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Managerial quality, team success, and individual player performance in major league baseball.

In recent years, much labor economics research has focused on the link between employee motivation and work performance in an attempt to broaden our understanding of the employment relationship. For example, models of efficiency wages, implicit contracts, and incentive pay schemes have all been designed to help explain variations in worker performance.

In this recent work on employee incentives, the functions of managers or supervisors are not studied in any detail. Managers are viewed as merely monitoring work performance of subordinates. Although this task is certainly an important function of managers, it is by no means their only or even their most important job.

In contrast to this work by labor economists, a voluminous literature in the personnel field has attempted to characterize the functions of managers. In addition to monitoring employee performance, successful managers plan strategies, train and motivate their subordinates, mediate disputes, and provide information to others in the organization. Thus, successful managers may enable firms to move closer to the frontier of their production functions or to reduce intrafirm transactions costs.

What does a firm get when it invests in a high-quality manager? That question is the central focus of this paper. I use 1969-87 data from major league baseball to estimate the impact of managerial quality on team and individual player performance. Both managers' ability to turn player inputs into victories and their ability to improve player performance are investigated.

Baseball data (or sports data in general) are particularly well-suited for this study because they include extensive measures of performance as well as pay. In this study, managerial quality and player performance at any time are both measured as predicted pay based on salary regressions. Thus, I am able to use market-related measures of these variables and to draw conclusions about costs and benefits of investing in managerial quality. In addition, I test the robustness of the estimates of managerial impact with respect to alternative (non-market) measures of managerial quality.

The Functions of Management

To develop hypotheses about the effect of management, some researchers have attempted to break down into component parts the functions that executives perform. For example, after observing several chief executives, Mintzberg (1973:54-94) concluded that there were roles common to successful managers. First, executives function in interpersonal roles such as that of a figurehead for the organization, a leader, and a liaison with those outside the organization. Second are the informational roles the executive takes on. These activities include monitoring the work of subordinates, disseminating information, and speaking on behalf of the unit to others inside the organization. Finally, the manager must use the information gathered to make decisions. In economic terms, managers may enable firms to produce more efficiently (Porter and Scully 1982) and may improve information flow within the firm (Williamson 1986).

The activities of baseball managers fall under the categories developed by Mintzberg (1973). In his 1984 ratings of American League baseball managers, James (1984) noted what he believed were each manager's best qualities. These included "confidence [and] strength" (p. 96); a "desire to win ... [and an] ability to form unlike and unrelated talents into a comprehensive whole" (p. 110); "ability to work with young players, help them develop their skills" (p. 117); lineup construction; "ability to command the respect of his players" (p. 132); "inventiveness . . . hard-working resourcefulness" (p. 147); and "intensity ... command of details" (p. 153).

Other qualities cited by James (1984) are related to decision-making, resource allocation, strategy, and monitoring. For example, managers must make basic staffing decisions such as the composition of the starting lineup, batting order, and pitching rotation (the order in which pitchers play). There are perhaps hundreds of decisions a manager must make in a game, such as those involving defensive alignments, substitutions, type of pitch to throw, baserunning tactics, and hitting placement. Managers must also monitor the players' performance, just as business executives must in general monitor the performance of their subordinates. For example, some of the team's players may do better against certain types of pitchers than against others. Successful baseball managers often ensure that the right player is performing against a particular alignment. In addition, successful baseball managers know the capabilities of their opponents and are thus able to effectively defend against them.

These examples indeed suggest that baseball managers perform many of the same functions that business executives do and may therefore have a similarly important influence on the success of the organization.(1)

Empirical Procedures

Measurement of Managerial Quality

Estimation of the various effects of managerial quality on team success and individual performance requires a consistent measure of managerial quality. I take a market-related approach to the measurement of managerial skill. Specifically, since managers are free agents when they sign contracts, in a competitive labor market one might expect their salaries to approach their marginal revenue products.(2) This reasoning suggests that a manager's salary is the appropriate measure of his quality. Unfortunately, managerial salary data are available only for 1987; but predicted salary (based on a salary regression to be described shortly) can be constructed for any manager in any season. I therefore use a manager's predicted salary, adjusted in a manner to be described, as the basic measure of his quality.

To implement this procedure, I obtained 1987 salary data and lifetime performance statistics on baseball managers.(3) The following wage equation was estimated for managers with previous major league managing experience: (1) In (MSAL) = [a.sub.0] + [a.sub.1]EXP + [a.sub.2]LPCT

+ [a.sub.3]NL + [u.sub.1] where MSAL = 1987 manager salary level, EXP = years of major league managerial experience before the 1987 season, LPCT = manager's lifetime pre-1987 winning percentage, NL = National League dummy variable, and [u.sub.1] is an error term.

In equation (1), experience (EXP) iS likely to have a positive coefficient for at least two reasons. First, managers may become more skilled as they learn by doing. Second, turnover among managers is generally accomplished at the team's "invitation." Those managers with long careers have demonstrated that they have the skills to be major league managers. A high level of experience is thus a signal of relatively high quality. Winning percentage (LPCT) is an obvious indicator of team success and is expected to have a positive coefficient. Finally, NL is included as a control for possible differences in the demand for managerial quality by league.

