring production into wins. S is maximized when all player offensive skills relative to the opponents' defensive skills are equated at the margin: i.e. Smax = Ejj (dS/dXi)Xi + (dS/dX1)Xj, i = 1, n; j = 1, m; and, i oj. OS is minimized when all player defensive skills relative to the opponents' offensive skills are equated at the margin: OSmin = Eij (dOS/dYi) Yi + (dOS/dYj)Y1. These dimensions of coaching qual-

MANAGERIAL EFFICIENCY AND SURVIVABILITY IN PROFESSIONAL TEAM SPORTS 407

ity are allocative in nature. Given a set of playing skills, scoring is maximized and opponent scoring is minimized by allocating those offensive and defensive skills in such a way that not one extra run or point can be produced or an opponent's one extra run or point stopped by a redistribution of playing assignments at any moment of time. Most of the estimating of managerial or coaching quality has been in this spirit. A problem with this approach is that the empirical analysis may suffer from omitted variables bias. To the extent that some important independent dimension of play- ing skill has been omitted (e.g. hustle, aggressive- ness, anticipation, clutch performance, etc.), as- cribing the difference between potential and ac- tual wins to the coaching function may be inap- propriate. The number of dimensions of playing skill measured in baseball is the greatest and in football the least. Moreover, the assumption of a linear homogeneous production function is rea- sonable in baseball, less reasonable in basketball, and probably not valid in football.

For our purposes, we will assume that managers and coaches allocate their offensive and defensive playing skills in such a way as to maximize scoring and minimize opponent scoring. We will take it that the observed S and OS are Smax and OSmin. The dimension of coaching quality that is mea- sured here is the actual win per cent relative to the potential win per cent, given S and OS. That is, the measure of coaching quality is 0 < W/W* < 1, where W*=W+ Emax.

The potential win per cent is the predicted win per cent plus the largest observed positive resid- ual from the equation estimated in (6). These regressions are reported elsewhere (Scully, 1992 p. 60). The largest positive error is associated with that head coach that achieved the largest actual win per cent compared to the predicted win per cent with the observed ratio of scoring to oppo- nent scoring. The efficiency of this best-practice head coach or manager is unity. All other head coaches will lie in the unit interval.

The choice of the estimation procedure for the production (win) function in Eqn (6) depends on the assumption made regarding the error term, E. Three specifications were employed: (1) the de- terministic frontier function; (2) the stochastic frontier function; and (3) the maximum-likelihood Gamma frontier function.

The deterministic frontier function is estimated by minimizing the sum of the absolute residuals.

The approach, therefore, considers all deviations from the efficient, frontier function as arising from technical inefficiency. A criticism is that only part of the error term may be deterministic; part may be truly stochastic. The error term may be of the form E = u + v, where u is a one-sided disturbance term representing the degree of man- agerial technical inefficiency and v is a symmet- ric, normally distributed random influence. In the case of the win production function, the random component would be luck; some games are won and some games lost, not for reasons of relative playing skill or coaching ability but due to referee error or other fates beyond the control of the contestants. Two stochastic frontier functions were estimated; one with a normally distributed error term, v, and the other with the error term assumed to be Gamma distributed. Neither of these specifications were superior to the de- terministic frontier estimates. Therefore, only the later utilized here.

Means and standard deviations of efficiency were calculated for all of the managers with two or more seasons managing or coaching. It is well known that there is a managerial learning curve; that is, efficiency rises at a decreasing rate over career length (see Porter and Scully, 1982). To capture the trend in efficiency the standard devia- tion of efficiency is included as a covariate in the survival analysis.

SURVIVAL ANALYSIS

Differences in the mean tenure and in the dis- tributions by sport have been noted. These dif- ferences, while not dramatic, suggest differences in the hazard (survival) rates by sport. Figure 2 presents the estimated Kaplan-Meier survival curves with Greenwood 95% confidence bands for managerial tenure in each of the three sports. Also in the figure are the survival curves (without the confidence bands) for all three sports. Since these survival probabilities are impossible to read accurately off of the graphs, Table 1 presents them for the tenure interval 2-15 years.

