What Makes a Good Coach? A Case for NBA Teams Playing up to

What Makes a Good Coach? A

Case for NBA Teams Playing up

to Their Potentials

JOSHUA BROWN, DR. GEORGE DAVIS, DR. GERALD GRANDERSON

Miami University

Bro[email protected]

March 9, 2020

Abstract

In this paper, we argue that using data from the playoffs when studying team performance

is theoretically superior to using data from the regular season. We develop a measure

of NBA playoff performance called the Playoffs Success Indicator (PSI) and apply it to

a stochastic frontier production function in order to study (1) performance in the NBA

playoffs, (2) how efﬁciently playoff teams perform given their current players, and (3) the

characteristics of coaches that affect that efﬁciency. We ﬁnd that, to be successful in the

playoffs, the average team should strive to be more well-rounded rather than looking for

one superstar. We also ﬁnd that playoff efﬁciency is positively associated with the number

of years a coach has been in the league and the number of wins he or she has accrued in

the playoffs. Finally, we ﬁnd that all playoff experience is not equal, and that a coach’s

past playoff losses are actually negatively associated with playoff efﬁciency.

I. INTRODUCTION

anagers and bosses are often paid

large amounts of money to en-

sure that their businesses run

smoothly. But are their efforts effective?

In most cases, data on individual bosses

and their workers’ productivity levels are

either not publicly available or simply not

collected, making it difﬁcult to empirically

test a boss’s value. However, with the large

amount of data collected and made public,

professional sports offers a unique opportu-

nity to examine how valuable coaches are

to their teams.

In the NBA in particular, it is an open

question whether a coach is doing a good

job or not. Some teams with several tal-

ented players may do well despite the

coach’s poor performance, while other

teams without much talent may have valu-

able coaches who help them win much more

than expected. In this paper, we study

ﬁrst how well NBA playoff teams play up

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

to their potential (that is, their efﬁciency)

given their levels of talent, and second, the

characteristics of coaches (like how long

they have been in the league and their play-

off experience) that affect that efﬁciency.

II. REVIEW OF THE

LITERATURE OF SPORTING

PRODUCTION FUNCTIONS

There have been a few papers that have esti-

mated production functions in professional

sports. Focusing on Major League Baseball,

the ﬁrst to estimate a sporting production

function was Rottenberg (1956). Interest-

ingly, he deﬁned the output of production

in terms of a single game’s revenue, where

the inputs to production were factors includ-

ing the teams involved in the game and the

teams’ staffs (managers, coaches, etc.).

Following Rottenberg, Scully (1974) also

examined a production function in Major

League Baseball. Scully took the more nat-

ural approach of deﬁning output in terms of

team performance and relating it to the sta-

tistical performance of the team’s players.

As a result, most papers have followed the

work of Scully and have deﬁned production

in terms of performance.

Studies of production functions have fo-

cused on more than just professional base-

ball. Carmichael et. al. (2001) and Daw-

son et. al. (2000) examined production

function efﬁciency in soccer, Atkinson et.

al. estimate a production function for wins

in the National Football League, and Zak

et. al. (1979) and Hoﬂer & Payne (2006)

formulated a production function for team

performance in the National Basketball As-

sociation and measured team efﬁciency as

well as its determinants.

Most similar to our current paper is

Hoﬂer & Payne (2006). Hoﬂer and Payne

deﬁne a production function for the nat-

ural log of team wins and use data from

the 1990–91 to 2001–02 regular seasons

to estimate the efﬁciencies of NBA teams

and the coach’s effect on those efﬁciencies.

They assume production of log wins to be a

function of the ratios of match-up-speciﬁc

statistics of a particular team relative to

its opponents. For example, the ratio of

shooting percentage is calculated by divid-

ing one team’s shooting percentage by the

shooting percentage of its opponents. Other

than shooting percentages, the other ratios

they consider are free throw percentage, re-

bounds, assists, steals, blocked shots, and

turnovers. They use coach winning percent-

age, tenure with current team, and tenure in

the league as variables associated with team

efﬁciency. Hoﬂer & Payne ﬁnd that higher

shooting percentage, rebounds, steals, and

blocked shots relative to opponents are as-

sociated with an increase in the number of

potential wins and that turnovers are asso-

ciated with a decrease. They also ﬁnd that

coach winning percentage, tenure with cur-

rent team, and tenure in the league tend to

raise a team’s win efﬁciency.

