Performance Analysis of Basketball Referees by Machine Learning

Techniques

Sheng-Wei Wang

and Wen-Wei Hsieh

Department of Applied Informatics, Fo Guang University, No. 160, Linwei Rd., Jiaoshi Township, Yilan, Taiwan, R.O.C.

Ofﬁce of Physical Education, National Tsing Hua University,

No. 1, Section 2, Kuang-Fu Rd., East District, Hsinchu City, Taiwan, R.O.C.

Keywords:

Basketball Referee, Performance Analysis, Machine Learning, Pocket Algorithm.

Abstract:

Basketball referees are important in a basketball game. In this paper, we analyze the performance of basketball

referees in a game from history data and using the machine learning techniques. The data are collected from

Taiwan Super Basketball League games. Weﬁrst observed that the teamwork is a key factor to the performance

of referee teams. Furthermore, the degree of teamwork are more important than the personal capabilities.

Then, we derived some classiﬁers by machine learning algorithms to further analyze the data set. Among the

three classiﬁers, a classiﬁer named linear classiﬁer using pocket algorithm, which is able to classify the data

points with most correct rate, performs better than the other two classiﬁers. The classiﬁer also proved the

importance of teamwork is much larger than that of personal capability. In the future, the classiﬁer can be

used to predict the performance of a referee team in a basketball game.

1 INTRODUCTION

Basketball is very popular all over the world. In order

to make the basketball games all over the world be

understood, the International Basketball Federation

(FIBA) published a set of documents for governing

the basketball sport. Among the documents publised

by FIBA, the Ofﬁcial Basketball Rules(FIBA, 2014)

is used to identify and deal with all situations in a bas-

ketball game.

In a basketball game, the referees play an impor-

tant role in ofﬁciating the game based on the basket-

ball rules. Originally, there are two referees being as-

signed to a basketball game. The two referees follow

the two men ofﬁciating mechanism described in refer-

ees’ manual to administrate a basketball game. How-

ever, when the game becomes faster and more intense,

there are some blind sides when the game is covered

by only two referees.

In 2000, FIBA started using three person ofﬁci-

ating(FIBA, 2010b) in the ofﬁcial tournament. Us-

ing three person ofﬁciating mechanism may decrease

some blind sides and make the game fairer. However,

some problems may occur because the three referees

may not work well with each other. For example, in a

body contact, the probability that one referee calls the

charging foul and the other calls the block foul will be

larger than that in two persons ofﬁciating.

In this paper, we discuss the performance of the

referees in a game with three referees. Intuitively,

three referees with good personal capability may im-

prove the referee team’s performance. However,

good personal capabilities does not necessarily re-

sult in good referees’ performance in a basketball

game(Lazarov, 2007; Carron, 1988). For example,

even though the referees who are selected to Olympic

Games are top FIBA referees whose personal capa-

bilities are deﬁnitely best among all referees in the

world, many disputes still occur in Olympic Games.

The main reason is that the referees are from different

countries and not familiar with each other so that they

cannot work together well.

This paper focused on how the degree of team-

work, in this paper we called teamwork capability,

affects the referee team’s performance. We use the

history data to analyze the importance of teamwork

and personal capabilities. Observations are ﬁrst made

to the raw data and found that the referee team’s per-

formance depends on the teamwork capability very

much. Then, we use the machine learning algorithms

to ﬁnd some classiﬁers which are able to classify the

collected data set into good or bad performance. One

Wang, S-W. and Hsieh, W-W.

Performance Analysis of Basketball Referees by Machine Learning Techniques.

DOI: 10.5220/0006031501650170

In Proceedings of the 4th International Congress on Sport Sciences Research and Technology Support (icSPORTS 2016), pages 165-170

ISBN: 978-989-758-205-9

165

classﬁer name linear classiﬁer using pocket algorithm

is able to classify the data with correct rate 68.6%.

The classiﬁer is an evidence that the teamwork ca-

pabilities are more important than the personal capa-

bilities in referee team’s performance. Prediction of

referee’s performance in future games is also an ap-

plication of the classiﬁers.

The reminder of this paper is organized as follows.

Next section reviews some previous works on how to

improve the teamwork in different areas. Observa-

tions of data are made in Section 3. We then applied

the machine learning techniques to make a classiﬁer

for referee’s performance in Section 4. Finally, some

concluding remarks and applications of this paper are

given.

