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Coaching team production.

COACHING TEAM PRODUCTION

The actual function of managers is the subject of much debate.

Using data on more than 3000 male college basketball players,

their coaches, and their skill levels, we find a positive and

significant relation between our ability to replicate an individual

coach's allocation of playing time across players and his winning

percentage. Although this result does not answer the central question

of just what it is that managers contribute, the results do

support the property rights paradigm: managers are the employees

of workers; and more generally, sports data can be used to help

understand related economic processes where quantifiable

measures of inputs and outputs are more costly to obtain.

"What is meant by performance? Input energy, initiative, work

attitude, perspiration, rate of exhaustion? Or output?...sometimes

by inspecting a team member's input activity we can better judge

his output effect...It is not always the case that watching input

activity is the only or best means of detecting, measuring, or

monitoring output effects of each team member, but in some cases

it is a useful way."

I. INTRODUCTION

A major tenet of the Alchian-Demsetz [1972] representation of the firm is that managers are hired by workers to prevent shirking and malfeasance in their own ranks. Absent overseers, individual workers bear only a fraction of the cost of shirking, and hence, everyone undersupplies labor relative to its opportunity cost. In this world, the managerial function is to monitor inputs and meter rewards, thereby reducing the incentive to shirk and raising each worker's marginal productivity. The more dependence there is in the marginal products of laborers, the more important the role of management. This view of supervision is simultaneously intuitively pleasing and difficult to quantify. This paper investigates the role of management in a setting where, indisputably, there is team production: intercollegiate basketball.(1)

Data on 3012 college basketball players across ten years and sixty-five teams are used to replicate one aspect of coaching, the allocation of playing time. Next, we attempt to link coaching decisions to winning. The goal is to determine if coaches who manage well, by our standards, are successful.

Section II motivates the paper. In section III the empirical methodology is detailed; the monitoring function is estimated and related to coaching success. Section IV contains a summary and conclusion.

II. COACHING DECISIONS

The essence of team production is interdependence and the inherent immeasurability of marginal productivity across workers. However, this does not mean that proxies for marginal productivity cannot be developed. Managers monitor worker inputs and deduce marginal products accordingly. Of course, some inputs are more cheaply quantified than others. Attitude is hard to measure, but heart rate is easy. Sweat is observed cheaply, but workers can feign exhaustion.

In the famous Chinese boatpullers fable, the coxswain uses his whip to insure that coolies pull efficiently, to persuade each worker to give the appropriate effort.(2) McManus [1975, 341] relates a story told by Cheung: "...boats are pulled upstream by a team of coolies prodded by an overseer with a whip....an American lady, horrified at the sight of the overseer whipping the men as they strained at their harness, demanded that something be done about the brutality. She was quickly informed... `Those men own the rights to draw boats over this stretch of water and they have hired the overseer and given him his duties.'" Here the monitor uses his vision, intuition, and experience to determine shirking, counseling the loafers with his whip. But employing subjective observation is just one way to monitor. Alternatively, work effort is objectively quantified by skin galvanometers, sphygmomanometers, and the like. Subjective evaluation requires human capital and physical presence while objective measurement necessitates investment in physical capital. Both methods mute the team production problem, and the choice turns on relative marginal products and the cost of machines versus manager's talent. Conceptually, competent subjective evaluation ought to be able to reproduce the outcome of proficient objective quantification, and vice versa.

Consider a team pulling boats under the two different monitoring techniques. The first manager is experienced and competent. He knows when to wield the whip (when the coolies are shirking) and when to shield it. Therefore, he uses subjective, visual evaluation of the workers to assess inputs. By contrast, the other manager is less subjectively adept, making relatively more type I and type II errors with the whip. Instead of relying on intuition, he attaches sphygmomanometers et al. to the workers, counseling with the whip on the basis of meter readings. Naturally, most managers use some combination of subjective and objective monitoring methods, depending on the relative costs.

This is precisely the research design here. Measures of basketball players' work effort come from published statistics on performance. It is not assumed or asserted that managers use these measures, though they might. If Alchian and Demsetz [1972] are correct, it is conceptually possible to mimic the coach's subjective evaluation of inputs, his allocation of playing time, using quantitative measures of player efforts.(3)

The goal is to reproduce managerial decisions regardless of how they are made, and then to determine if there is a link between a team's success and our ability to replicate coaching decisions. If coaches' decisions can be cloned using only objective measures of player skill and if coaches who appear to employ this model win more games, then at least one conclusion follows: coaches who assign playing time based on quantifiable playing skills are more successful. Moreover, a link between our ability to mimic managerial decisionmaking on the basis of quantifiable worker inputs and managerial success (winning) constitutes testimony in support of the view that managers are hired by workers to police malfeasance in their own ranks, the Chinese coolie story.

Consider the theoretical alternative. Suppose (i) managerial decisions could be replicated using only quantifiable measures of worker skills. Specifically, imagine that the way coaches allocate playing time in a basketball game can be successfully modeled using individual player characteristics. But (ii) suppose there was no relation between our ability to reproduce an individual coach's allocation of playing time and his winning record. What would this mean? For one thing, it would imply that the primary managerial function is not to monitor inputs and meter rewards, but some other unidentified job. Thus, a necessary but not sufficient condition for us to be successful is for managers to be integrally involved in the organization of team production, delimiting malfeasance and motivating workers.