III. THE STOCHASTIC

FRONTIER PRODUCTION

FUNCTION

A production function is deﬁned as an equa-

tion that expresses the relationship between

inputs and output. In theory, production

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

functions operate under the assumption that

none of the inputs is used wastefully, and

therefore that output is maximized given in-

put. However, full production efﬁciency is

unlikely in the real world, and since most

estimation procedures for production func-

tions have the interpretation of average out-

put for a given level of inputs, using those

estimates as a benchmark for potential out-

put is not likely to yield accurate results.

Developed in 1977 by Aigner et. al. and

modiﬁed for panel data by Batesse & Coelli

(1995), Stochastic Frontier Analysis allows

for the estimation of maximum output (a

Stochastic Production Frontier, or just a

frontier) by employing a composite error

term. In our context, output (

) refers to a

measure of team

’s performance in season

, potential output (

∗

) refers to a measure

of team

’s best possible performance in

season

, and input (

) refers to a vector

of team-speciﬁc qualities that inﬂuence a

team’s performance. Efﬁciency refers to

how close to potential output a team per-

forms and is deﬁned as observed output di-

vided by potential output



∗



The error term has two components:

and

. The

are assumed to be inde-

pendently and identically distributed with

normal distributions and mean zero (

∼

N(0, σ

)

). They capture the idea that fron-

tier output is not ﬁxed but rather is sub-

ject to random positive or negative shocks

that affect potential output. The

are

non-negative and assumed to be indepen-

dently and identically distributed and to

follow a normal distribution truncated be-

low zero (denoted here as

∼ N(0, σ

)

Since the

are non-negative, they capture

how far below the frontier observed output

lies. Using the distribution assumptions, the

model is estimated by maximum likelihood.

The Stochastic Frontier Production model

is given by the following:

ln (Y

) = f (X

) + v

− u

(1)

ln (Y

∗

) = f (X

) + v

(2)

i = 1,. . . , N

t = 1, . . . , T .

Graphically, this model can be repre-

sented in two variables as shown below.

The red curve represents maximum attain-

able output (

∗

) for all levels of input (

)

and each black dot represents the observed

output (

) for a speciﬁc team

in season

The vertical distance between each dot and

the curve represents how far from potential

output team

performed in season

, which

is given by u

Notice that the dependent variable is

logged. This is done to facilitate calculat-

ing the (technical) efﬁciency (TE) for each

team:

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

ln (Y

) = ln(Y

∗

) − u

ln (Y

) − ln (Y

∗

) = −u



∗



= −u

∗

= e

−u

T E

= e

−u

. (3)

In addition to estimating how efﬁciently

a team operates, we are also interested in

how characteristics of a coach are related

to a team’s efﬁciency. There are two main

approaches that have been used in the lit-

erature to estimate the characteristics that

affect production efﬁciency.

One common approach that has been

used in the literature to estimate the deter-

minants of efﬁciency is a two-step proce-

dure. Once the ﬁrm-speciﬁc efﬁciencies

have been estimated (as in equation 3), this

method takes the estimated efﬁciencies and

uses them as the dependent variable in a

second-stage regression (see Pitt and Lee,

1981). However, the ﬁrst-stage regression

is likely to suffer from the omitted variable

bias (Wang & Schmidt, 2002). Additionally,

as Wang & Schmidt (2002) also discuss, the

small variance in the estimated efﬁciencies

is likely to lead to a downward bias in the

coefﬁcients in the second stage.

A second common approach only re-

quires one step. The one-step procedure

jointly estimates the parameters of the pro-

duction frontier and the parameters of the

determinants of efﬁciency by treating the

non-negative component of the error term

as a function of a vector of variables hy-

pothesized to affect efﬁciency, denoted

Speciﬁcally, the mean of the non-negative

error term

was previously assumed to be

zero. This assumption is relaxed when in-

cluding determinants of efﬁciency in the

model, and the mean of

is replaced

with the vector of variables that affect ef-

ﬁciency,

. All parameters are then esti-

mated via maximum likelihood (Batesse &

Coelli, 1995).

It is important to notice that this implies

that the

are now assumed to be associ-

ated with inefﬁciency, not efﬁciency, since

is non-negative and is subtracted from

the model. That is, a positive coefﬁcient

on any of the variables

means that the

speciﬁc variable has a negative association

with efﬁciency (since it has a positive as-

sociation with inefﬁciency). The model is

now given by

ln (Y

) = f (X

) + v

− u

(4)

= g(Z

) + w

(5)

ln (Y

∗

) = f (X

) + v

(6)

i = 1,. . . , N

t = 1, . . . , T .