2 PREVIOUS WORKS

To improve a referee team’s performance, improving

personal capabilities and improving teamwork capa-

bilities are both important. Most previous literatures

only discussed how to improve the personal capabili-

ties of a referee(Helsen and Bultynck, 2004; Hoseini

et al., 2011; Feinstein, 2009; Stern, 2010; Nevill et al.,

2002; Mirjamali et al., 2013; Wang et al., 2013; Stew-

art and Ellery, 2004; Leicht, 2008; Serkan, 2014;

Balmer et al., 2007; Guill´en and Feltz, 2011). On

the other hand, some research efforts have been pro-

posed to improve the teamwork capabilities in differ-

ent areas(Gladstein, 1984; Magyar et al., 2004; Heuze

et al., 2006; Tjosvold, 1988; Austin, 2003). Lazarov

points out the importance of teamwork in ofﬁciating

a basketball game (Lazarov, 2007).

In order to improve the teamwork of referees in

a basketball game, FIBA proposes some solutions to

make games proceed ﬂuently without disputes:

• FIBA publishes the referees manual to let referees

all around the world use the same mechanisms in

ofﬁciating(FIBA,2010b). By obeyingthe manual,

the referees are able to identify their coverage area

and the dual calls will be reduced.

• FIBA conducts many referees camps and clinics

throughout the world. In the camps and clinics,

new rules and mechanisms are introduced for the

referees.

• In a referees clinic, the candidate of FIBA referees

must pass the English test to become a FIBA ref-

eree(FIBA, 2010a). By English test, the referees

who hope to become a FIBA referee must learn

English so as to communicate with other referees

and the teams which is able to reduce the disputes

and misunderstandings.

1 1.5 2 2.5 3 3.5 4 4.5 5

1.5

2.5

3.5

4.5

Average Personal Capability (AVG

)

Average Teamwork Capability (AVG

)

Figure 1: The collected data from 207 Super Basketball

League games in Taiwan.

3 THE HISTORIC DATA

In this section, we ﬁrst introduce the basic parameters

of the collected data. From the data, we can make

some interesting observations.

3.1 Background Information

In this paper, the data is collectd from the Super Bas-

ketball Leagues in Taiwan from 2013 to 2015 (2 sea-

sons). The number of referees and the number of

games are 49 and 207 respectively. The 49 referees

are top referees in Taiwan and 26 of them are active

or former FIBA referees. A personal capability value

is associated with each referee. The value is from

1 to 5 and is the average of four scores obtained by

4 technical committee members in Taiwan. A team-

work capability value is associated with each pair of

two referees. The value ranges also from 1 to 5 and is

the average of values scored by the same 4 technical

committee members.

In each game, a score is given to each referee

and the score ranges from 1 to 3. Normalization is

applied to the data because different scores may be

given by different committees on the same game. Af-

ter normalization, the average of the scores in each

game is calculated. By our deﬁnition, we said a ref-

eree team performs good if the average performance

is larger than or equal to 2.3. The reason we se-

lecting 2.3 as the threshold is that in the 207 games,

the games with good referees performance is approxi-

mately 50%. The referee teams which do not perform

good performanceis said that their performences need

improvement.

We then analyze the referee capabilities in each

game. For each game, the average personal capablity

icSPORTS 2016 - 4th International Congress on Sport Sciences Research and Technology Support

166

2.0~2.5 2.5~3.0 3.0~3.5 3.5~4.0 4.0~4.5 4.5~5.0

Average Personal/Teamwork Capabilities

Percentage of number of games

with good performance

Average Personal Capability

Average Teamwork Capability

Figure 2: Percentages of games with good performance.

AVG

and the average teamwork capability AVG

are

calculated. The relationships between the referees

performance and the referees capabilities is shown in

Fig. 1.

3.2 Observations

We plot the collected data in ﬁg.1. The X-axis and

Y-axis are the average personal capabilities and the

average teamwork capabilities respectively. The data

with “o” label are the game with good performance

while the data with “x” label are the game with per-

formances needed improvement. From this ﬁgure, we

can make the following observations:

• The data can not be separated clearly. The per-

formances with the same AVG

and AVG

val-

ues are not necessarily the same. This is because

that there are some other factors affect the perfor-

mance of referees. For example, the both teams of

a gaem, the physical, psycological preparation of

the referees, and etc.

• The relationship between the average personal ca-

pability and the average teamwork capability is

dependent. From the ﬁgure, we found that when

a referee team’s average personal capability high,

it probably has high teamwork capability. Even

though the two capabilities is dependent, we hope

to ﬁnd the degree of the dependence and how they

affect the referees’ performance.