Of course, the coaching function in basketball has many dimensions: recruiting, training, scheduling, organizing practice, devising offensive and defensive strategies, and motivating, above and beyond allocating playing time. Nevertheless, a positive relation between (i) the assignment of playing time and quantifiable player inputs and (ii) winning can be interpreted to mean that a necessary condition for coaching success is the ability to pick the right team members. Managers are indifferent between workers who, on the one hand, can supply 100 foot pounds effort, but shirk and supply only 90; and those on the other hand who do not shirk but can supply only 90 foot pounds effort. Empirically, one can observe only the manager's choice, not the shirking. Hence, if a coach's decisions regarding playing time can be replicated then there exists a single proxy for three managerial chores: finding the efficient production frontier, choosing the right team members, and monitoring shirking.(4) The next two sections are devoted to duplicating coaching decisions with regards to assigning playing time.

III. EMPIRICAL METHODOLOGY

The research design is straightforward. First we attempt to reproduce coaches' assignment of playing time. Here the minutes played throughout an entire season by each player on the team are estimated as a function of his individual playing skills. The more competently a coach monitors players' skills, prevents shirking, uses the right combination of players, and trains them, the more likely his team is to win, other things equal. Hence, the next question is whether a coach's winning record is a function of our ability to reproduce his playing time decisions. If the probability that playing time is rewarded based on quantifiable measures of player skills is linked with winning, then successful coaches do at least two things: find the efficient production frontier and employ the requisite inputs.

The data include inputs by 3012 players from sixty-five schools over as many as ten years,(5) with the season average or total for each player of points scored, field goal and free-throw shooting percentage, rebounds garnered, personal fouls committed, steals made, turnovers committed, shots blocked, and assists earned. Also included is the playing time each individual was awarded by the coach--the total minutes played throughout the season. Summary statistics for all players are reported in Table I. The per minute data for some players are distorted by the fact that they played very little. For this reason, summary statistics are also reported for players who played a minimum of 100 minutes. The average player in the sample played 467 minutes and scored 164 points or .3237 points per minute. In the class of players with more than 100 minutes, the average playing time was 605 minutes and points scored was 214 or .3276 per minute.(6)

TABLE I

Summary Statistics
 Standard Minimum Maximum
Variable N Mean Deviation Value Value
 All players
Games Played 2768 22.675 8.888 1.0 37.0
Minutes Played 2982 466.973 368.604 1.0 1354.0
Field Goal Percentage 2963 451.091 130.79 10.0 1000.0
Free Throw Percentage 2905 638.712 188.54 20.0 1000.0
Rebounds 2982 72.798 72.20 10.0 500.0
Assists 2982 34.546 41.939 0.0 367.0
Steals 2982 15.755 16.505 0.0 113.0
Turnovers 2808 33.789 28.502 0.0 145.0
Blocked Shots 2968 7.0371 4.297 0.0 207.0
Fouls 2982 45.249 32.763 0.0 168.0
Points 2979 164.4031 63.301 0.0 1090.0
Rebounds/Minute 2982 0.165 0.098 0.0 1.0
Points/Minute 2979 0.323 0.148 0.0 2.0
Fouls/Minute 2982 0.117 0.065 0.0 1.0
Steals/Minute 2982 0.034 0.038 0.0 1.205
Blocked Shots/Minute 2968 0.014 0.028 0.0 .514
Turnover/Minute 2808 0.081 0.069 0.0 2.0
Assists/Minute 2982 0.069 0.057 0.0 0.600
 Players who played more than 100 minutes
Games Played 2091 26.822 5.014 5.00 37.0
Minutes Played 2257 604.846 317.935 101.00 1354.0
Field Goal Percentage 2266 475.473 73.898 43.00 846.0
Free Throw Percentage 2266 672.503 127.447 0.00 1000.0
Rebounds 2257 93.971 70.926 0.00 500.0
Assists 2257 44.870 43.388 0.00 367.0
Steals 2257 20.354 16.405 0.00 113.0
Turnovers 2127 43.439 26.169 0.00 145.0
Bloacked Shots 2247 9.122 15.861 0.00 207.0
Fouls 2257 58.013 27.218 0.00 168.0
Points 2254 213.619 158.934 4.00 1090.0
Rebounds/Minute 2257 0.155 0.072 0.00 .435
Points/Minute 2254 0.327 0.114 0.0128 .812
Fouls/Minute 2257 0.105 0.037 0.00 .294
Steals/Minute 2257 0.032 0.018 0.00 .228
Blocked Shots/Minute 2247 0.014 0.019 0.00 .187
Turnovers/Minute 2127 0.074 0.026 0.00 .228
Assists/Minute 2257 0.071 0.051 0.00 .538


Several versions of equation (1) were estimated:

Min = alpha I + Epsilon

(1) where Min = minutes played per season,

I = a vector of measurable player skills (inputs),

alpha = a vector of coefficients, and

Epsilon = an error term, by weighted least squares for four categories of players (all, more than 100 minutes playing time, more than 500 minutes, and less than 100 minutes); the results reported in Table II speak for our ability to reproduce coaching decisions about playing time.(7) Specifically, players who shoot better from the field or the free-throw line are assigned more playing time. Players who rebound more, score more, garner more steals, block more shots, commit fewer turnovers, make more assists, and foul less, play more. The R square is 0.52; the monitoring model explains just over half of coaches' decisions with regards to the assignment of playing time. Given the folklore about the complexity of coaching and the intricacies of managing a sports team, the ability of this model to explain coaches' behavior is impressive. All told, these results speak highly for the hypothesis that managers monitor inputs and assign playing time on the basis of quantifiable player skills.

One important coaching duty is to train players. For this reason some players should get to play more than their skill levels dictate, especially if they are young and educable. This suggests that quantifiable inputs are less useful in determining playing time for individuals who play just a bit, ones being trained, and are best for players who play a lot, those already trained. Coaches also reward players with playing time for reasons other than direct output; for example, they are kin, they practice hard, or their parents are rich alumni.(8) In general, coaches are not likely to play these players much in total, and most likely they will play only when the outcome of the game is in little doubt.(9) All told, this means that players who get playing time for all these other reasons do not play much.

Due to this effect, the sample of players was bifurcated. Arbitrarily, they were split into those with more and those with less than 100 minutes playing per season. The coefficient estimates are reported separately in Table II, and they are not the same (the tests of equality are uniformly significant at the 5 percent level); moreover, the overall fit of the less than 100 minutes equation is substantially weaker. The R square is .193, contrasted with .524. The two F-ratios are significantly different at the 1 percent level.

Alternative Specifications

There are two potential problems with the specification of the playing time equation. First the model does not constrain the number of minutes available for assignment, although the allocable minutes in a game are finite. This means that the error terms for the monitoring equations must sum to zero in a particular year.(10) Furthermore, coaches whose teams play more games will, by our specification, appear to reward players more than the average, given each player's skill. To account for this, the playing time equation using the proportion of allocable minutes played as the dependent variable was also estimated. The results are not significantly different from those reported in Table II. Secondly, the apportionment of playing time takes place as part of a complex simultaneous problem as compared to the static characterization. For example, suppose that a coach's decisions are based not just on a player's absolute skill level, but on his relative ability compared to all other players on his team. Econometrically, the error terms for a single coach are not independent across players. They are across many coaches. To address this, the monitoring equations normalizing each player's skills by the average skills of his teammates were also estimated. The normalized results reported in Table III are not substantially different from the absolute results reported in Table II.

The playing time equations were also estimated in log and semi-log form. The sample sizes are smaller because some players have zero inputs, but overall the basic results are the same. The regressions are highly significant, the coefficients have comparable signs, and the explanatory power of the models is approximately the same.(11) In all events, the results reported in Table II are not overly sensitive to model specification.

The next step is to estimate the parameters of equation (1), the assignment of playing time model, for each coach individually, and then to relate them to his winning performance to see if our ability to replicate playing time maps into higher winning percentage.

Winning Percentages of Individual Coaches

The monitoring function was estimated separetly for fifty-five coaches by weighted least square.(12) Summary statistics on these regressions are reported in Table IV. The coaches in the sample, their coaching records, and

