In the domain of Sport Analytics, Global Positioning Systems devices are intensively used as they permit to retrieve players' movements. Team sports' managers and coaches are interested on the relation between players' patterns of movements and team performance, in order to better manage their team. In this paper we propose a Cluster Analysis and Multidimensional Scaling approach to find and describe separate patterns of players movements. Using real data of multiple professional basketball teams, we find, consistently over different case studies, that in the defensive clusters players are close one to another while the transition cluster are characterized by a large space among them. Moreover, we find the pattern of players' positioning that produce the best shooting performance.

1. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Players Movements and Team Shooting
Performance: a Data Mining approach for
Basketball.
Rodolfo Metulini
University of Brescia - Department of Economics and Management
Palermo - June 20th, 2018

2. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Table of contents
1 Overview
2 Data & Methods
3 Analysis & Results
4 Future developments
5 Acknowledgm. & References

3. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Aims
To study the interaction between players in the court, in relation to
team performance
Analysts want to explain movements in reaction to a variety of
factors and in relation to team performance
• Goal I: to segment the game into homogeneous phases in terms
of players’ spatial relations, to retrieve significant moments of
the game
• Goal II: to characterize game phases in terms of team
(shooting) performance

4. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Global Positioning Systems (GPS)
• Object trajectories capture the movement of players or the ball
• Trajectories are captured using optical- or device-tracking and
processing systems
• The adoption of this technology and the availability of data is
driven by various factors, particularly commercial and technical

5. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Play-by-play
Play-by-play (or ‘event-log”) reports a sequence of relevant events
that occur during a match
• Players’ events (shots, fouls)
• Technical events (time-outs, start/end of the period)
• Web scraping techniques (user-friendly R and Phyton routines)
• Video analysis

6. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Cluster Analysis in Sport Literature
• Sampaio & Janeira (2003) investigate the discriminatory
power of game statistics between winning and losing teams in
the Portuguese Professional Basketball League
• Carpita et al. (2013,2015) identify the drivers that most
affect the probability to win a football match
• Ross (2007) segment team sport spectators identifying
potential similarities according to demographic variables
• Gonccalves (2018), using GPS data, applies a two-step cluster
to classify the regularity in team-mates dyads positioning.

7. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Cluster analysis on time instants
Metulini, Manisera & Zuccolotto (2017) split an amatorial basketball
game in a number of separate time-periods, each identifying homogeneous
spatial relations among players in the court
Improvements in 2018 paper:
• analysis extended to multiple matches,
• use of professional basketball games,
• use of the active moments of the games only (applying a filtering
procedure on the initial dataset),
• introduction of transition moments.
• We characterize clusters in terms of team performance

8. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Our dataset(s)
• We have tracked data from three games played by Italian professional
basketball teams, at the Italian Basketball Cup Final Eight. Data
provided by MYagonism MYa
• Each player worn a microchip, collecting the position (1 cm2
pixels),
velocity and acceleration in the x-axis (court length), y-axis (court
width), and z-axis (height)
• The initial dataset considers the full game length, for all the ms in
which the system captured at least one player. We cleaned it by
dropping inactive moments, according to our filtering procedure
• The final dataset for team 1 counts for 206,332 rows, team 2 counts
for 232,544 rows, while team 3 counts for 201,651 rows (Frequency:
80/90 Hz)

9. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Filtering Procedure
From: Metulini, R., Filtering procedures for sensor data in basketball. Statistics & Applications. 2017-2
Full data matrix X (nrow = T);
↓
1-A Remove row if players on the court = 5
↓
1-B Remove row if a player is on the free throw circle
↓
1-C Remove row if players veloc-
ity < h2 for h3 consecutive seconds
↓
Reduced data matrix (nrow = T’ ≤ T)
↓
2-A Assign offense or defense labels
↓
2-B Assign actions’ sorting
↓
Reduced data matrix with actions’ labelling and sorting

10. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Approach - I
• We consider 5 total lineups from 3 different games
• Separately to each one, we apply a k-means cluster analysis to group
objects
• We group time instants
• The similarity is expressed in terms of distance between players’
dyads.
• We, consistently along different lineups, find k = 6 based on the
value of the between deviance (BD) / total deviance (TD) ratio for
different numbers of clusters

11. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Profiles plot
05101520
C1 13.31%
dsred.d13
dsred.d16
dsred.d17
dsred.d18
dsred.d36
dsred.d37
dsred.d38
dsred.d67
dsred.d68
dsred.d78
05101520
C2 19.76%
dsred.d13
dsred.d16
dsred.d17
dsred.d18
dsred.d36
dsred.d37
dsred.d38
dsred.d67
dsred.d68
dsred.d78
05101520
C3 3.4%
dsred.d13
dsred.d16
dsred.d17
dsred.d18
dsred.d36
dsred.d37
dsred.d38
dsred.d67
dsred.d68
dsred.d78
05101520
C4 29.8%
dsred.d13
dsred.d16
dsred.d17
dsred.d18
dsred.d36
dsred.d37
dsred.d38
dsred.d67
dsred.d68
dsred.d78
05101520
C5 6.41%
dsred.d13
dsred.d16
dsred.d17
dsred.d18
dsred.d36
dsred.d37
dsred.d38
dsred.d67
dsred.d68
dsred.d78
05101520
C6 27.31%
dsred.d13
dsred.d16
dsred.d17
dsred.d18
dsred.d36
dsred.d37
dsred.d38
dsred.d67
dsred.d68
dsred.d78
Figure: Profile plots representing, for each of the 6 clusters, the
average distance among players’ dyads. Lineup 1 in CS1.
Profiles plot for other case studies Go to

12. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Multidimensional scaling
−10 −5 0 5 10
−4−2024
C1 13.31%
Dimension 1
Dimension2
1
3
6
7
8
−10 −5 0 5 10
−4−2024
C2 19.76%
Dimension 1
Dimension2
1
3
6
7 8
−10 −5 0 5 10
−4−2024
C3 3.4%
Dimension 1
Dimension2
1
3
6
7
8
−10 −5 0 5 10
−4−2024
C4 29.8%
Dimension 1
Dimension2
13
6
7
8
−10 −5 0 5 10
−4−2024
C5 6.41%
Dimension 1
Dimension2
1
3
6 7 8
−10 −5 0 5 10
−4−2024
C6 27.31%
Dimension 1
Dimension2
1
3
6
78
Figure: Map representing, for each of the 6 clusters, the average
position of the five players in the two dimensions. Lineup 1 in CS1.
Multidimensional scaling for other case studies Go to

13. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Transition matrix
Cluster 1 2 3 4 5 6
TR 8.41 21.76 82.11 7.08 54.49 10.53
D 22.74 10.28 6.6 70.48 23.98 17.95
O 68.85 67.97 11.29 22.45 21.53 71.52
Table: Percentages of time instants classified in Transition (TR)
Defense (D) or Offense (O), for each cluster. Lineup 1 in CS1.
Cluster label C1 C2 C3 C4 C5 C6
C1 - 11.27 10 8.45 15 10.34
C2 31.03 - 10 23.94 15 35.34
C3 0.00 1.41 - 0.00 0 7.76
C4 34.48 21.13 0 - 25 35.34
C5 3.45 4.23 0 4.23 - 11.21
C6 31.03 61.97 80 63.38 45 -
Table: Transition matrix reporting the relative frequency subsequent
moments (t, t + 1) report a switch from a group to a different one.
Lineup 1 in CS1.

14. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Team Shooting Performance -
Video Analysis
Play-by-play data are not freely available online for this tournament
We retrieve shoots by doing a video analysis:
• We install an app in the smartphone to take trace of time (aTimeLogger)
• We open the video of the match, which is available online
• We trace made/missed shoots with aTime Logger while running the video
• The App create a .txt report with the shooting events and related ms, which can be attach to the
final dataset

15. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Team Shooting Performance
Cluster label Made Missed Total %
C1 2 2 4 50%
C2 0 2 2 0%
C3 0 0 0 -
C4 0 0 0 -
C5 0 1 1 0%
C6 5 3 8 62.5%
Lineup 1 7 8 15 46.7%
Table: Team Shooting performance. Lineup 1 in CS1. Duration:
8m:21s

16. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Examples
An example of offensive play which ends in Cluster C6
An example of a transition-to-offensive play which ends in Cluster C6

17. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Highlights
• Spacing matters
• The team (shot-) performs better when a player is free to shot
• The team goes in search of the best pattern for a good shot
(average length in a cluster: 2 seconds)

18. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Future research
• Examining the effect of external factors, such as coach advices
(playbooks, tactics)
• Including ball trajectories
• ...

19. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
Acknowledgements
Big & Open Data Innovation (BODaI) laboratory BODaI
Big Data analytics in Sports (BDS) laboratory BDS
Paola Zuccolotto, Marica Manisera (University of Brescia) and Tullio
Facchinetti (University of Pavia)

20. Movements
and
Performance
Metulini
Overview
Data &
Methods
Analysis &
Results
Future
developments
Acknowledgm.
& References
References
1. Sampaio, J., Janeira, M.: Statistical analyses of basketball team performance: understanding teams wins
and losses according to a dierent index of ball possessions. International Journal of Performance Analysis in
Sport 3.1 (2003): 40-49.
2. Carpita, M., Sandri, M., Simonetto, A., Zuccolotto, P. (2013). Football mining with r. Data Mining
Applications with R.
3. Carpita, M., Sandri, M., Simonetto, A., Zuccolotto, P. (2015). Discovering the drivers of football match
outcomes with data mining. Quality Technology & Quantitative Management
4. Ross, S. D.: Segmenting sport fans using brand associations: A cluster analysis. Sport Marketing
Quarterly, 16.1 (2007): 15.
5. Gonalves, B. S. V.: Collective movement behaviour in association football. UTAD Universidade de
Tras-os-Montes e Alto Douro (2018)
6. Metulini, R., Marisera, M., Zuccolotto, P.: Space-Time Analysis of Movements in Basketball using Sensor
Data. Statistics and Data Science: new challenges, new generations SIS2017 proceeding. Firenze Uiversity
Press. eISBN: 978-88-6453-521-0 (2017).
7. Metulini, R.: Filtering procedures for sensor data in basketball. Statistics&Applications 2 (2017).

21. Movements
and
Performance
Metulini
More
0510152025
C1 11.32%
dsred.d14
dsred.d15
dsred.d17
dsred.d110
dsred.d45
dsred.d47
dsred.d410
dsred.d57
dsred.d510
dsred.d710
0510152025
C2 24.45%
dsred.d14
dsred.d15
dsred.d17
dsred.d110
dsred.d45
dsred.d47
dsred.d410
dsred.d57
dsred.d510
dsred.d710
0510152025
C3 14.42%
dsred.d14
dsred.d15
dsred.d17
dsred.d110
dsred.d45
dsred.d47
dsred.d410
dsred.d57
dsred.d510
dsred.d710
0510152025
C4 6.21%
dsred.d14
dsred.d15
dsred.d17
dsred.d110
dsred.d45
dsred.d47
dsred.d410
dsred.d57
dsred.d510
dsred.d710
0510152025
C5 40.4%
dsred.d14
dsred.d15
dsred.d17
dsred.d110
dsred.d45
dsred.d47
dsred.d410
dsred.d57
dsred.d510
dsred.d710
0510152025
C6 3.2%
dsred.d14
dsred.d15
dsred.d17
dsred.d110
dsred.d45
dsred.d47
dsred.d410
dsred.d57
dsred.d510
dsred.d710
(a) lineup 2, CS1
05101520
C1 2.17%
dsred.d12
dsred.d14
dsred.d15
dsred.d16
dsred.d24
dsred.d25
dsred.d26
dsred.d45
dsred.d46
dsred.d56
05101520
C2 34.52%
dsred.d12
dsred.d14
dsred.d15
dsred.d16
dsred.d24
dsred.d25
dsred.d26
dsred.d45
dsred.d46
dsred.d56
05101520
C3 8.4%
dsred.d12
dsred.d14
dsred.d15
dsred.d16
dsred.d24
dsred.d25
dsred.d26
dsred.d45
dsred.d46
dsred.d56
05101520
C4 10.59%
dsred.d12
dsred.d14
dsred.d15
dsred.d16
dsred.d24
dsred.d25
dsred.d26
dsred.d45
dsred.d46
dsred.d56
05101520
C5 9.18%
dsred.d12
dsred.d14
dsred.d15
dsred.d16
dsred.d24
dsred.d25
dsred.d26
dsred.d45
dsred.d46
dsred.d56
05101520
C6 35.14%
dsred.d12
dsred.d14
dsred.d15
dsred.d16
dsred.d24
dsred.d25
dsred.d26
dsred.d45
dsred.d46
dsred.d56
(b) lineup 1, CS2
051015
C1 5.46%
dsred.d12
dsred.d15
dsred.d16
dsred.d18
dsred.d25
dsred.d26
dsred.d28
dsred.d56
dsred.d58
dsred.d68
051015
C2 20.5%
dsred.d12
dsred.d15
dsred.d16
dsred.d18
dsred.d25
dsred.d26
dsred.d28
dsred.d56
dsred.d58
dsred.d68
051015
C3 4.3%
dsred.d12
dsred.d15
dsred.d16
dsred.d18
dsred.d25
dsred.d26
dsred.d28
dsred.d56
dsred.d58
dsred.d68
051015
C4 12.65%
dsred.d12
dsred.d15
dsred.d16
dsred.d18
dsred.d25
dsred.d26
dsred.d28
dsred.d56
dsred.d58
dsred.d68
051015
C5 36.11%
dsred.d12
dsred.d15
dsred.d16
dsred.d18
dsred.d25
dsred.d26
dsred.d28
dsred.d56
dsred.d58
dsred.d68
051015
C6 20.98%
dsred.d12
dsred.d15
dsred.d16
dsred.d18
dsred.d25
dsred.d26
dsred.d28
dsred.d56
dsred.d58
dsred.d68
(c) lineup 2, CS2
05101520
C1 26.55%
dsred.d25
dsred.d26
dsred.d29
dsred.d210
dsred.d56
dsred.d59
dsred.d510
dsred.d69
dsred.d610
dsred.d910
05101520
C2 4.49%
dsred.d25
dsred.d26
dsred.d29
dsred.d210
dsred.d56
dsred.d59
dsred.d510
dsred.d69
dsred.d610
dsred.d910
05101520
C3 3.85%
dsred.d25
dsred.d26
dsred.d29
dsred.d210
dsred.d56
dsred.d59
dsred.d510
dsred.d69
dsred.d610
dsred.d910
05101520
C4 20.92%
dsred.d25
dsred.d26
dsred.d29
dsred.d210
dsred.d56
dsred.d59
dsred.d510
dsred.d69
dsred.d610
dsred.d910
05101520
C5 37.8%
dsred.d25
dsred.d26
dsred.d29
dsred.d210
dsred.d56
dsred.d59
dsred.d510
dsred.d69
dsred.d610
dsred.d910
05101520
C6 6.39%
dsred.d25
dsred.d26
dsred.d29
dsred.d210
dsred.d56
dsred.d59
dsred.d510
dsred.d69
dsred.d610
dsred.d910
(d) lineup 1, CS3
Back to Lineup1, CS1