Notice that the only difference is that

now assumed to be a function of the vector

of variables Z

IV. PLAYOFFS SUCCESS

INDICATOR

The NBA playoffs is a tournament that con-

sists of 16 teams, 8 in the eastern confer-

ence and 8 in the western conference. Each

team has a ranking (or seed number) from

1 (best) to 8 (worst), which is determined

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

by its performance in the regular season.

Teams compete in best-of-seven series to

decide who moves on to the next round,

and the team in each conference that wins

3 series is that conference’s champion. Fi-

nally, the conference champions compete

in a

and ﬁnal series to determine the

league champion. It is important to note

that the tournament is designed with the

intention that teams with higher seed num-

bers have easier paths to the championship.

The graphic below summarizes the NBA

playoffs for each conference.

In order to study how closely to their po-

tential NBA playoff teams perform given

their levels of talent, we must ﬁrst choose

a measure of performance (

). However,

because teams do not all play the same num-

bers of games, the standard measures of per-

formance in sports fail to accurately capture

success when applied to the playoffs.

To see why the standard measures fail

to capture success in the playoffs, consider

measuring success by a team’s winning per-

centage



wins

total games



. Now suppose team

1 wins its ﬁrst playoff series in 4 games

and loses its second series in 7 games.

That means team 1’s winning percentage is

= 64%

. Now suppose that team 2 wins

the championship but does so by winning

all four series in 7 games. That means that

team 2 won 16 games and lost 12 games

for a total winning percentage of

= 57%

This is summarized in the two preceding

graphics. Clearly team 2 had more success

than team 1, but winning percentage alone

is unable to capture that. Therefore, we de-

veloped our own measure of success, called

the Playoffs Success Indicator (PSI).

A team’s success in the playoffs depends

on two main factors: the number of series

a team wins and its total win percentage

in the playoffs. To develop a measure of

playoff success, we ﬁrst ranked every possi-

ble playoff win-loss record (101 of them in

total) from best to worst by the following

method:

1. Any team that wins the championship

(gets to the 5th series) had more suc-

cess than any team who did not

Any team that made it to the ﬁnals

(gets to the 4th series) had more suc-

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

cess that any team who did not

Any team that made it to the 3rd series

had more success than any team who

did not

Any team that made it to the 2nd series

had more success than any team who

did not

Teams that made it to the same series

were compared by total winning per-

centage, since they each played com-

parable numbers of games

Once the records were ranked, we went in

search of a measure that would keep the

ranking the same. This measure does just

that:

PSI = playoff win% × highest series

(7)

φ ≥ 2.

We chose to use

φ = 2,3,and, 4

(PSI2, PSI3,

PSI4, respectively) as our measures of suc-

cess in the playoffs. However, due to es-

timation issues, we were forced to drop

PSI2 and keep only PSI3 and PSI4. No-

tably, our PSI has the theoretically attrac-

tive quality of being a convex function with

respect to highest series, meaning that each

subsequent series win is given more weight

than the last.

V. MEASURE OF TALENT

John Hollinger, former ESPN analyst and

current vice president of the Memphis Griz-

zlies, developed the Player Efﬁciency Rat-

ing (PER). In simple terms, PER is a per-

minute weighted average of almost every

observable player, team, and league statistic.

Positive statistics like scoring points and re-

trieving rebounds increase a player’s PER,

and negative statistics like missing a shot

or turning the ball over to the other team

decrease it. PER is made to be compara-

ble between teams by adjusting for a team’s

pace of play so that players on teams that

play more slowly are not unfairly penalized.

It is also adjusted to be comparable between

years by scaling so that the yearly average

is always 15. PER is intended to capture

a per-minute rating of a player’s statistical

performance in one number. We use it as a

measure of player skill

VI. DATA

Our data set spans 17 NBA postseasons

(playoffs), consisting of data from the 2003

postseason until the 2019 postseason. Each

observation is one team in one season for

a total 272 observations. We observed 75

different coaches during this time period.

To be clear, beginning with the 2003 play-

offs was not arbitrary. Before 2003, the ﬁrst

round of the playoffs was a best-of-ﬁve se-

ries, and the remaining three rounds were

best-of-seven series. In 2003, the format

was changed so that the ﬁrst round is now

consistent with the rest.