In order to understand how the two capabilities af-

fect the performances of the referee teams, we calcu-

late the percentages of number of games with good

performance when the value of capabilities is between

a range. Fig. 2 shows the relationships and we can

make the following observations:

• The relationship between the average teamwork

capability and the percentage of games with good

1 1.5 2 2.5 3 3.5 4 4.5 5

1.5

2.5

3.5

4.5

Average Personal Capability (AVG

)

Average Teamwork Capability (AVG

)

AVG

+AVG

=6.9167

Figure 3: Linear classiﬁer with equal weight.

performance is an increasing function. When the

referees work together well, the performance will

be better.

• The relationship between the average personal ca-

pability and the performance is not an increasing

function. When the average personal capability is

high, the percentage of games with good perfor-

mance is not as high as expected. After analyz-

ing the raw data, we found that the reason that the

teamwork capabilities are small in these games.

We have already known that the teamwork is very

important to the performance of referees in a game.

Next, we hope to use the data for future analysis and

applications.

4 CLASSIFIERS OF REFEREE

TEAM’S PERFORMANCE

The data can also be used for further analysis of ref-

eree team’s performance. In this section, we use ma-

chine learning techniques(Abu-Mostafa et al., 2012;

Gallant, 1990) to ﬁnd some classiﬁers which can

which can separate the data with minimum errors.

When a classiﬁer is obtained, we can use the clas-

siﬁer to predict referees’ performance in the future.

Also, we can analyze the performance in a mathemat-

ical manner.

4.1 Linear Classiﬁer with Equal Weight

The assumption of linear classiﬁer with equal weights

assumes that the personal capability and the team-

work capability are equally important. The classiﬁer

is to ﬁnd a line whose slope is −1. The equation of

Performance Analysis of Basketball Referees by Machine Learning Techniques

167

1 1.5 2 2.5 3 3.5 4 4.5 5

1.5

2.5

3.5

4.5

Average Personal Capability (AVG

)

Average Teamwork Capability (AVG

)

radius=3.4771

Figure 4: Circle classiﬁer with equal weight

this line can be written as follows where c is a con-

stant.

AVG

+ AVG

= c (1)

The value of c is determined by a linear search tech-

nique such that the number of data points which is not

classiﬁed correctly is minimum. Fig. 3 shows the re-

lationship of the data set and the linear classiﬁer with

equal weights. In our data set, the value of c with

minimum error points is 6.9167 and the number of er-

ror classiﬁed data points is 72 (Correct rate: 65.2%).

That is, if AVG

plus AVG

of a referee team in a game

is larger than 6.9167, the performance is expected to

be good based on this classiﬁer.

4.2 Circle Classiﬁer with Equal Weight

Circle classiﬁer with equal weights uses the same as-

sumption as the linear classiﬁer with equal weights

except that the classiﬁer is a quadrant. The center of

the circle is set to (1, 1) and the radius is a constant r.

The equation of the circle is as follow.

(AVG

− 1)

+ (AVG

− 1)

= r

(2)

The value of r is also determined by linear search

and the number of incorrectly classiﬁed data points

is minimum. In the data set, the value of r is 3.4771

and the number of incorrectly classiﬁed data points is

73 (Correct rate: 64.7%). That is, if AVG

plus AVG

of a referee team in a game is larger than 3.4771

the performance is expected to be good based on this

classiﬁer. The classiﬁer is shown in ﬁg. 4.

4.3 Linear Classiﬁer using Pocket

Algorithm

The two previous classiﬁers both assume that the

personal capability and the teamwork capability are

1 1.5 2 2.5 3 3.5 4 4.5 5

1.5

2.5

3.5

4.5

Average Personal Capability (AVG

)

Average Teamwork Capability (AVG

)

1.33325 AVG

+8.5001 AVG

=33

Figure 5: Linear classiﬁer using pocket algorithm

equally important to the referee team’s performance.

However, in the observations shown in Section 3, the

teamwork capability seems more important than the

personal capability. A data point d can be represent

by a two-tuple X

= (AVG

(d), AVG

(d)) and the per-

formance of d, denoted as y

, is set to be 1 if the per-

formance is good; otherwise, it is set to be −1.

Generally, the linear classiﬁer can be written as

follows.

× AVG

+ w

× AVG

+ w

= 0 (3)

where w = w

, w

is the vector of coefﬁcients.