The parameter estimates from (1) are then used as follows to compute managerial quality. I calculate (2) MQUAL = [b.sub.1]EXP + [b.sub.2]LPCT, where MQUAL iS the measure of managerial quality and b, and b2 are ordinary least squares (OLS) estimates of [a.sub.1] and [a.sub.2] respectively. MQUAL iS, up to a constant term, predicted salary, standardizing for league. An advantage of using predicted salary is that measures of managerial quality can be obtained as long as the variables EXP and LPCT are available. Actual salary data are needed only in estimating equation (1) to obtain the weights to apply to these performance measures. As discussed in detail below, I experimented with several alternative specifications for the managerial salary equation, and the results were robust to these tests.(4)

The market-related measure of managerial quality can be contrasted with other measures of managerial quality or efficiency that have recently appeared in the literature on the economics of sports. First, Porter and Scully (1982) in effect define managerial quality as a manager-specific dummy variable impact in a model determining winning percentage (controlling for offensive and defensive inputs).

Second, Clement and McCormick (1989) attempt to measure the quality of college basketball coaches and then relate this measure to team success. The authors assume that high-quality coaches make better lineup decisions than low-quality coaches. A coach's quality is measured by the [R.sup.2] from a regression of his players' minutes played on per-minute performance statistics (rebounds, points, and so on)--individual players are the data points.

Third, Pfeffer and Davis-Blake (1986) use separate single measures of NBA coaches' ability such as past record or past experience. Although these measures are, spirit, similar to the approach taken re, they impose an implicit weighting of past record or experience--in each case weight is 100%, as only one performance measure is used in any particular regression.

None of these studies examined the impact of managers on subordinates' performance levels. In addition, my measure applies market-based weights to managerial characteristics unlike previous work on sports.(5)

To test the robustness of my treatment of managerial quality, I use two alternative definitions of quality (in addition to the market-based measure), as suggested by the above review of previous literature. First, I use as regressors the variables that determine managerial salary (rather than use predicted salary). As noted, Pfeffer and Davis-Blake (1986) use such variables one at a time. The procedure used here does not depend on managerial salary equation and may thus introduce less noise than MQUAL does into the estimation of the impact of managerial quality. Second, as suggested by Porter and Scully's (1982) work, I use manager-specific dummy variables from equations determining team winning percentage. These dummy variables are used in models determining player performance but not team performance (since team performance equations are used to generate the measures of managerial quality in the first place). The procedures used to generate the manager-specific dummy variables are described below.

Effects of Managerial Quality on Team and Individual Performance

The impact of managerial quality on organizational success is analyzed in two stages. First, the effect of managers on team success given player performance is estimated. This analysis focuses on manager's strategic skills: for a given level of laying performance, do higher-quality managers produce more victories? Second, I estimate the effect of manager quality on players' performance. Specifically, I attempt to answer the following question: do high-quality managers get better performance from a player relative to his (the player's) established career playing performance level than low-quality managers? This phase of the analysis captures the motivational impact of leadership.

To some degree, such a dichotomy between the strategic and motivational functions of managers is artificial. In particular, a manager can improve a player's performance statistics by playing him in specific circumstances (for example, playing a left-handed batter against right-handed pitchers). On the other and, what may appear to be strategic effects of good managers may in fact be motivation of players to perform well in crucial instances. Further, we are implicitly giving the manager credit for outcomes that may also be influenced by team executives and other coaches. Crediting managers for the effects of other coaches may be valid to some extent, since managers often bring in their own coaching staffs.

Team Performance

The effect of managers on team performance is analyzed using major league baseball team data from 1969 through 1986 (subject to some restrictions to be mentioned shortly) to estimate the equation [Mathematical Expression Omitted] where t subscripts refer to year, WPCT = team's winning percentage, SREL = (team's runs scored)/(team's runs allowed), MQUAL and NL are as defined above, and [u.sub.3] is an error term.

The sample for equation (3) is restricted to teams with experienced managers so that managerial quality can be computed. Further, all cases in which a manager took over during the season are eliminated because team scoring and defense information is available only for the entire season. In equation (3), the MQUAL coefficient measures the impact of managerial quality on team success, given scoring and defensive inputs (SREL) and past team performance ([WPCT.sub.t-1]). Past winning percentage is included to account for unmeasured aspects of the team's ability to win games. The National League dummy variable is included in order to sharpen the interpretation of the offense and defense statistics, which may vary by league.(6)

Equation (3) provides a relatively stringent test of the impact of managerial strategy, since it controls for scoring relative to runs allowed. It might be argued, however, that scoring is to some degree a function of managerial strategy and that (3) may therefore understate the impact of managerial strategy. To take account of this possibility, I estimate an alternative model similar to (3) except that SREL iS replaced by the measurable aspects of player performance that affect scoring and defense: [Mathematical Expression Omitted] where SA = team slugging percentage; ERA = team earned run average; SB = team stolen bases; FA = team fielding percentage; BA = team batting average; K = batters struck out by the team's pitchers; BB = batters walked by the team's pitchers; Y72 and Y81 are, respectively, dummy variables for the strike-shortened seasons of 1972 and 1981, which have expected levels Of SB, K, and BB that differ from those for normal seasons; and [u.sub.4] is an error term. All variables are measured for the same year as team winning percentage.

In (4) the MQUAL coefficient now combines two aspects of managerial strategic skill: the manager's ability to turn slugging percentage, batting average, earned run average, and so on, into runs scored and runs allowed; and his ability to turn runs scored and runs allowed into victories. The coefficient on MQUAL in (4) can be compared with that on MQUAL in (3) to draw conclusions about the relative importance of these aspects of strategy.(7) Although it is natural to interpret the MQUAL coefificient in these models as the impact of managerial quality on victories or (runs scored)/(runs allowed) controlling for playing performance, it is possible that "clutch" play varies across teams for reasons other than the effect of the manager. Further, if players' innate clutch-playing ability is correlated with managerial quality, then we may be misinterpreting the impact of managers. The control for past winning percentage, however, lessens the likelihood of that kind of misinterpretation.