TABLE II

Minutes Played per Season

Weighted by Fouls
 All players
 F-ratio = 326.30 Rsquare = 0.5239
 n = 2679
Variable Estimate s.e. t-ratio prob > ~t~
Intercept 358.848 44.695 8.0288 0.0001
Field Goal Percentage 0.67421 0.0639 10.550 0.0001
Free Throw Percentage 0.28550 0.0388 7.3578 0.0001
Rebounds/Minute 303.808 77.726 3.9087 0.0001
Points/Minute 504.948 43.261 11.671 0.0001
Fouls/Minute -3923.5 120.56 -32.54 0.0001
Steals/Minute 480.044 224.85 2.1349 0.0329
Blocked Shots/Minute 1350.27 212.26 6.3612 0.0001
Turnovers/Minute -891.67 180.87 -4.929 0.0001
Assists/Minute 722.945 110.98 6.5138 0.0001
 Players with more than 100 minutes playing time
 F-ratio = 254.57 Rsquare = 0.5199
 n = 2126
Variable Estimate s.e. t-ratio prob > ~t~
Intercept 388.910 52.102 7.4643 0.000
Field Goal Percentage 0.68774 0.0751 9.1524 0.0001
Free Throw Percentage 0.27105 0.0444 6.0984 0.000
Rebounds/Minute 368.665 87.000 4.2375 0.000
Points/Minute 483.917 47.988 10.083 0.000
Fouls/Minute -4268.7 147.77 -28.88 0.000
Steals/Minute 833.557 287.21 2.9022 0.003
Blocked Shots/Minute 1327.12 236.42 5.6134 0.000
Turnovers/Minute -770.52 217.95 -3.535 0.000
Assists/Minute 616.968 125.75 4.9063 0.000
 Players with more than 500 minutes playing time
 F-ratio = 113.82 Rsquare = 0.4546
 n = 1239
Variable Estimate s.e. t-ratio prob > ~t~
Intercept 656.789 55.798 11.77 0.0001
Field Goal Percentage 0.52026 0.0780 6.669 0.0001
Free Throw Percentage 0.09595 0.0471 2.035 0.042
Rebounds/Minute 253.664 81.829 3.099 0.002
Points/Minute 358.484 44.316 8.089 0.000
Fouls/Minute -3632.9 178.65 -20.3 0.000
Steals/Minute 1234.37 281.26 4.388 0.000
Blocked Shots/Minute 601.907 215.61 2.791 0.005
Turnovers/Minute -455.38 226.39 -2.01 0.044
Assists/Minute 386.289 115.72 3.337 0.000
 Players with less than 100 minutes playing time
 F-ratio = 14.31 R square = 0.1926
 n = 578
Variable Estimate s.e. t-ratio prob > ~t~
Intercept 67.4877 4.4060 15.317 0.0001
Field Goal Percentage 0.03797 0.0066 5.6920 0.0001
Free Throw Percentage 0.00794 0.0041 1.8939 0.0588
Rebounds/Minute -0.4350 9.7861 -0.044 0.9646
Points/Minute -34.098 7.9303 -4.299 0.0001
Fouls/Minute -84.952 11.747 -7.231 0.0001
Steals/Minute 8.58841 16.178 0.5308 0.5957
Blocked Shots/Minute 41.9937 26.910 1.5605 0.1192
Turnovers/Minute -56.438 15.328 -3.681 0.0003
Assists/Minute 6.42270 18.011 0.3566 0.7215


TABLE III

Playing Time Equation with Player Inputs Normalized for Relative Skill

Weighted by Fouls
 All players
 F-Ratio = 319.76 Rsquare = 0.5188
 n = 2679
Variable Estimate s.e t-ratio prob > ~t~
Intercept 283.908 39.583 7.172 0.0001
Normalized Field Goal Percentage 273.332 25.070 10.90 0.0001
Normalized Free Throw Percentage 171.411 21.403 8.008 0.0001
Normalized Rebounds/Minute 84.9239 11.209 7.575 0.0001
Normalized Points/Minute 167.639 12.274 13.65 0.0001
Normalized Fouls/Minute -368.08 12.503 -29.4 0.0001
Normalized Steals/Minute 16.4769 6.2581 2.632 0.0085
Normalized Blocks/Minute 6.36101 1.6091 3.953 0.0001
Normalized Turnovers/Minute -93.152 12.547 -7.42 0.0001
Normalized Assists/Minute 65.5410 6.8753 9.532 0.0001


Each player's skills are normalized by the average player skills on his team.

TABLE IV

Summary Statistics

Individual Coaches' Assignment of Playing Time Equations
 Standard
 Mean Deviation Minimum Maximum
F-ratio 10.654 18.097 0.4800 137.42
Level of significance 0.038 0.120 0.0001 0.82
Degrees of freedom 38.527 29.604 1. 123
Rsquare 0.672 0.144 0.35585 0.99


the individual regression parameters are reported in Table V.(13) In order to relate a coach's performance record to his coaching ability it is imperative to control for his stock of talent. Each coach's average stock of inputs was calculated and normalized relative to the overall average stock of inputs. For example, we calculated the average points per minute that a particular coach's players scored, weighting each player's points by the number of minutes he played, and then divided this number by the overall weighted-average points scored per minute from the entire pool of players. Similarly, talent ratios were calculated for all seven player skills that are valuable,(14) and then the average of these ratios for each player. The resulting variable, Talent1, measures a player's overall talent relative to his peers. Similarly, a player's bad work characteristics were calculated, measured by his personal fouls committed relative to his peers and the relative number of turnovers he caused. The average of these two last player characteristics is called Talent2, and it measures a player's undesirable work habits. Then each coach's winning percentage was regressed on his relative stock of inputs, Talent1 and Talent2, and measures of his coaching ability, as measured by the playing time model. Several proxies are used for the last; Rsquare, weighted