Average PER is the average PER for all

players on a team who played at least an

average of 15 minutes per game during the

regular season immediately preceding the

playoffs, and it is intended to measure the

average talent level for a team. Max PER

The formula to calculate John Hollinger’s PER

is provided in the appendix.

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

Table 1: Summary Statistics

Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max

Average PER 272 15.9 1.1 11.4 15.1 16.6 19.1

Max PER 272 23.2 3.4 16 20.7 25.7 32

PSI2 272 3.1 4.7 0.2 0.3 3.0 23.5

PSI3 272 11.3 23.0 0.2 0.3 7.0 117.6

PSI4 272 46.4 113.0 0.2 0.3 17.2 588.1

Seasons With Current Team 272 4.5 4.3 1 2 5 23

Total Seasons 272 8.6 6.9 1 3 13 31

Career Win % 272 0.6 0.1 0.3 0.5 0.6 0.9

Playoff Losses 272 33.3 30.2 4 10 44.5 115

Playoff Wins 272 38.8 45.5 0 8 56.2 229

Time Trend 272 9.0 4.9 1 5 13 17

is the highest PER on a team, and it is in-

tended to capture the best player on the

team. PSI2, PSI3, and PSI4 are the mea-

sures of playoff success discussed earlier.

You will notice that the minimum value of

PSI2, PSI3, and PSI4 is 0.2 and not 0. In or-

der to log-transform PSI2, PSI3, and PSI4,

we replaced the zero values of PSI2, PSI3,

and PSI4 with the next lowest value of 0.2,

as we do not believe there is a signiﬁcant

difference between teams who lost in the

ﬁrst round by only winning one game ans

teams who did not win a single game.

The next 5 variables in the table describe

characteristics about a team’s coach. Sea-

sons With Current Team is the number of

seasons a coach has been with his current

team; Total Seasons is the total number

of seasons that he has coached in his ca-

reer; Career Win % is his career regular

season winning percentage; Playoff Games

is the total number of playoff games he has

coached; and Playoff Wins is the total num-

ber of wins in the playoffs he has accrued

up to this point in his career. Finally, we in-

cluded a time trend, which equals 1 for the

2003 playoffs, 2 for the 2004 playoffs, and

increments all the way to 17 for the 2019

playoffs. Table 1 provides some summary

statistics.

VII. MODEL

We estimated 2 general models which con-

sist of 8 speciﬁc models. The only differ-

ence between the two general models is

that the ﬁrst uses PSI3 as the measure of

playoff success and the second uses PSI4.

We employ a Translog speciﬁcation for the

variables that we believe affect team per-

formance (equation 8). We also include

dummy variables for a team’s seed in that

portion of our speciﬁcation to see the effect

of a team’s strength of schedule on success.

We employ a quadratic speciﬁcation for the

variables that we believe affect efﬁciency

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

(equation 9). We also include a time trend

in both.

Since the Cobb-Douglas speciﬁcation

is nested inside the Translog speciﬁca-

tion (and the linear is nested inside the

quadratic), the four speciﬁc models we es-

timated for each general model were the

following.

• Translog-Quadratic (T-Q)

• Translog-Linear (T-L)

• Cobb-Quadratic (C-Q)

• Cobb-Linear (C-L)

The general speciﬁcation is below.

ln ( PSI3/4

) = β

+ β

ln ( avgPER

) +

(avgPER

) + β

ln ( maxPER

)

(maxPER

) + β

[ln (avgPER

) × ln (maxPER

)]

+ β

seed2

+ β

seed3

+ β

seed4

+ β

seed5

+ β

seed6

+ β

seed7

+ β

seed8

+ β

timeTrend

+ β

[timeTrend

× ln (avgPER

)]

+ β

[timeTrend

× ln (maxPER

)] + v

− u

(8)

= δ

+ δ

numSeasonsWithCurrentTeam

+ δ

numSeasonsWithCurrentTeam

+ δ

numSeasonsOverall

+ δ

numSeasonsOverall

+ δ

careerWinPct

+ δ

careerWinPct

+ δ

totalPlayoffGames

+ δ

totalPlayoffLosses

+ δ

totalPlayoffLosses

+ δ

totalPlayoffWins

+ δ

timeTrend

+ w

. (9)

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

VIII. RESULTS AND

DISCUSSION

Tables 2 and 3 summarize the results for our

models. First, we examine the determinants

of success in the NBA playoffs. Since it is

difﬁcult to interpret the magnitudes of the

coefﬁcients on interaction terms by them-

selves, table 2 shows the elasticities at the

means for 3 variables in all 8 of our models.