Estimation of equations (3) and (4) poses at least two specific econometric problems. First, since MQUAL is an estimated regressor, the usual OLS standard error formula will in general give a biased estimate, although OLS will lead to consistent coefficient estimates, as in any instrumental variables estimation. The asymptotic standard errors for (3) and (4) were computed using a procedure developed by Murphy and Topel (1985), which takes account of the fact that MQUAL iS an estimated regressor. When MQUAL iS replaced by EXP and LPCT, there are no estimated regressors, and the Murphy-Topel (1985) procedure is no longer necessary.

Second, problems associated with the use of time-series--cross-section data may be present in estimating (3) and (4). Unfortunately, sample restrictions (due to missing data) prevent the use of an error components generalized least squares (GLS) model, a common technique for such problems. As a check on the results, however, I also estimated (3) and (4) using individual team dummies, a procedure suggested by Mundlak (1978) for handling time-series--cross-section models with fixed effects that may be correlated with the explanatory variables. In such models, the error components GLS approach will in general lead to biased coefficients; but the results obtained using the dummy variable approach will be unbiased, though relatively inefficient (due to the inclusion of the dummy variables), as long as there are no dynamic effects. Even with team dummies, however, biases may remain due to the inclusion of the lagged dependent variable (Nickell 1981).

Individual Player Performance

To estimate the impact of managers on player performance, we need to control for playing ability. The aim is to test whether players are able to get more from their playing ability under high-quality managers than under low-quality managers. Playing ability and player performance under a particular manager are measured again using the market-based approach--they are estimated as predicted salary, adjusted for location and league effects. Further, I isolate a sample of teams taken over by new managers in the 1969-87 period.(8) A player's ability is his predicted salary based on his career up to the season in question, with adjustments for league and location effects. Player performance under the new manager is adjusted predicted salary for the season in question. Thus, the new manager will not in general have an effect on our measure of the player's ability.

Separate analyses were performed for pitchers and non-pitchers. Log salary regressions for 1987 were run in order to obtain the parameter estimates necessary for the computation of player quality and performance. The variables for these regressions are described in the Appendix.

The player salary regressions are used as follows to estimate player ability and performance under the new manager.

Nonpitchers

For nonpitchers, the following equations express, respectively, measures of prior ability (HLQUAL) and current performance (HSQUAL): (5) HLQUAL = [g.sub.1]SA + [g.sub.2]BA + [g.sub.3]WA + [g.sub.4]SBG + [g.sub.5]FA (6) HSQUAL = [g.sub.1]SSA + [g.sub.2]SBA + [g.sub.3]SWA + [g.sub.4]SSBG + [g.sub.5]SFA, where [g.sub.1] through [g.sub.5] are the corresponding regression coefficients from equation (A1); SA, BA, WA, SBG, and FA are lifetime statistics (as of the beginning of the season in question) referring to, respectively, slugging average, batting average, walks per at bat, stolen bases per game, and fielding average; and SSA, SBA, SWA, SSBG, and SFA are the corresponding performance statistics for the season in question. Equations (5) and (6), respectively, express player ability (previous performance) and playing performance during the season in question as market weighted sums of the relevant playing statistics.

These measures of ability and specific aspects of performance are then used to estimate the impact of managerial quality on playing performance: (7) RHQUAL = [k.sub.0] + [k.sub.1]MQUAL + [k.sub.2]AGE35
             + [k.sub.3]EXP10 + [k.sub.4]EXP3
             + [k.sub.5]INF + [k.sub.6]CATCH + [u.sub.7],


where RHQUAL = HSQUAL - HLQUAL; AGE35 is a dummy variable for players over 35 years old; EXP10 iS a dummy variable for players with more than 10 years of major league experience; EXP3 is a dummy variable for players with less than three years of major league experience; INF and CATCH are, respectively, dummy variables for infielders and catchers; U7 is an error term; and MQUAL iS as defined earlier. The dependent variable in (7) is the player's performance during the season in question relative to his established performance level. It is the log of the ratio of season and lifetime performance levels, since the lifetime levels are already in log salary units. The major explanatory variable of interest iS MQUAL, the quality of the manager who took over the team for this season. Age and experience variables are included in order to account for the normal patterns of improvement and decline in performance over a player's. career. In particular, if older players customarily perform at a level below their career averages, this deterioration will be picked up by the AGE35 and EXP10 variables. On the other hand, EXP3 may account for the possibility that younger players on average are improving. Position variables are included as controls.

Pitchers

Pitching ability (PLQUAL) and season performance (PSQUAL) are expressed as follows: (8) PLQUAL = [h.sub.1]ERA + [h.sub.2]CPCT + [h.sub.3]PW

+ [h.sub.4]SG + [h.sub.5]PSG (9) PSQUAL = [h.sub.1]SERA + [h.sub.2]SPCT + [h.sub.3]SPW

+ [h.sub.4]SSG + [h.sub.5]SPSG, where h, through h5 are the corresponding regression coefficients from equation (A2); ERA, CPCT, PW, SG, and PSG are lifetime statistics as of the beginning of the season in question for, respectively, earned run average, winning percentage, fraction of games started times winning percentage, saves per game, and fraction of games started times saves per game; and SERA, SPCT, SPW, SSG, and SPSG are the corresponding statistics for the season in question.