TABLE V

Coaching Records and Individual Coaching Equations
 Degrees of Winn
ing
Coach (Rsquare)*(F-ratio) Rsquare F-ratio Freedom Perc
ent
Digger Phelps 137.20 0.9984 137.4 2 .695
5
Eldon Miller 15.916 0.6753 23.57 102 .601
5
Stan Morrison 13.449 0.8216 16.37 32 .569
0
Gary Colson 12.999 0.9916 13.11 1 .500
0
Hugh Durham 12.241 0.9825 12.46 2 .705
9
Guy Lewis 11.611 0.5915 19.63 122 .691
3
Terry Holland 10.281 0.5693 18.06 123 .690
9
J.D. Barnett 10.185 0.6370 15.99 82 .719
1
Nebraska(1) 9.8935 0.6712 14.74 65 .609
8
Billy Tubbs 9.8863 0.7599 13.01 37 .701
2
Bobby Knight 9.6505 0.6619 14.58 67 .689
5
Rollie Massimino 9.3325 0.6832 13.66 57 .693
7
John Thompson 9.2408 0.6312 14.64 77 .798
5
Bob Weltlich 8.0429 0.8502 9.46 15 .566
7
M.K. Turk 7.6517 0.6501 11.77 57 .518
5
Dave Bliss 7.3346 0.6584 11.14 52 .533
3
John McLeod 7.1424 0.8796 8.12 10 .620
7
Lou Henson 6.8443 0.5569 12.29 88 .636
1
Dwayne Morrison 6.6774 0.7081 9.43 35 .430
6
Steve Yoder 6.5736 0.7761 8.47 22 .392
9
Don Devoe 6.0968 0.5714 10.67 72 .643
6
Mike Krzyewski 5.6922 0.6642 8.57 39 .560
4
Bill Cofield 5.4713 0.6120 8.94 51 .379
6
Lee Hunt 5.3674 0.7147 7.51 27 .436
8
Tom O'Neill 5.3402 0.7197 7.42 26 .220
9
Jerry Tarkanian 5.2694 0.7984 6.60 15 .850
7
VMI(1) 5.1845 0.7151 7.25 26 .309
5
John Orr 5.0790 0.6325 8.03 42 .475
9
Jim Harrick 4.9610 0.5920 8.38 52 .638
6
Sonny Allen 4.5813 0.6319 7.25 38 .409
1
Frank McGuire 4.9538 0.9538 4.58 2 .592
6
Jim Haller 4.1518 0.5399 7.69 59 .412
1
Gene Bartow 3.9600 0.5706 6.94 47 .677
0
Len Stevens 3.9548 0.7785 5.08 13 .410
7
Jim Killingsworth 3.7080 0.6669 5.56 25 .555
6
Marshal(1) 3.6846 0.5379 6.85 53 .612
7
Jim Boeheim 3.6164 0.7550 4.79 14 .702
1
U. of Pittsburgh(1) 3.4436 0.9183 3.75 3 .464
3
Gerry Gimelstob 3.4178 0.6341 5.39 28 .513
3
Gary Williams 3.3981 0.7154 4.75 17 .714
3
Bill Foster 3.0605 0.4858 6.30 60 .560
7
Tom Davis 2.9141 0.7005 4.16 16 .725
8
MTSU(1) 2.8405 0.4940 5.75 53 .528
2
Rich Falk 2.7720 0.5923 4.68 29 .407
0
Joe Williams 2.6239 0.7169 3.66 13 .557
4
Cliff Ellis 2.0959 0.5175 4.05 34 .603
3
Bruce Parkhill 2.0770 0.6552 3.17 15 .240
7
Dick Harter 2.0093 0.4239 4.74 58 .562
6
Bill Foster-USC(2) 1.9607 0.4051 4.84 64 .590
9
Rick Majerus 1.9138 0.6934 2.76 11 .606
6
Baptist College(1) 1.2844 0.6116 2.10 12 .472
7
Gene Keady 1.0212 0.5461 1.87 14 .715
9
George Raveling 0.9364 0.4237 2.21 27 .563
2
John Batch 0.5772 0.3585 1.61 26 .371
8
Lefty Driesell 0.3890 0.8104 0.48 1 .641
7


(1)Data sources did not identify the coaches at these schools for the relevant period. It was assumed that the coach was unchanged over the period of the data. (2)This Bill Foster coached at the University of South Carolina during the period of these data. Rsquare (Rsquare times F-ratio), the degrees of freedom, and the F-ratio, all from his individual playing time equation.(15) Each of these regression statistics is a measure of our ability to reproduce an individual coach's playing time decisions. It is our assessment of a coach's ability to put the right players on the court.

The regression results are reported in Table VI. Using any metric, there ia a positive relation between our measure of coaching performance and winning percentage. The elasticity of winning with respect to quantifiable playing time assignment using weighted Rsquare (the first specification in Table VI) is 0.0196 at the mean; 10 percent increase in the use of quantifiable player input to allocate playing time is associated with a 0.196 percent increase in winning percentage.

The evidence presented here can also be interpreted to mean that team selection is a viable task in almost any team production setting. Arguably, collegiate basketball is the ultimate team production process, and yet over half of coaches' decisions with respect to awarding playing time are described by a single equation, using only the publicly generated data on

TABLE VI

Coach's Winning Performance as a Function of Playing Time Assignment
Independent Variable Coefficient/t-ratio
Intercept 0.1383 0.1363 -0.0018 0.1363
 (0.64) (0.63) (0.01) (0.63)
F-ratio x Rsquare 0.0014 0.0014
 (1.95) (2.02)
Rsquare 0.1759
 (1.61)
F-ratio 0.0014
 (2.02)
Talent1 0.8679 0.8416 0.8225 0.8416
 (6.56) (6.24) (5.99) (6.24)
Talent2 -0.5503 -0.5374 -0.4964 -0.5374
 (2.91) (2.84) (2.55) (2.84)
Degrees of freedom in 0.0004 0.0009 0.0003
playing time equation (0.79) (1.57) (0.76)
Rsquare 0.527 0.536 0.522 0.536
F-ratio 18.91 14.42 13.67 14.42
Number of observations 55 55 55 55


player inputs. If we were privy to other quantifiable input data which coaches surely are (such as number and extent of injuries, arrival time at practice, and the like), we expect that our ability to predict playing time would only improve. For example, we do not know player position (guard, forward, or center), or height, age, or weight. This reduces the ability to predict playing time, but there is no reason to expect that our existing predictions are biased by the omissions.