From table 2, we see that 5 of the 8 elas-

ticities on avgPER are statistically different

from zero and all 8 are positive. Therefore,

if the average team (meaning the team with

average talent and the average star player

in the average year) increases its average

skill level by 1 %, it would expect to see

an increase of at least 2.22% (depending on

which model speciﬁcation you believe) in

its success in the playoffs.

Conversely, all 8 elasticities on maxPER

are not statistically different from zero and

are all negative. That is, we cannot con-

clude that the average team would expect its

success in the playoffs to change from get-

ting a star player who is 1% more talented

than the one it already has. If anything,

we expect that team to perform worse in

the playoffs after getting the improved star

player.

All of this suggests a very important

takeaway for the decision-makers on NBA

teams. Our results suggest that the key to

success in the playoffs is having a well-

rounded team, not simply having a super-

star.

In table 3, we also notice that not only

are almost all of the signs on the seed vari-

ables signiﬁcantly different from zero and

negative, but they also decrese signiﬁcantly

as seed number increases. This implies that

being a higher seed number plays a very

important role in the success of a playoff

team.

Now we examine the determinants of ef-

ﬁciency



∗



in the NBA playoffs (the re-

sults below the dividing line in table 3).

Recall that a positive coefﬁcient on one of

these variables implies a positive associa-

tion between that variable and inefﬁciency,

or a negative association between that vari-

able and efﬁciency.

Among all 8 speciﬁcations, 3 variables

seem to have a consistent and statistically

signiﬁcant association with efﬁciency. No-

tably, a coach’s career regular season win-

ning percentage did not have a consistent

nor signiﬁcant association with efﬁciency.

This suggests that the regular season and

the playoffs require very different skill sets

to perform well. The ﬁrst of the three is the

number of seasons a coach has been in the

league, which is statistically signiﬁcant in

both its linear and quadratic terms in 4 of

the 8 speciﬁcations. In all 4 of those speci-

ﬁcations, the association between a coach’s

tenure and playoff efﬁciency begins nega-

tive, and after 7-9 seasons of experience

becomes positive. Therefore, our results

imply that, when hiring a coach, NBA team

owners should look for coaches with at least

7 years of head coaching experience.

Second is the number of playoff games

a coach has lost in his career. Some people

may believe that although not the ideal re-

sult, a loss in the playoffs is still valuable ex-

perience for the coach. However, since the

coefﬁcient on playoff losses is positive in

all 8 of our speciﬁcations, our results vehe-

mently refute that belief. In fact, in the mod-

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

Table 2: Elasticities at Means

Model Speciﬁcation:

T-Q PSI3 T-Q PSI4 C-Q PSI3 C-Q PSI4 C-L PSI3 C-L PSI4 T-L PSI3 T-L PSI4

avgPER 3.16 3.75

∗∗

3.04

∗∗

3.90

∗∗∗

2.22

∗

2.50 3.07 3.14

∗∗

(−) (2.12) (1.30) (0.77) 1.32 1.71 (2.88) (1.73)

maxPER − 0.53 − 0.86 − 0.61 − 0.62 − 0.33 − 0.27 − 0.42 − 0.29

(1.94) (0.83) (0.60) (0.71) (0.63) (0.81) (0.98) (0.81)

timeTrend 0.06 0.09 0.06

∗

0.03 − 0.003 − 0.002 0.030 − 0.04

(1.21) (0.13) (0.04) (0.03) (0.03) (0.04) (0.02) (0.04)

Notes:

∗

p<0.1;

∗∗

p<0.05;

∗∗∗

p<0.01

The variance-covariance matrix for the T-Q model with PSI3 as the dependent

variable is not positive semideﬁnite, so we were unable to estimate the standard

error for the elasticity of avgPER. The variance-covariance matrix for the T-L

model in with PSI4 as the dependent variable is singular.

els in which we allowed for a non-constant

effect of playoff losses on efﬁciency (T-Q

and C-Q), not only is the association be-

tween the two negative, but it increases as

the number of playoff losses increases.

Finally, and most convincingly, we exam-

ine the association between previous play-

off game wins and efﬁciency. In all 8 of our

speciﬁcations, the coefﬁcients on playoff

wins were both statistically signiﬁcant and

negative. As such, we robustly and categor-

ically conclude that previous winning expe-

rience in the playoffs is the most important

factor (of the ones we considered) associ-

ated with a team performing efﬁciently in

the playoffs. In fact, not only do we ﬁnd a

positive correlation, but in the models that

allow for a non-constant effect of playoff

wins on efﬁciency, we ﬁnd that the effect

statistically signiﬁcantly increases as play-

off wins increase. Thus, our results imply

that not all playoff experience is equal.