The impact of managerial quality on pitching performance is estimated as follows: (10) RPQUAL = [m.sub.0] + [m.sub.1]MQUAL

+ [m.sub.2]AGE35 + [m.sub.3]EXP10 + [m.sub.4]EXP3

+ [m.sub.5]NODH + [m.sub.6]LINODH + [u.sub.10], where RPQUAL = PSQUAL - PLQUAL; NODH is a dummy variable for pitchers in a league or time with no designated hitter (that is, for those who were in the National League or played during seasons prior to 1973); LINODH = fraction of a pitcher's lifetime innings (prior to the season in question) in a league or time with no designated hitter; [u.sub.10] is an error term; and MQUAL, AGE35, EXP10, and EXP3 are as defined earlier.

Equation (10) for pitchers is similar to (7) for nonpitchers except for the addition of the designated hitter variables. Since the designated hitter rule has resulted in more scoring, the pitcher's measured performance needs to be adjusted for the presence or absence of this rule. NODH serves to adjust the current season's performance, and LINODH adjusts the established lifetime ability level.

Since both equations (7) and (10) have an estimated regressor (managerial quality), the asymptotic standard errors are computed using the Murphy and Topel (1985) procedure (see above). Further, the samples are restricted to experienced players so that lifetime performance can be computed. Specifically, nonpitchers with at least two full years of experience or more than two partial years are included, and pitchers with at least one full year or more than one partial year are included.(9) In addition, I restrict the analysis to starting players (or regular relief pitchers) who played full-time (or nearly so) during the season in question. This restriction is made so that the analysis can abstract from the question of injuries. The result of these steps is a sample of full-time, established players who were not injured seriously enough to take them out of the lineup for sustained periods, and who would likely have had full-time positions on the team regardless of who was managing and regardless of whether they had "hot" seasons.

In the models of player performance, I use two other measures of managerial quality besides MQUAL. First, as in the model of team performance, MQUAL iS replaced with EXP and LPCT. Second, I use the managerial dummy variable approach. This second procedure confronts the issue of what credit to give managers for individual player performance in estimating managerial quality. I take two polar approaches to the issue, hoping to get bounds for true managerial quality. First, I estimated the following linear equation on the 1969-86 sample of teams: (11) WPCT = f(WPCT lagged, SA, ERA, SB,
            FA, BA, K, BB, NL, Y72, Y81,
            manager-specific dummies).


I used the manager-specific dummy variable coefficients from (11) to calculate for each player QDUM1. This index of managerial quality is a measure of the manager's ability to turn inputs such as slugging and pitching into victories, controlling for the team's established ability to win.

Second, since managers can influence players' performance levels, I estimated a model without the player inputs: (12) WPCT = g(WPCT lagged, managers-specific

dummies).

The manager-specific dummy variable coefficients from (12) were used to compute QDUM2 for each player. QDUM2 gives the manager credit for playing performance that contributes to current victories, controlling for the team's established ability to win.

Since QDUMI and QDUM2, respectively, give the manager none or all of the credit for playing performance, they may bracket the manager's true contribution to victories. Since these manager-specific coefficients are estimated regressors, the Murphy-Topel (1985) procedure is again used in the second stage regressions.

Results

Team Performance

The 1987 managerial salary regression results are as follows (standard errors in parentheses): In MSAL = 9.0954 + .0235*Exp (.9697) (.0133) + 5.600*WPCT + .3682*NL, (1.8722) (.1814) [R.sup.2] = .4632, n = 22, where ***, **, and * mean that the coefficient is significantly different from zero at, respectively, the 1%, 5%, and 10% levels on two-tailed tests.

According to this equation, experience, winning percentage, and placement in the National League all have positive effects on salary. The impact Of EXP iS Significant at better than the 10% level; the effects of WPCT and NL are significant at the 1% and 5% levels, respectively.

Table 1 presents estimates of the impact of managerial quality on winning percentage and scoring-to-defense ratio (SREL). The major results are for MQUAL, the measure of managerial quality. In column 1 of Table 1, the effect of managerial quality is estimated holding constant the scoring-to-defense ratio, as well as the league and last year's winning percentage. The effect of managerial quality is positive and is significant at the 9% level on a two-tailed test. This coefficient is an estimate of managerial strategy given team scoring. In effect, I find that high-quality managers get more victories out of a given runs scored-runs allowed ratio than do low-quality managers.(10) [TABULAR DATA 1 OMITTED]

As mentioned earlier, however, better managers may get better SREL values for given offensive and defensive inputs. This possibility is investigated indirectly in column 3 and more directly in column 4 of Table 1. In column 3, the coefficient on MQUAL iS substantially larger and more significant than in column 1 (the significance level is 6.8% on a two-tailed test). The column 3 MQUAL effect is an estimate of the sum of the effects of managerial strategy on victories given SREL and on SREL given the inputs that affect runs allowed and runs scored (slugging average, earned run average, and so on). Finally, column 4 of Table 1 shows positive although insignificant effects of MQUAL on SREL given these inputs.(11)

As noted, the results in Table 1 include teams whose managers may have been with the team the previous year as well as cases in which the team was taken over by a new manager. Inclusion Of [WPCT.sub.t-1] in part accounts for a team's established ability to win, and in Table 1, it is seen that previous winning percentage makes no difference once we have controlled for current offensive and defensive performance. Thus, having an established ability to win, controlling for current offensive and defensive performance, may be an overrated indicator of team quality. The good teams are good because they score many runs and do not give up many runs. Further, the small (and insignificant) [WPCT.sub.t-1] coefficients in columns 1 and 3 do not suggest any appreciable difference between the long-run and short-run effects of managerial quality on winning, controlling for offensive and defensive performance.(12)

Related to the issue of past winning percentage is the possible impact of new management. When a dummy variable was included for a change in management, the basic results were unchanged and the new manager coefficient was insignificant and small. Further, there was no evidence of any interaction effects between managerial quality and the presence of a new manager. Thus, there is no evidence of any succession effects. Finally, addition of team dummy variables, as well as addition of year dummy variables, did not affect the basic results.