As noted earlier, for each individual coach, the error terms are not independent; the coach must resolve an optimization problem subject to the constraint that only five players participate at any one time. Moreover

different positions on the floor require different skills (guards versus center). Earlier inquiries suggest that this is not a serious problem; nevertheless, Table VII lists the highest twenty residuals and the lowest twenty in the sample of players who played more than 100 minutes. Our suspicion is that injured players dominate in the negative residuals category, and friends, family, and rich kids are the bulk of the positive errors. For example, Vince Hamilton of Clemson was injured for a large portion of the 1982 season, and as a consequence, his per minute statistics predict he should have played more than he did. The authors will supply the errors for all observations on request. There is no obvious pattern in the tails of the erros, that is, all guards, implying that the ommited variables problems are not serious.

In addition, the average stock of talent available to each coach was calculated, using the average of a player's good and bad work skills, Talent1 and Talent2. These are proxies for the coach's overall ability to evaluate talent, recruit players, and train them, as distinct from his on-the-court assignment of playing time. Based on the average of good player skills, Talent1, in order, Guy Lewis, Jerry Tarkanian, Billy Tubbs, John Thompson, Jim Boeheim, Jim Harrick, Joe Williams, Sonny Allen, Gene Bartow, and Cliff Ellis are ranked at the top. In reverse order, Dwayne Morrison, Bob Weltlich, Tom O'Neill, Lee Hunt, Rich Falk, and Jim Haller rank at the bottom. That is, they had the worst players to work with, the players who scored the least shot the worst, and so forth. Using undesirable player skills, Talent2, Tom O'Neill, Dick Harter, Gary Colson, Bill Cofield, and John Bach had the worst players, those that made many turnovers and fouled a lot. Using this latter metric, Gene Keady, Jim Killingsworth, Billy Tubbs, and Lefty Driesell had the best players.(16)

The coach's average pool of talent, Talent1, was regressed on the metric of his ability to assign playing time efficiently (the weighted R square from the playing time equation). There is no relation. At least in this sample, good on-court coaching is not linked with quality recruiting, and vice versa. This implies that good coaching encompasses two completely different talents. This suggests that using only a coach's winning record to assay his on-court management ability may be inappropriate. From a managerial perspective, it is consistent with the casual observation that personnel and other management decisions are frequently separated.

IV. CONCLUSIONS

The actual function of managers is difficult to measure. What has been accomplished here is the quantification of one dimension of managing team production: the choice of workers. Managerial choice is quantified by attempting to replicate coaching decisions on the assignment of playing time

TABLE VII

Highest and Lowest Residuals from the Minutes

Played Equation
 Minutes Predicted
Player School Year Played Minutes Residual
t-ratio
 Negative Residuals
John Briggs SMU 83 150 956.24 -806.24
-3.45
Gary Carter Tennessee 81 228 998.59 -770.59
-3.306(*)
Mark Newlen U. VA. 75 131 867.97 -736.97
-3.167
Paul Crowley S. Miss. 84 133 841.55 -708.55
-3.051
D. Shaffer Clemson 83 165 861.00 -696.00
-2.992
Boyzi Perry Baptist 82 305 994.37 -689.37
-2.957
Simcik UAB 82 219 895.74 -676.74
-2.970
Ed Littleton Tennessee 81 112 775.92 -663.92
-2.848(*)
K. Lambiotte U. VA. 82 122 765.94 -643.94
-2.761
R. Whitman Indiana 79 145 786.54 -641.54
-2.753
Petrovic Northwestern 84 137 775.73 -638.73
-2.741
G. Stepheson MTSU 84 126 763.34 -637.34
-2.730
V. Hamilton Clemson 82 114 748.39 -634.39
-2.719(**)
(unknown) S. ALA. 83 229 849.77 -620.77
-2.666
Arnold FSU 84 170 790.63 -620.63
-2.666
G Jefferson U. VA. 78 190 809.77 -619.77
-2.660
G. Montgomery Illinois 84 462 1071.76 -609.76
-2.615
Kevin Woods Tennessee 81 180 777.47 -597.47
-2.563
K. Cadle Penn St. 75 104 699.04 -595.04
-2.563
G. Shropshire VCU 82 140 731.92 -591.92
-2.540