These results also have implications out-

side of the world of sports. As we men-

tioned earlier, data on managers and the

workers they supervise is often not available

to the public or simply does not exist, mak-

ing it difﬁcult to empirically assess the ef-

fect that a manager has on how smoothly his

business runs. However, our results suggest

that three things should be taken into con-

sideration when deciding whether to hire

someone as a manager:

The amount of experience he or she

has as a manager

2. His or her past failures

3. His or her past successes.

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

Table 3: Frontier Maximum Likelihood Estimates

Dependent variable:

ln(PSI3) ln(PSI4) ln(PSI3) ln(PSI4) ln(PSI3) ln(PSI4) ln(PSI3) ln(PSI4)

Model T-Q PSI3 T-Q PSI4 C-Q PSI3 C-Q PSI4 C-L PSI3 C-L PSI4 T-L PSI3 T-L PSI4

Constant 47.06

∗∗∗

−25.35 −3.64 −4.88

∗∗∗

−1.98 −1.52 47.42

∗∗∗

58.69

∗∗∗

(0.27) (111.66) (3.62) (0.99) (3.65) (4.69) (0.99) (4.51)

ln(avgPER) 22.36

∗∗∗

53.96 3.04

∗∗

3.90

∗∗∗

2.22

∗

2.50 22.52

∗∗∗

24.65

∗∗

(0.13) (75.25) (1.30) (0.77) (1.32) (1.71) (0.96) (9.89)

ln(avgPER)

−20.71

∗∗∗

−26.62 −21.05

∗∗∗

−26.87

∗∗∗

(0.18) (30.85) (0.92) (3.98)

ln(maxPER) −50.80

∗∗∗

−32.14 −0.61 −0.62 −0.33 −0.27 −50.63

∗∗∗

−57.71

∗∗∗

(0.33) (34.10) (0.60) (0.71) (0.63) (0.81) (0.95) (11.64)

ln(maxPER)

5.90

∗∗∗

3.95 6.06

∗∗∗

4.11

(0.33) (9.28) (0.88) (9.26)

ln(avgPER) × ln(maxPER) 11.92

∗∗∗

7.30 11.80

∗∗∗

16.29

∗∗

(0.29) (13.81) (0.65) (6.37)

seed2 0.24

∗∗∗

0.25 0.20 0.29 0.04 0.01 0.17 0.06

(0.04) (0.39) (0.30) (0.48) (0.30) (0.39) (0.72) (0.38)

seed3 −0.93

∗∗∗

−1.26

∗∗∗

−1.01

∗∗∗

−1.30 −1.14

∗∗∗

−1.47

∗∗∗

−1.11 −1.40

∗∗∗

(0.11) (0.39) (0.30) (0.86) (0.31) (0.39) (0.98) (0.39)

seed4 −1.82

∗∗∗

−2.44

∗∗∗

−1.90

∗∗∗

−2.30

∗∗∗

−2.15

∗∗∗

−2.79

∗∗∗

−2.10

∗∗

−2.71

∗∗∗

(0.08) (0.41) (0.32) (0.70) (0.31) (0.40) (0.97) (0.39)

seed5 −1.95

∗∗∗

−2.66

∗∗∗

−2.06

∗∗∗

−2.68

∗∗∗

−2.18

∗∗∗

−2.85

∗∗∗

−2.31

∗∗

−2.75

∗∗∗

(0.18) (0.45) (0.33) (0.66) (0.32) (0.42) (0.92) (0.42)

seed6 −2.82

∗∗∗

−3.72

∗∗∗

−2.93

∗∗∗

−3.76

∗∗∗

−3.00

∗∗∗

−3.87

∗∗∗

−3.08

∗∗∗

−3.75

∗∗∗

(0.02) (0.41) (0.32) (0.78) (0.32) (0.42) (0.97) (0.42)

seed7 −3.27

∗∗∗

−4.33

∗∗∗

−3.43

∗∗∗

−4.31

∗∗∗

−3.63

∗∗∗

−4.66

∗∗∗

−3.68

∗∗∗

−4.53

∗∗∗

(0.31) (0.44) (0.33) (0.53) (0.33) (0.42) (0.94) (0.42)