The material importance to teams of managerial quality can be estimated using information on the impact of winning on net revenues. According to Scully (1989: 155), a one point increase in team winning percentage (for example, an increase from .500 to .501) in 1984 raised team revenue by $31,696. From Table 1 we see that an increase in managerial quality of .1 (in log salary units) raises the winning percentage by 0.94-1.25 points. Therefore, in 1987 dollars, an increase in managerial quality of .1 units raises revenue by $32,576-$43,319.(13) At the mean salary, such an increase in MQUAL COSTS $26,976, or 62-83% of the revenue generated by the increase in wins the higher-quality manager will bring.(14)

Player Performance

Table 2 contains estimates of the impact of managerial quality on players' performance relative to their lifetime performance. The major results in Table 2 are for MQUAL. The effects Of MQUAL range from .2008 to .2600 and are significant at better than the 5% level on two-tailed tests for both pitchers and nonpitchers. When a high-quality new manager takes over a team, the average starting player's performance relative to his lifetime statistics (accumulated under other managers) is greater than when a low-quality manager takes over the team.(15)
Table 2. Effect of Managerial Quality on
Player Performance, 1969-87.
(Asymptotic Standard Errors in Parentheses)
              Nonpitchers   Pitchers
              (Dependent    (Dependent
Explanatory   Variable =    Variable =
Variable      RHQUAL)       RPQUAL)
Constant      -.5073(**)    -.7233(**)
              (.1995)       (.3265)
MQUAL          .2008(**)     .2600(**)
              (.1005)       (.1288)
AGE35         -.1685(*)      .2248(*)
              (.0917)       (.1348)
EXP10         -.1738(***)    .0978
              (.0599)       (.0974)
EXP3          -.0702         .1173
              (.0992)       (.0905)
INF            .0321          --
              (.0416)         --
CATCH          .0581
              (.0654)
NODH            --           .0889
                            (.0916)
LINODH          --           .0615
                            (.1069)
[R.sup.2]      .1194         .0513
Sample Size      290          257
  Sources: See Table 1 for MQUAL; player salary, used
in the construction of the dependent variables, is
taken from Chass (1987); the other variables come
from Reichler (1988).
  Variable Definitions: RHQUAL = HSQUAL- HLQUAL,
where HSQUAL iS the player's season performance
and HLQUAL is his career average performance prior
to the current season; HSQUAL and HLQUAL are
defined by equations (5) and (6) in the text; RPQUAL
= PSQUAL - PLQUAL, where PSQUAL is a pitcher's
season performance and PLQUAL is his career average
performance prior to the current season; PSQUAL and
PLQUAL are defined by equations (8) and (9); AGE35 iS
a dummy variable for players over 35 years old; EXP10
is a dummy variable for players with more than 10
years of major league experience; EXP3 is a dummy
variable for players with less than 3 years of major
league experience; INF and CATCH are, respectively,
dummy variables for infielders and catchers; NODH is
a dummy variable for pitchers in a league or time
with no designated hitter; LINODH = fraction of a
pitcher's lifetime innings prior to the current season
in a league or time with no designated hitter.
(*) Coefficient is significantly different from zero at
the 10% level; (**) the 5% level; (***) the 1% level
(two-tailed tests).


The findings in Table 2 can be used to estimate the value of the improved playing performance caused by an increase in managerial quality. Suppose that a team hires a manager of a quality that is .1 units higher than the quality of the old manager. The empirical results in Table 2 give estimates of the resulting improvement in player performance. To compute the size of this improvement, note that the estimates in Table 2 are for starting players and regular relief pitchers, all of whom have full-time playing statistics for the season in question. In our sample, there is an average of about six nonpitchers and five pitchers per team. Thus, ignoring any impact of managers on bench players, a .1 unit increase in MQUAL raises the total playing performance of hitters by about .12 units and that of pitchers by .13 units. Thus, the total increase in playing performance caused by a .1 unit increase in MQUAL is .25 units. Since player salaries averaged about $410,000 in 1987, this increase in playing performance would, at the mean, cost about $116,450.(16) Whether this improvement is permanent is an open question; but this conservative estimate of the short-run effects of managerial quality implies a large dollar impact on player performance.