For simplicity for computation, we extend X

to be

a three-tuple X

′

= (1, AVG

(d), AVG

(d)) and the

equation of the classiﬁer can be written as follows.

w· X

′

= 0 (4)

In order to ﬁnd the vector (w

, w

) such

that the number of incorrectly classiﬁed data points

is minimum, pocket algorithm(Abu-Mostafa et al.,

2012; Gallant, 1990; Rosenblatt, 1958) is used. Pro-

cedure of the pocket algorithm works as follows.

Step 1. Initially, let (w

) equals to (1, 1, 1).

Calculate the number of incorrectly classiﬁed data

points and let N

err

be the number of incorrectly

classiﬁed data points.

Step 2. Randomly choose a data point d which is in-

correctly classiﬁed. The new weight w

′

can be

calculated as follow

′

← w+ y

× X

′

(5)

Step 3. Calculate the number of incorrectly classiﬁed

data points N

′

err

based on the new weight w

′

. If

′

err

is less than N

err

, let N

err

= N

′

err

and remember

the weight w

′

icSPORTS 2016 - 4th International Congress on Sport Sciences Research and Technology Support

168

Step 4. If the number of repeated computation is less

than the predeﬁned value, go to Step. 2; other-

wise, the algorithm terminates. In our program,

the value is set to 10

After applying the pocket algorithm, the equation of

the classiﬁer applied on the data set is as follows and

the slope is −0.157.

1.33325AVG

+ 8.5001AVG

− 33 = 0 (6)

That is, if (1.33325AVG

+ 8.5001AVG

− 33) value

of a referee team in a game is larger than 33, the per-

formance is expected to be good based on this clas-

siﬁer. Fig. 5 shows the relationship between the data

points and the classiﬁer. The number of incorrectly

classiﬁed data points is 65 (Correct rate: 68.6%).

From the equation and ﬁgure, we have following ob-

servations:

• The slope of the classiﬁer is larger than -1 and still

less than 0. This means that the performance of a

referee team is affected by both the average per-

sonal capability and the average teamwork capa-

bility. The teamwork capability is more important

than the personal capability.

• From equation (6), we found that if the value

AVG

is large enough, performance of a referee

team will be probably good. However, if the value

of AVG

is high but the value of AVG

is not large

enough, the performance may need improvement.

• When applying the algorithm to the data set, the

equation will be different if the random incor-

rectly classiﬁed data points chosen in Step. 2 of

the algorithm are different. Even though the equa-

tions are different, they all yield the same mini-

mum number of incorrectly classiﬁed data points.

The equations are close to each other. There-

fore, the observations described above can also be

made from the different equations.

5 CONCLUSIONS

In this paper, we analyze the performance of basket-

ball referee teams in a game. In the past, only per-

sonal capabilities of the referees are considered. We

also consider the teamwork capabilities between the

referees in addition to their personal capabilities.

The data from Taiwan Super Basketball League

are analyzed. We ﬁrst observed that the teamwork ca-

pability is a key factor to the performance of referee

teams. Furthermore, the teamwork capabilities are

more important than the personal capabilities. Then,

we derived three classiﬁers to further analyze the data

set. Among the three classiﬁers, a classiﬁer named

linear classiﬁer using pocket algorithm performs bet-

ter than the other two classiﬁers. The linear classiﬁer

using pocket algorithm is able to classify the data set

with 68.6% correct rate. The classiﬁer also proved

the importance of teamwork is much larger than that

of personal capability.

The classiﬁers may change with more and more

input data. This paper provides an approach to ana-

lyze the referee team’s performance in different coun-

tries or different tournaments. If more and more

data can be obtained from different countries or FIBA

games, this research can be applied to these referees

and games. Therefore, the classiﬁer for the games

can be derived and some concluding remarks can be

made.

In the future, this research can be extended as fol-

lows.

• The classiﬁers have been derived and they can be

used as a predictor to the referee team’s perfor-

mance in the future games. The predictor can be

used and the correctness can be computed.

• The personal capability of a referee and the

teamwork capability between two referees may

change. In the future, a feedback mechanism af-

ter a game should be devised. If a game ends

with good referees’ performance, the personal ca-

pabilities of the three referees and the teamwork

capabilities between the three referees should be

increased; otherwise, they should be decreased.

In the meantime, the parameters of the classiﬁer

should be recalculated to ﬁt the new data.

• When the database of referees personal capabil-

ities and teamwork capabilities has been estab-

lished, a recommend system can be designed. In

a tournament, the selection and assignment of the

referees can recommended by the system in order

to maximize the number of games with good per-

formance.

ACKNOWLEDGEMENTS

This research was supported by the Ministry of

Science and Technology, Taiwan, under grant

MOST104-2221-E-431-001.

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