in basketball games using the actual performances by the players. Our ability to reproduce management decisions varies considerably across coaches; and more importantly, the coaches for whom we best replicate decisions have the highest winning percentages, other things the same. Several implications follow from this result. First, coaches who base their playing time decisions on player perfomance are more likely to win. This means that coaches who observe player performance best, most quickly assimilate that information and make the appropriate substitutions, are most likely to win. This suggests
 Positive Residuals
K. Hammonds MTSU 84 1076 624.10 451.90
1.937
L. Heard Georgia 82 1117 662.43 454.57
1.952
B. Bender Duke 79 1089 632.88 456.12
1.955
D. McClain Villanova 84 1191 731.04 459.96
1.970
D. Brown Houston 79 503 41.27 461.73
1.982
G. McClain Villanova 84 1210 747.04 462.96
1.984
K. Mitchell Wisconsin 78 204 -263.00 467.00
2.012
V. Garlick Penn St. 82 119 -349.86 468.86
2.025
E. Smith Georgetown 81 1166 696.38 469.62
2.012
B. Douglas Illinois 84 1174 687.58 486.42
2.086
Huffman VMI 84 1109 621.74 487.26
2.089
D. Meagher Duke 83 942 446.27 495.73
2.122
F. Brown Georgetown 81 955 458.69 496.31
2.130
T. Amaker Duke 83 1235 737.25 497.75
2.134
Laurence Held Pacific 82 932 431.81 500.19
2.144
R. Whitman Indiana 78 1258 752.47 505.53
2.167
Cucinella TCU 82 1002 491.92 510.08
2.189
V. Taylor Duke 79 1119 606.99 512.01
2.193
J. Bryan Duke 81 146 -369.95 515.95
2.231
Mann Ga. Tech 79 999 462.49 536.51
2.302


(*)Declared academically ineligible in midseason. (**)Injured during the season. Other players may have been injured or quit; data sources are incomplete in this regard. that some coaches are better monitors than others, perhaps not a surprising result; but it also implies that recruiting, pre-game planning, cajoling of referees, scheduling, and the rest are not the only management chores. Coaches must also monitor players and meter rewards.

Clearly, the role of managers in the firm is complicated. They must organize production, write a multitude of complex contracts, and make product line, financial and investment decisions. What has been demonstrated here is that there is a great deal of evidence that the first of these functions is an important and time-consuming activity of managers, and the tradition in the property rights literature is not denied; managers are the employees of workers.

REFERENCES Alchian, Armen, and Harold Demsetz. "Production, Information Costs, and Economic

Organization." American Economic Review, December 1972, 777-95. Cheung, Steven. "The Contractual Nature of the Firm." The Journal of Law and Economics, April

1983, 1-21. Daly, George and William J. Moore. "Externalities, Property Rights, and the Allocation of

Resources in Major League Baseball." Economic Inquiry, January 1981, 77-95. El-Hodiri, M. and James Quirk. "An Economic Model of a Professional Sports League." Journal

of Political Economy, November/December 1971, 1302-19. Fleisher, Arthur, A. III, Brian F. Goff, William F. Shughart II, and Robert D. Tollison. "Crime

or Punishment?: Enforcement of the NCAA Football Cartel." Journal of Economic Behavior

and Organization, forthcoming 1988. Goff, Brian L., William F. Shughart II, and Robert D. Tollison. "Homo Basketballus." Unpublished

manuscript, George Mason University, 1986. Higgins, Richard, and Robert D. Tollison. "Economics at the Track." Unpublished manuscript,

George Mason University, 1986. Holahan, William L. "The Long-Run Effects of Abolishing the Baseball Player Reserve System."

Journal of Legal Studies, January 1978, 129-37. Hunt, Joseph W. and Kenneth A. Lewis. "Dominance, Recontracting, and the Reserve Clause:

Major League Baseball." American Economic Review, December 1976, 936-43. Lehn, Kenneth. "Property Rights, Risk Sharing, and Player Disability in Major League Baseball."

Journal of Law and Economics, October 1982, 343-65. McCormick, Robert E., and Robert D. Tollison. "Crime on the Court." Journal of Political

Economy, April 1984, 223-35. McCormick, Robert E., and Robert D. Tollison. "Crime and Income Distribution in a Basketball

Economy." International Review of Law and Economics, June 1986, 115-24. McManus, John. "The Costs of Alternative Economic Organizations." Canadian Journal of

Economics, August 1975, 334-50. Nardinelli, Clark. "Corporal Punishment and Children's Wages in Nineteenth Century Britain."

Explorations in Economic History, 19, July 1982, 283-95. Porter, Philip K., and Gerald W. Scully. "Measuring Managerial and Allocative Efficiency: The

Case of Baseball." Southern Economic Journal, January 1982, 642-50. Scully, Gerald W. "Pay and Performance in Major League Baseball." American Economic Review,

December 1974, 915-30. Zak, Thomas A., Cliff J. Huang, and John J. Siegfried. "Production Efficiency: The Case of

Professional Basketball." Journal of Business, July 1979, 379-92.