Alternative Specifications for Managerial Quality

Table 3 contains selected results for alternative measures of managers' quality. The first two columns indicate the impact of EXP and LPCT, the two variables that make Up MQUAL in (2), separately.(17) The table suggests that managerial winning percentage is a more important determinant of team winning percentage and player performance than is experience.(18) [TABULAR DATA 3 OMITTED]

The EXP results in Table 3 might cause one to question the use of the constructed variable MQUAL as the basic measure of managerial quality (recall that MQUAL iS used because it allows the computation of dollar costs). Using MQUAL iS equivalent to using EXP and LPCT with restrictions on the latter two variables' coefficients (derived from equation 2). A Wald test of these restrictions accepted them in all cases in the analysis of teams (that is, all of Table 1) and nonpitchers; for pitchers, however, the Wald test rejected these restrictions at the 5% level. These Wald tests give at least some support to the basic MQUAL construction, which has the advantage of being a readily interpretable summary measure of managerial quality. The findings for pitchers must, however, be qualified in view of the Wald test result.

The second two columns of Table 3 test the impact of manager-specific dummies on player performance. For nonpitchers, both manager-specific dummy variable specifications (QDUM1 and QDUM2) show significant, positive effects on player performance. For pitchers, however, only the latter (QDUM2) has a significant effect, although the impact of QDUM1 for pitchers at least has the anticipated sign. As suggested earlier, QDUM1 may underestimate and QDUM2 may overestimate the manager's contribution.

I tested the basic results for robustness with respect to alternative specifications of the managerial wage equation (1) and therefore of the market-based measure of managerial quality. In each case, the basic findings in Tables 1 and 2 were unchanged. First, if there is monopsony in the labor market for managers, then in a bargaining model, alternative wages would affect managers' negotiated baseball salaries. I added local labor market variables (as proxies for such alternative incomes and, perhaps, for compensating differentials) to equation (1), and the variables (population and per capita income) were always insignificant in the regression.

Second, in an attempt to control for the inputs a manager has had to work with, I entered a variable equaling the career ratio of runs scored to runs allowed for the manager's teams in his career (CREL). Again, this variable had an insignificant coefficient and did not affect the second stage results. Moreover, I added a further control for managerial performance--the number of divisional championships won (TITLES). As before, this variable did not improve the managerial salary regression and did not affect the subsequent analysis.

Finally, Appendix Table (A3) shows what happens when CREL and TITLES (along with EXP and LPCT) are added to the team and player performance regressions. The dominant effect Of LPCT remains for each analysis of teams and remains for players when TITLES is entered; for players, however, the separate effects of CREL and LPCT cannot be disentangled. Note, however, that CREL did not have a significant effect on managerial salaries, whereas the LPCT effect on managers' salaries remained large, positive, and significant in all tests, bolstering the interpretation of past winning percentage as an important indicator of managerial quality.

Conclusions

I have tested the effects on organizational success of two functions baseball managers perform that are similar to those performed by all managers, according to the human resource management literature: making strategic decisions concerning the allocation of employees (players) and training and motivating employees (players). A unique feature of this study is its use of market-based measures of managerial quality and player performance. (The robustness of the results with respect to non-market measures of managerial quality was also tested.) Managerial quality was defined as the predicted salary a manager would receive based on his performance. Thus, the cost of obtaining more victories or better player performance through the superior skills of a high-quality manager was computed.

Managerial quality was found to have had a positive, usually significant effect on team winning percentage, controlling for team offensive and defensive inputs, as well as on player performance relative to player ability. One implication of these results is that if players can capture the value of their improved performance, they may be willing to take a lower initial salary to play for a better manager. Also, according to these estimates, major league baseball teams appear to be getting a bargain when they hire better managers.

APPENDIX

Regressions Used for the Computation of Player Performance

This Appendix describes log salary regressions used for computing player performance.

Nonpitchers

(A1) In (HSAL) = [e.sub.0] + [e.sub.1]SA + [e.sub.BA] + [e.sub.3]WA

+ [e.sub.4]FA + [e.sub.5]INF + [e.sub.6]CATCH + [e.sub.7]SBG

+ [e.sub.8]ABLACK + [e.sub.9]WHISP + [e.sub.10]BHISP

+ [e.sub.11]POP + [e.sub.12]INC + [e.sub.13]SEASONS

+ [e.sub.14]GAMES + [e.sub.15]AB + [e.sub.16]NL + [u.sub.A1'] where HSAL = 1987 compensation level, including base salary, prorated signing bonus, and the present value of deferred payments (taken from Chass 1987); SA = career slugging percentage (based on pre-1987 performance); BA = career batting average; WA = career walks per at bat; FA = career fielding average; INF = dummy for the infield positions of second base, shortstop, and third base; CATCH = dummy variable for catchers; SBG = stolen bases per game; ABLACK = dummy variable for non-hispanic black players; WHISP = dummy variable for white Hispanic players; BHISP = dummy variable for black Hispanic players; Pop = 1986 population in the team's metropolitan area; INC = 1985 per capita income in the team's metropolitan area;(19) SEASONS = number of seasons played; GAMES = number of games played; AB = number of at bats; NL = National League dummy variable; and [u.sub.A1] is an error term.

Pitchers

(A2) In (PSAL) = [f.sub.0] + [f.sub.1]ERA + [f.sub.2]PSTART

+ [f.sub.3]SEASONS + [f.sub.4]GAMES + [f.sub.5]IP + [f.sub.6]PGA

+ [f.sub.7]PIN + [f.sub.8]CPCT + [f.sub.9]PW + [f.sub.10]SG

+ [f.sub.11]PSG + [f.sub.12]ABLACK + [f.sub.13]WHISP

+ [f.sub.14]BHISP + [f.sub.15]NL + [f.sub.16]POP + [f.sub.17]INC

+ [u.sub.A2'] where the new variables are PSAL = 1987 pitcher compensation (see above definition for nonpitchers); ERA = career earned run average; PSTART = fraction of career games started; IP = career innings pitched; PGA = PSTART * GAMES; PIN = PSTART * IP; CPCT = career winning percentage; PW= PSTART * CPCT = = number of saves per game; PSG = PSTART * SG; [u.sub.2] is an error term.