seed8 −3.08

∗∗∗

−4.12

∗∗∗

−3.26

∗∗∗

−4.22

∗∗∗

−3.34

∗∗∗

−4.28

∗∗∗

−3.54

∗∗∗

−4.16

∗∗∗

(0.08) (0.44) (0.33) (0.86) (0.33) (0.42) (0.93) (0.43)

timeTrend 0.22 0.37 0.06

∗

0.03 −0.003 −0.02 −0.06 −0.39

(0.62) (1.08) (0.04) (0.03) (0.03) (0.04) (0.80) (0.80)

timeTrend

0.01 0.003 0.01 0.004

(0.01) (0.01) (0.01) (0.01)

timeTrend × ln(avgPER) 0.06 0.05 0.18 0.17

(0.04) (0.35) (0.37) (0.30)

timeTrend × ln(maxPER) −0.12

∗

−0.14 −0.15 −0.05

(0.06) (0.17) (0.22) (0.17)

γ 0.00000001

∗∗∗

0.003

∗∗∗

0.001

∗∗∗

0.00000001 0.0001

∗∗∗

0.021

∗∗∗

0.00000001

∗∗∗

0.0001

(0.0000000006) (0.000003) (0.000001) (0.000002) (0.0000004) (0.000008) (0.0000005) (0.0000002)

1.36

∗∗∗

2.20

∗∗∗

1.36

∗∗∗

2.22

∗∗∗

1.46

∗∗∗

2.41

∗∗∗

1.63

∗∗∗

2.36

∗∗∗

(0.02) (0.19) (0.12) (0.26) (0.14) (0.21) (0.22) (0.20)

Variables that Affect Inefﬁciency

Constant −0.47 0.74 0.74 −1.50 0.44 0.41 0.11 0.47

(0.28) (2.89) (2.13) (0.88) (0.62) (1.34) (0.58) (0.93)

numSeasonsCurrentTeam −0.03

∗∗∗

0.05 0.03 0.02 −0.01 −0.002 −0.02 0.47

∗∗∗

(0.01) (0.15) (0.06) (0.14) (0.03) (0.05) (0.04) (0.04)

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

Dependent variable:

ln(PSI3) ln(PSI4) ln(PSI3) ln(PSI4) ln(PSI3) ln(PSI4) ln(PSI3) ln(PSI4)

Model T-Q PSI3 T-Q PSI4 C-Q PSI3 C-Q PSI4 C-L PSI3 C-L PSI4 T-L PSI3 T-L PSI4

numSeasonsCurrentTeam

0.0002 −0.003 −0.002 −0.005

(0.004) (0.01) (0.003) (0.01)

numSeasonsOverall 0.28

∗∗∗

0.40

∗∗

0.32

∗∗∗

0.53

∗∗∗

−0.02 −0.01 −0.02 −0.01

(0.02) (0.18) (0.11) (0.16) (0.03) (0.06) (0.04) (0.05)

numSeasonsOverall

−0.02

∗∗∗

−0.03

∗∗∗

−0.02

∗∗∗

−0.03

∗∗∗

(0.001) (0.01) (0.01) (0.01)

careerWinPct −0.02 −5.70 −4.95 1.53 0.61 1.59 −0.03 −0.01

(0.31) (10.41) (7.13) (0.98) (1.06) (2.03) (0.83) (1.42)

careerWinPct

2.32

∗∗∗

8.05 6.76 2.73

∗∗

(0.43) (9.95) (6.02) (1.09)

PlayoffLosses 0.04

∗∗∗

0.05 0.04 0.06 0.08

∗∗∗

0.10

∗∗∗

0.04

∗∗

1.70

∗∗∗

(0.003) (0.04) (0.03) (0.05) (0.02) (0.03) (0.02) (0.02)

PlayoffLosses

0.001 0.001

∗∗

0.001

∗∗

0.001

∗∗∗

(0.001) (0.0004) (0.0003) (0.001)

PlayoffWins −0.11

∗∗∗

−0.12

∗∗∗

−0.10

∗∗∗

−0.18

∗∗∗

−0.08

∗∗∗

−0.11

∗∗∗

−0.03

∗∗∗

0.09

∗∗∗

(0.02) (0.05) (0.02) (0.04) (0.01) (0.03) (0.01) (0.02)

PlayoffWins

0.0003

∗∗∗

0.0003

∗

0.0002

∗∗∗

0.0005

∗∗∗

(0.0000) (0.0001) (0.0001) (0.0001)