(*)Department of Economics and Center for Policy Studies, Clemson University. We are grateful to the Clemson University Athletic Department, especially Bob Bradley, for help on this project. We also thank Armen Alchian, Tom Borcherding, Harold Demsetz, Matt Lindsay, MikeMaloney, and two referees for their comments. The standard caveat applies.

(1)There is a small literature on the application of economics to sports and vice versa. For example, see El-Hodiri and Quirk [1971], Scully [1974], Hunt and Lewis [1976], Holahan [1978], Zak, Huang, and Siegreid [1979], Daly and Moore [1981], Lehn [1982], Porter a Scully [1982], McCormick and Tollison [1984; 1986], Higgins and Tollison [1986], Fleisher et al. [1988], and Goff, Shughart, and Tollison [1986].

(2)Cheung [1983, 8] repeats his story, and Nardinelli [1982] discusses a similar phenomenon in British textile mills.

(3)This is a sufficient but not necessary condition. Our inability to reproduce coaching decisions does not mean that someone else, perhaps luckier or more qualified, could not.

(4)This follows regardless of the methodology used to replicate coaching decisions. Some player skills are inherently unquantifiable to outside observers; they are only seen through the eyes of the individual coach. These include defensive alignment, movement away from the ball, rebounding position in a team rebouding sense, hustle, and the like. If these skills are collinear with quantifiable characteristics such as rebounding and scoring, we will have no problem reproducing coaching decisions; otherwise we will have trouble. The evidence is presented in section IV.

(5)The data were obtained from the individual schools. Requests were mail ed to all NCAA Division I schools that participate in basketball, asking for ten years' data, generating some seventy-five replies. Of these, ten did not report the required data, and many supplied, less than ten years' data. The remaining sample includes sixty-five schools, varying in number of years.

(6)Per minute statistics are employed as the measures of inputs because each of the characteristics is a positive function of minutes played. The more a player plays, the better chance he has to score, rebound, and foul. Hence, rebounds per minute and so forth are the appropriate assessment of a player's physical abilities.

(7)Given the nature of the data, we anticipated the problem of heteroskedasticity, linked with points scored or fouls committed. Consequently, the log of the squared OLS from equation (1) were regressed on the log of points, fouls, and several other variables that could have been linked to the variance of the error term. Only fouls in significantly associated with the estimated variance of the error term. Consequently, weighted least squares is appropriate. For brevity's sake the OLS estimates are not reported. We will supply them on request. The only significant difference is that the coefficient on rebounds per minute has a negative coefficient.

(8)We note that other managers have similar descretion, commonly referred to as a agency costs.

(9)Two sons of coaches, Danny Tarkanian and Chuck Driesell, had positive residuals in playing time more than two standard errors above the predictions of our equation.

(10)This problem is partially muted by the use of many years' data for some coaches.

(11)It can be argued that including points scored in the minutes equation along with shooting percentages amounts to over-identifying the equation. This problem is handled in several ways. First, by argument, points scored is distinct from shooting percentage and is not logically a linear transformation of shooting percentage and/or minutes played. Players with the ability to get open, players with a lot of confidence, players who command the respect of their teammates get the ball more, and hence they have the capacity to shoot more. Second, points per minute are deleted from the regressions, and the basic results are unaltered ( the R raised to 2 declines to .4998). Third, the positive and significant coefficient on points per minute stands as testimony to its usefulness.

(12)Of course, winning is but a means to an end for players and coaches; salary is the real goal. Moreover, the data come from a nonproprietary setting. Hence, the classic problems of the labor-managed firm stand to be present. That is, university officials may not have the right incentives to insure that coaches have the right encouragement. It turns out that neither of these appears to be a serious problem. Although complete salary data are not generally available for college (or professional) basketball coaches. USA Today (Dec. 9, 1986, pp. 10-12C) reports survey data for some public school coaches. They list base salary and perquisites for twenty-one of our fifty-five coaches. We regressed first base salary and then full salary on average winning percentage across the twenty-one coaches in levels, logs, and using weighted least squares. In all cases the relation was positive and significant at the 1 percent level. On average, the winning elasticity of salary was about 1.0. We will supply the salary data or the estimates on request. To us, this means that even if winning is not the only measure of output on the basketball court, it certainly is an appropriate proxy.

(13)The coaches are ranked in the table on the basis of weighted R raised to 2 (weighted by F-ratio). As such the table reflects our ranking of these coaches' ability to ascertain player skill and meter playing time accordingly.

(14)These are field-goal shooting percentage, free-throw shooting percentage, and rebounds, assists, steals, blocked shots, and points scored (all per minute).

(15)We included degrees of freedom to control for variations in sample size across coaches. It also proxies the probability for type II error.

(16)Note that there is a positive statistical relation between Talent1 and Talent2 in the data set. The R raised to 2 is very low, 0.0144, but the F-ratio is 39.39, significant at the 1 percent level with 2707 observations. That is, players that foul the most per minute and make the most turnovers per minute are also the ones that score the most, rebound the most, make the most assists and steals, and shoot the best.
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Author:CLement, Robert C.; McCormick, Robert E.
Publication:Economic Inquiry
Date:Apr 1, 1989
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