Equations (A1) and (A2) contain basic playing performance statistics as well as longevity variables, race, market factors (pop and INC-to allow for the possibility of compensating differentials, a test that was also implemented for managers), and league. The model for nonpitchers includes offensive and defensive performance as well as the other salary-influencing variables. INF and CATCH are included because of the defensive importance of these positions. [TABULAR DATA (A1) and (A2) OMITTED]

The model for pitchers requires further comment. In particular, this model includes measures of winning and saves, and it might be argued that, controlling for ERA, these variables are indicators of the quality of offensive or defensive support for the pitcher. On the other hand, some pitchers may be better at winning or saving games than others, even controlling for their overall support and earned run average. Thus, we cannot say a priori whether the winning percentage and saves variables represent pitcher quality. My basic argument for their inclusion is that F-tests reject at far better than the 1% level the hypothesis that these variables do not affect salary, all else (including ERA) equal.(20) If winning and saves were unrelated to pitching performance when ERA is controlled for, then the former variables should not affect salaries. Finally; interactions with PSTART are included because of the possibility that winning and saves mean different things for pitchers who are primarily starters and those who are primarily relievers.

Tables (A1) and (A2) show the coefficients from the analyses of the log of 1987 compensation for nonpitchers and pitchers, respectively. For hitters, slugging average, batting average, fielding average, position, stolen bases, and number of times at bat all have significant effects on compensation in the expected direction. For pitchers, earned run average, winning percentage (at least for starting pitchers), and saves (for relief pitchers) have important effects on compensation.

A further interesting set of findings in the appendix tables concerns the impact of race on salary. In no case is a race dummy variable significant. Further, the point estimates for minority groups are positive four out of six times. These findings for race are consistent with those of Christiano (1988), who also does not find discrimination against black players in 1987. (1) Although baseball managers do not actually hire and fire players, they do affect playing time, and managers' input is sought by team executives in player retention decisions. (2) The possibility of monopsony power in the labor market for managers is discussed below. (3) Salary data on managers come from Sports Illustrated, April 20, 1987, p. 81; managerial performance data are taken from Reichler (1988); in some tests I use local market data drawn from U.S. Department of Commerce (1987, Table 34, pp. 28-30) and Statistics Canada (1987, Table 2.8, pp. 2-17. (4) Note that I do not include the NL coefficient in the measure of managerial quality. That coefficient is excluded because it is doubtful that league affiliation is associated with managerial quality consistently throughout the 1969-86 period. In addition, the constructed MQUAL iS affected only by variables directly related to the manager's behavior. The results were not changed by including league as an explanatory variable in equations determining managerial or individual success. Further, lack of data precluded an analysis of the issue of long-term contracts for managers. This issue could complicate the interpretation of the salary equation. Finally, the lack of managerial salary data for years before 1987 prevents the inclusion of salary as a measure of quality. (5) Although not a study of sports managers, Smith, arson, and Alexander's (1984) examination of united Methodist ministers did use a market-based measure of leadership. Specifically, the authors used corrected for tenure differences as a measure managerial quality among ministers. This measure was related to various indicators of organizational success such as church attendance, membership, and budget. The authors' measure of managerial quality thus assumed that experience had no effect on productivity. Unlike in this paper, no attempt was made to estimate the impact of leadership on subordinate performance. (6) The model was also estimated excluding NL, with no change in the basic results. (7) In addition to estimating (2) and (3), I also implemented a model in which SREL was the dependent variable and SA, ERA, etc., were inputs, giving a more direct estimate of the manager's ability to turn playing performance into scoring and defense. (8) The incidence of such events is too small( about 50 such cases) to allow the basic team analysis (equation 1) to be restricted to cases in which the team was taken over by a new manager. The fact that there are roughly 11 "regular" players (with usable data) per team, however, makes it possible to follow this procedure for individual players. (9) In some cases, players with multiple previous seasons were excluded when these seasons involved a trivial amount of playing time. In addition, when Sparky Anderson took over the Detroit Tigers in 1979, he managed the team for 105 games. Since I do not know how the players performed during these games, and pre-1980 performance levels are affected by Anderson's 105 games in 1979, I exclude this team from the analysis. The results are not affected when the 1979 or 1980 Detroit Tigers are included. (10) The impact of MQUAL iS much larger and more significant in column 2 of Table 1 than in column 1. This difference is due to the exclusion of SREL in column 2. The increase in the MQUAL coefficient in column 2 suggests either that the better managers are hired by teams that happen to have better players or that they get better performance out of the players. The latter possibility is tested below. In addition, when SREL was replaced by scoring and runs allowed entered separately, the results were unchanged (the coefficients on these two variables were of the same magnitude and of opposite sign, and their sum was not significantly different from zero, justifying the use of the combined variable SREL). (11) The models in Table 1 in effect treat the processes generating SREL and WPCT given SREL as recursive. When SREL iS treated as an endogenous variable in the column 1 specification of Table 1, however, the results are virtually identical to those reported here. In addition, the Murphy-Topel asymptotic standard error correction implies that the basic regression model has a specific, non-scalar error structure. When generalized least squares using this error structure was implemented, the results (the observed determinants of team and individual player performance) were virtually identical to those in Tables 1 and 2. (12) In Table 1, lagged winning percentage becomes significant when SREL iS Omitted (column 2). Thus, the weak effects for [WPCT.sub.t-1] with SREL or BA, SA, etc., included may be due to the correlation of past winning with current offense and defense, rather than with the measure of managerial quality. (13) Inflation figures are taken from U.S.B.L.S. (1991:76). (14) This calculation assumes that expenses for coaches other than the manager remain the same. (15) My estimate of the impact of managerial quality on player performance implicitly assumes that new managers are assigned randomly to teams. It is possible, however, that teams with chronic underachievers are more likely to bring on high-quality managers. The MQUAL coefficients in Table 2 may in fact reflect the impact of managerial quality on underachieving players rather than on players chosen at random. Nonetheless, it is still of interest that high-quality managers can have an effect in such situations. Further, the performance variables used in the player salary regressions themselves may have been affected by the players' managers. Nonetheless, the player salary regressions should still give reasonable estimates of the market value of these performance levels. (16) The actual effect might be even larger than indicated, since full-time players are likely to earn more than the average. (17) The results in Table 3 were not affected by the inclusion of a quadratic term for managerial experience. (18) The inclusion of the past season's winning percentage in the Teams equation reduces the likelihood that this finding is tautological. (19) For teams in the United States, INC iS taken from U.S. Department of Commerce (1987, Table 709, p. 431). For Canada, 1985 per capita income (taken from Statistics Canada 1987, Tables 2.19 and 5.27, pp. 2-22 and 5-39) is available only for provinces; the players for Montreal and Toronto were therefore assigned to their respective provinces. Canadian dollars were converted to American dollars using the exchange rate figures in U.S. Department of Commerce (1987, Table 1417, p. 822). (20) In particular, the F-statistic for inclusion of the winning percentage and save variables was 5.01, with a 1% critical value of about 3.41. In addition, hits, walks, and strikeouts per inning pitched were also entered as explanatory variables. However, F-tests accepted the null hypothesis at conventional levels that these variables did not affect salary (the F-statistic was .934, with a 5% critical value of about 2.65).