22. Movements
and
Performance
Metulini
More
−5 0 5 10
−40246
C1 11.32%
Dimension 1
Dimension2
1
4
57
10
−5 0 5 10
−40246
C2 24.45%
Dimension 1
Dimension2
1
4
5
7
10
−5 0 5 10
−40246
C3 14.42%
Dimension 1
Dimension2
1
4
5
7
10
−5 0 5 10
−40246
C4 6.21%
Dimension 1
Dimension2
1
4
5
7
10
−5 0 5 10
−40246
C5 40.4%
Dimension 1
Dimension2
14
5
710
−5 0 5 10
−40246
C6 3.2%
Dimension 1
Dimension2
1
4
5
7
10
(e) lineup 2, CS1
−10 −5 0 5
−4024
C1 2.17%
Dimension 1
Dimension2
1
2
4
5
6
−10 −5 0 5
−4024
C2 34.52%
Dimension 1
Dimension2
1
2
4
5
6
−10 −5 0 5
−4024
C3 8.4%
Dimension 1
Dimension2
1
2
4
5
6
−10 −5 0 5
−4024
C4 10.59%
Dimension 1
Dimension2
1
2
4
5
6
−10 −5 0 5
−4024
C5 9.18%
Dimension 1
Dimension2
1
2
4
5
6
−10 −5 0 5
−4024
C6 35.14%
Dimension 1
Dimension2
124
5
6
(f) lineup 1, CS2
−10 −5 0 5
−4024
C1 5.46%
Dimension 1
Dimension2
1
2
5
6
8
−10 −5 0 5
−4024
C2 20.5%
Dimension 1
Dimension2
1
2
5
6
8
−10 −5 0 5−4024
C3 4.3%
Dimension 1
Dimension2
1
2
5
6
8
−10 −5 0 5
−4024
C4 12.65%
Dimension 1
Dimension2
1
2
5
6
8
−10 −5 0 5
−4024
C5 36.11%
Dimension 1
Dimension2
1
2
5
6
8
−10 −5 0 5
−4024
C6 20.98%
Dimension 1
Dimension2
1 2 5
6
8
(g) lineup 2, CS2
−5 0 5 10
−4024
C1 26.55%
Dimension 1
Dimension2
2
5
6
9
10
−5 0 5 10
−4024
C2 4.49%
Dimension 1
Dimension2
2
5
6
9 10
−5 0 5 10
−4024
C3 3.85%
Dimension 1
Dimension2
2
5
6
9
10
−5 0 5 10
−4024
C4 20.92%
Dimension 1
Dimension2
2
5
6
9
10
−5 0 5 10
−4024
C5 37.8%
Dimension 1
Dimension2
25 69
10
−5 0 5 10
−4024
C6 6.39%
Dimension 1
Dimension2
2
5
6
9
10
(h) lineup 1, CS3
Back to Lineup1, CS1