Observations 272 272 272 272 272 272 272 272

Number of Panels (Teams) 33 33 33 33 33 33 33 33

Number of Time Periods (Seasons) 17 17 17 17 17 17 17 17

Number of Coaches 75 75 75 75 75 75 75 75

Log-Likelihood Value -427.39 -492.83 -427.76 -496.15 -437.90 -504.93 -445.40 -502.74

Mean Efﬁciency 0.50 0.35 0.43 0.52 0.59 0.54 0.76 0.56

Note:

∗

p<0.1;

∗∗

p<0.05;

∗∗∗

p<0.01

The variance-covariance matrix for the T-Q model with PSI3 as the

dependent variable (1) is not positive semideﬁnite, and the variance-

covariance matrix for the T-L model in with PSI4 as the dependent

variable (8) is singular.

IX. CONCLUSION

In this paper, we have argued that play-

off data is theoretically superior to regular

season data when measuring team perfor-

mance. Since no measure of playoff per-

formance exists, we developed the PSI as a

way to numerically measure how successful

a team was in the NBA playoffs. Employing

the Stochastic Frontier Production Function

method, we ﬁnd that, in order to have the

best chance to boost playoff performance,

the average team’s strategy should be to

build a more well-rounded team instead of

spending all its money on one all-star.

We also ﬁnd that, when hiring a coach,

team owners should consider length of a

coach’s tenure and the number of playoff

wins he has accrued as the factors that will

most likely increase how efﬁciently the

team will perform in the playoffs. Finally,

we ﬁnd that not all experience is equal, and

that losing in the playoffs is actually as-

sociated with a decrease in a team’s efﬁ-

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

ciency. As a ﬁnal thought, Larry Bird once

remarked that he never learned anything

from losing. Perhaps he was right.

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[2]

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[5]

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What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

The Journal of Business, 52(3), 379.

doi: 10.1086/296053

———–

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

X. APPENDIX

Below is the calculation of John Hollinger’s PER. Included also are the deﬁnitions of the

abbreviations from the calculation. All statistics are per game.

uPER =

min



3P +



× AST





2 − f actor ×

tmAST

tmFG



× FG





0.5 × FT ×



2 −

tmAST

tmFG



−

[

VOP × T O

]

−

[

VOP × DRBP ×

(

FGA − FG

)]

− [VOP × 0.44

(

0.44 +

(

0.56 × DRBP

))

(

FTA − FT

)

]

+ [VOP ×

(

1 − DRBP

)

(

T RB − ORB

)

]

[

VOP × DRBP × ORB

]

[

VOP × ST L

]

[

VOP × DRBP × BLK

]

− PF ×



lgFT

lgPF

− 0.44 ×

lgFTA

lgPF

×VOP



Where

factor =

−



0.5 ×

lgAST

lgFG





2 ×

lgFG

lgFT



VOP =

lgPT S

lgFGA − lgORB + lgT O + 0.44 × lgFTA

and

DRBP =

lgT RB − lgORB

lgT RB

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

1. min = Minutes Played By Player

2. Pts = Points Scored By Player

3. lgPTS = League Average of Points

4. tmPTS = Team Average of Points

5. FG = Field Goals By Player

6. lgFG = League Average of Field Goals

7. tmFG = Team Average of Field Goals

8. FGA = Number of Field Goals Attempted

9. lgFGA = League Average of Field Goals Attempted

10. 3P = Three-Point Field Goals Scored By Player

11. FT = Free Throws By Player

12. lgFT = League Average of Free Throws

13. FTA = Free Throw Attempts by Player

14. TRB = Total Rebounds By Player

15. lgTRB = League Average of Rebounds

16. tmTRB = Team Average of Rebounds

17. ORB = Total Offensive Rebounds By Player

18. lgORB = League Average of Offensive Rebounds

19. tmORB = Team Average of Offensive Rebounds

20. DRB = Total Defensive Rebounds By Player

21. lgDRB = League Average of Defensive Rebounds

22. tmDRB = Team Average of Defensive Rebounds

23. AST = Total Assists By Player

24. lgAST = League Average of Assists

What Makes a Good Coach? • March 2020 • Brown, Davis, Granderson

25. tmAST = Team Average of Assists

26. TO = Total Turnovers By Player

27. lgTO = League Average of Turnovers

28. STL = Steals By Player

29. BLK = Blocks By Player