REFERENCES

Chass, Murray. 1987. "57 Millionaires, 66 Who Make Minimum $62,500 on Opening-Day Rosters." The Sporting News, April 27, pp. 18-19. Christiano, Kevin. 1988. "Salaries and Race in Professional Baseball: Discrimination 10 Years Later." Sociology of Sport Journal, Vol. 5, No. 2 (June), pp. 136-49. Clement, Robert C., and Robert E. McCormick. 1989. "Coaching Team Production." Economic Inquiry, Vol. 27, No. 2 (April), pp. 287-304. James, Bill. 1984. The Bill James Baseball Abstract, 1984. New York: Ballantine. Milkovich, George, and John Boudreau. 1988. Personnel/Human Resource Management, 5th ed. Plano, Tex.: Business Publications, Inc. Mintzberg, Henry. 1973. The Nature of Managerial Work. New York: Harper & Row. Mundlak, Yair. 1978. "On the Pooling of Time Series and Cross Section Data." Econometrica, Vol. 46, No. 1 (January), pp. 69-85. Murphy, Kevin M., and Robert H. Topel. 1985. "Estimation and Inference in Two-Step Econometric Models." Journal of Business and Economic Statistic, Vol. 3, No. 4 (October), pp. 370-79. Nickell, Stephen. 1981. "Biases in Dynamic Models with Fixed Effects." Econometrika, Vol. 49, No. 6 (November), pp. 1417-26. Pfeffer, Jeffrey, and Alison Davis-Blake. 1986. "Administrative Succession and Organizational Performance: How Administrator Experience Mediates the Succession Effect." Academy of Management Journal Vol. 29, No. 1 (March), pp. 72-83. Porter, Philip K., and Gerald W. Scully. 1982. "Measuring Managerial Efficiency: The Case of Baseball." Southern Economic Journal, Vol. 48, No. 3 (January), pp. 642-50. Reichler, Joseph, ed. 1988. The Baseball Encyclopedia, 7th ed. New York: Macmillan. Scully, Gerald W. 1989. The Business of Major League Baseball. Chicago: University of Chicago Press. Smith, Jonathan, E., Kenneth P. Carson, and Ralph A. Alexander. 1984. "Leadership: It Can Make a Difference." Academy of Management Journal, Vol. 27, No. 4 (December), pp. 765-76. Sports Illustrated, April 20, 1987. Statistics Canada. 1987. Canada Yearbook 1988. Ottawa: Statistics Canada. U.S. Bureau of Labor Statistics. 1991. Monthly Labor Review, Vol. 114, No. 9 (September), p. 76. U.S. Department of Commerce. 1987. Statistical Abstract of the United States, 1988. Washington, D.C.: GPO. Williamson, Oliver. 1986. Economic Organization: Firms, Markets and Policy Control. New York: New York University Press.

LAWRENCE M. KAHN(*) (*) Lawrence M. Kahn is Professor of Economics and Labor and Industrial Relations, University of Illinois at Urbana-Champaign. He thanks Robert Aliber, Stefan Gerlach, Roger Koenker, and Aloysius Siow for helpful comments and suggestions.

A data appendix with additional results, and copies of the computer programs used to generate the results presented in the paper, are available from Lawrence M. Kahn at the Institute of Labor and Industrial Relations, University of Illinois, 504 E. Armory Avenue, Champaign, IL 61820-6297.
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