Naturally, the first question is, do these survival probabilities in fact differ by sport? The appropri- ate test is the log rank test (Savage, 1956). This test compares the actual and the predicted fail- ures for each group and uses the x2 statistic. The result for the comparison across sports is X 2(2) =

408 GERALD W. SCULLY

{a) Baseball (b) Basketball

0 20 Yesrs 40 60ears20 Years 40 60

(} Football

I ~~~~~~~~~~~~~~~~~~~~()I

o :

&- .5 go &.5

C.5

0 ~~~~~~~~~~~~~~~~~~~0

0 20 Years 40 20 Years 40 60

Figure 2. Kaplan-Meier survival with Greenwood confidence limits.

Table 1. Survival Probabilities of Managers by Sport

Tenure Baseball Basketball Football

2 0.790 0.655 0.776 3 0.637 0.486 0.647 4 0.521 0.380 0.506 5 0.427 0.338 0.423 6 0.341 0.303 0.321 7 0.285 0.239 0.250 8 0.243 0.190 0.218 9 0.213 0.148 0.173

10 0.180 0.134 0.141 11 0.161 0.113 0.115 12 0.142 0.106 0.103 13 0.124 0.077 0.090 14 0.105 0.063 0.083 15 0.086 0.056 0.077

5.0, prob. = 0.082. On the basis of the log rank test, the survival curves are statistically different from each other.

The next question of importance is the form underlying the distribution; i.e. whether it follows the exponential (a one-parameter distribution) or the Weibull (a two-parameter distribution). While

other distributions can be employed, they involve difficulties, in part because the qualitative shape of the hazard (monotonicity, log concavity, etc.) and in part because they yield complex hazard functions that do not have the constant hazard as a special case.

One test that distinguished between the expo- nential and the Weibull is to estimate ln(-ln(S(t))) = -ln(A) +p ln(t), where S(t) is the survival function (the hazard function is Ap(At)P- . Thus, the parameters can be esti- mated by linear regression. If the underlying dis- tribution is exponential, p = 1. The alternative, p # 1, implies a Weibull distribution and if p > 1, the hazard is increasing and otherwise decreasing. The results by sport were as follows: baseball (p = 1.148, t = 129.7), basketball (p = 0.954, t = 112.1), and football (p = 1.190, t = 103.5). All the coefficients were statistically different from unity, accepting that the underlying distribution is Weibull. The problem with the test is that the standard errors are serially correlated, so that the results can be taken only as approximate. An alternative test is to estimate the Weibull parameters directly. The estimated p = 1/o-

MANAGERIAL EFFICIENCY AND SURVIVABILITY IN PROFESSIONAL TEAM SPORTS 409

comes from the Weibull regressions in Table 2. All the p's in the Weibull regressions are signifi- cantly greater than unity. We accept that the underlying distribution is Weibull.

There are several parameterizations of the max- imum-likelihood Weibull regression models. The parameter estimates may be in log expected time, log relative hazard or hazard ratios. The log ex- pected time parameterization is chosen, since we want to focus directly on expected survival time relative to managerial efficiency. Estimation is of the form:

A(t) = (tWl1f) exp( ,0 + EpiXi + e) (7)

where cr is the shape parameter (or p = 1/cr), estimated from the data, and E has an extreme value distribution scaled by o-. The method of estimation is maximum-likelihood via Newton-Raphson.

The Weibull regressions appear in Table 2. In general, the estimation of the hypothesized rela- tionship between managerial efficiency and tenure

is successful. All the x2s are significant at well above the 99% level. The efficiency measure is always positive (higher efficiency is associated with longer (log) expected survival time and is highly significant (the t-values are asymptotic t-values) in all sports. The standard deviation of efficiency also is positively associated with (log) expected survival time, but is not statistically significant in football and only weakly significant in basketball (p = 0.27). In the Weibull regression that com- bines all the sports, all the variables, including the intercept and slope dummies, are highly signifi- cant.

The expected survival times related to manage- rial efficiency (the standard deviation of efficiency is set at the mean) are graphed in Fig. 3. The efficiency measure is at the mean and -2 o- and +2o-. The means and standard deviations of the managerial efficiency measure by sport were: baseball (0.7737, o- = 0.0337), basketball (0.7171, a= 0.0947) and football (0.5771, o- = 0.0734). The lower mean efficiency of head coaches in football is a natural consequence of a higher noise-to-sig-

Table 2. Weibull Maximum Likelihood Regressions of Survival

Variable Baseball Basketball Football All sports

Constant -5.624 - 1.759 0.142 -5.696 (4.77) (3.35) (0.39) (4.99)

Efficiency 9.195 4.697 3.063 9.291 (6.22) (7.03) (6.08) (6.49)

cr Efficiency 10.353 1.390 0.085 10.578 (4.23) (1.12) (0.08) (4.45)

Basketball 3.989 (3.14)

Football 5.838 (4.87)

Eff* Basket -4.688 (2.93)

Eff* Foot -6.232 (4.10)

of Eff* Basket -9.214 (3.40)

of Eff* Foot -10.489 (4.02)

Sigma 0.716 0.650 0.688 0.693 or(Sigma) 0.030 0.038 0.037 0.020 Log Likelihood -313.5 -155.1 -174.8 - 644.2 X2 34.2 33.3 26.3 100.5 N 267 142 156 565

Note: Asymptotic t-values in parentheses.

410 GERALD W. SCULLY

Expected Tenure Baseball

12

8

_ ~~~~~~Football

4

Basketball

-2 Sigma Mean +2 Sigma Efficiency

Figure 3. Expected survival times related to managerial efficiency.

nal ratio. The theoretical standard deviation of the win per cent of a 0.500 club (or a league containing clubs of equal playing strengths) is 0.5/ fg, where g is the number of games during the season. The theoretical standard deviation in football with 16 season games is 3.2 times that of baseball with 162 season games.

CONCLUSION

In the modern theory of the firm the function of the manager is to maximize the principals' resid- ual claim. In professional team sports this means maximizing the club's win per cent with the play- ing talent at hand. Bottom-finishing clubs may get there because they lack talented players or be- cause they are managed poorly. Generally, the two can be distinguished.

Here the decision to retain or terminate the coach was modelled and estimated. Managerial tenure was shown to be linked to managerial efficiency or the ability of the coach to extract the

largest win per cent from a given set of player inputs.

NOTES

1. Data on the win per cent, points or runs scored during the season and opponent points or runs scored were collected from standard sports record sources. The data for baseball are from 1876 to 1989 and are contained in The Baseball Encyclopedia. All teams and leagues were included, except for the Union Association teams in the 1884 season. Too many teams folded too early in the league to make their inclusion valid. The data for basketball are from The Sports Encyclopedia: Pro Basketball, 3rd edition, and cover all leagues and teams from the 1937-8 season the 1989-90 season. The data for football are from 1933 to 1989 and for all leagues and teams. Prior to the 1960 season the data are from the Official 1985 National Football League Record and Fact Book; for the period 1960-89, the data are from The Sports Encyclopedia: Pro Football, 8th edition. The head coach list prior to 1960 was obtained from the Pro Football Guide, 1990 edition.

2. The residuals from the regressions estimated on the basis of Eqn (6) were examined and no pattern related to trend was found. Several tests were per-

MANAGERLAL EFFICIENCY AND SURVIVABILITY IN PROFESSIONAL TEAM SPORTS 411

formed on the residuals (e.g. the squared residuals against trend) with no significant results.

REFERENCES

A.A. Alchian and H. Demsetz (1972). Production, in- formation costs, and economic organization. Ameri- can Economic Review, 62, 777-95.

R.H. Coase (1937). The Nature of the Firm. Economica N.S., 4, 386-405.

H.G. Manne (1965). Mergers and the market for cor- porate control. Joumal of Political Economy, 73, 110-20.

P.K. Porter and G.W. Scully (1982). Measuring man- agerial efficiency: the case of baseball. Southem Economic Joumal, 48, 642-50.

L.R. Savage (1956). Contributions to the theory of rank order statistics. Annals of Mathematical Statistics, 27, 590-615.

G.W. Scully (1989). The Business of Major League Base- ball, Chicago: The University of Chicago Press.

G.W. Scully (1992). Coaching quality, turnover, and longevity in professional team sports. In Advances in the Economics of Sport (edited by G.W. Scully), Greenwich, CT: JAI Press, 53-65.