The document describes a procedure to automatically identify inactive periods in basketball games using only sensor-tracked player movement data. The procedure filters out moments when fewer than 5 players are on the court, a player is shooting free throws, or all players' speeds are below a threshold for a set period of time. Parameters for the thresholds are tuned using a "pseudo-ROC" method comparing the results to a video-based ground truth. The tuned procedure is able to accurately detect active and inactive moments to help analysts evaluate player and team performance without watching full game video. Future work aims to extend the method to identify offensive and defensive plays.

1. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Detecting and classifying moments in
basketball matches using sensor tracked data
Rodolfo Metulini1, Tullio Facchinetti2, Paola Zuccolotto1
1. Department of Economics and Management, University of Brescia
2. Department of Industrial, Computer and Biomedical Engineering,
University of Pavia
Milano - June 21th, 2019

2. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Table of contents
1 The Context
2 Data & Methods
3 Results
4 Conclusions
5 Acknowledgm. & References

3. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
The Context
• Tools to evaluate offensive performance (Oliver, 2004), in terms of
shots (Zuccolotto et al., 2018), possessions per game (Kubatko et al.
2007). New suite of defensive metrics (Franks et al., 2015)
• Also players’ positioning during the game allows a deep
characterization of the performance of single players and the whole
team, both from offensive and defensive perspective
• analysis of players movements must be restricted to active periods
only, to properly capture the interesting features of a game
• This paper proposes a procedure to automatically identify inactive
periods in a basketball game by just using players’ tracked data
The procedures applies to European basketball, in cases where:
1 information on the movement of players has been captured with the
use of an appropriate localization technology; but
2 relevant information are not recorded by the play-by-play; and
3 nobody is in charge to track the moments when game is
active/inactive.

4. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Players’ movements in literature
Works on several aspects of NBA are abundant:
• Wu & Bornn (2017, The American Statistician) provide a guide on
how to manage with SportVU sensor data technology for visual
offensive analysis
• Miller & Bornn (2017, MIT Sloan Conf.) catalogues NBA league
strategies according to players’ movements and D’Amour et al.
(2015, MIT Sloan Conf.) showed that more open shots opportunities
are associated to more frequent and faster ball’s movement
Little attention was paid to non-American leagues:
• Metulini (2018, SIS) uses tracked data to split games into clusters of
homogeneous spatial distances among players, looking for those with
better team shooting performance
• Metulini et al. (2018, JQAS) apply a vector autoregressive model to
show that larger surface area occupied by players is positively related
to a large number of scored points by the team

5. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Sensor tracked data
• Localization technologies capture the movement of players or the ball
• Technologies could be based either on optical- or on device-tracking
and processing systems
• The adoption of this technologies and the availability of data is
driven by various factors, particularly commercial and technical

6. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Data (i)
• Tracked data from three games (case studies, CS) played by Italian
professional basketball teams, at the Italian Basketball Cup Final
Eight (Data provided by MYagonism)
• Position, velocity and acceleration of the players during the full
game length, including those waiting on the bench, along x-axis
(court length), y-axis (court width) and z-axis (vertical)
• 10 (for CS1 and CS3) and 11 (for CS2) players of one team, rotating
in the court, have been analysed
• We do not consider accelerations and the z-axis
• Measured positions expressed in centimetres (cm), and the estimated
accuracy of the tracking system is around 30 cm
• at a sampling frequency of 50 Hz, corresponding to a measurement
every 20 milliseconds (ms)

7. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Data (ii)
• The final set X(t), is made of 505, 291 time instants in CS1, 520, 782
in CS2 and 435, 084 in CS3.
• Time instants are not evenly spaced, so we denote with T(t) the
actual time corresponding to instant t.
The measurements made at instant t contains the following information:
• The vector of the position for the i-th player along the x− and the
y− axis, denoted as Pi (t) = [px
i (t), py
i (t)] (superscript x and y are
used, respectively, for court length and court width);
• The vector of the velocity for the i-th player along the x− and the
y− axis, denoted as Vi (t) = [vx
i (t), vy
i (t)] , measured in km/h.
• The speed of player i in the court at time t, where ζt is the set of
players in the court at time t:
Si (t) =
Vi (t)Vi (t), i ∈ ζt
0, i ∈ ζt ;

8. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Filtering Procedure (i)
Figure: Flow chart representing the criteria used in the procedure.
Criteria are based on the positioning in FIBA court

9. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Filtering procedure (ii)
Let xt be the generic row of X(t) containing the measurements of all the
players at time t:
• Criterion A labels as inactive all the rows xt when the number of
players inside the court is different from 5
• Criterion B detects as inactive the rows xt when a player is shooting a
free-throw (FT), by considering when his position on the court lies
in the circle Cr of radius r = 1.80m centred on the FT area center
• Criterion C detects as inactive the rows xt when all the five players’
speed is below a given threshold ¯Smin
, for a period Tspd
i (t) of length
equal or larger than ¯Tspd

10. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Tuning parameters ¯Smin
and ¯Tspd
• The filtering procedure involves the determination of parameters ¯Tft
,
¯Smin
and ¯Tspd
. Different values for these parameters lead to a
different reduced set Xr(t) and to a different filtered game length
• We let ¯Tft
to be equal to 10 seconds
• We could search for ¯Smin
and ¯Tspd
with a objective function based
on game length (i.e. length as close as possible to 40 minutes)
30
35
40
45
50
3133
34
36
37
38
39
40
41
42
43
44
45
47
48
49
50
1.0 1.5 2.0 2.5 3.0 3.5 4.0
8.0
8.5
9.0
9.5
10.0
10.5
11.0
Sec
Km/h
Figure: CS1
25
30
35
40
45
50
29
31
32
35
36
37
38
39
40
41
42
43
44
45
46
1.0 1.5 2.0 2.5 3.0 3.5 4.0
8.0
8.5
9.0
9.5
10.0
10.5
11.0
Sec
Km/h
Figure: CS2
25
30
35
40
45
2729
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
46
1.0 1.5 2.0 2.5 3.0 3.5 4.0
8.0
8.5
9.0
9.5
10.0
10.5
11.0
Sec
Km/h
Figure: CS3
Figure: Filtered game length (in minutes) subject to different
parameters’ ¯Smin
[km/h, y-axis] and ¯Tspd
[s, x-axis] combinations.

11. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Tuning parameters with
Pseudo-ROC curves using a
ground truth
• The drawback of the tuning strategy is the lack of verification
against a ground truth
• We overcome this shortcoming by manually extracting the ground
truth by means of a video-based annotation of the games, and
• by developing a performance evaluation method - that we will call
“Pseudo ROC” - to tune the parameters according to the ground
truth

12. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Video-based annotation
We retrieve active and inactive moments by doing a video analysis:
1 We watch the streaming of the game
2 In the meantime, we take trace of the active/inactive moments
3 At the end, we save the final report in .csv
action sec active
play 1 1
stop 5 0
play 13 1
stop 47 0

13. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
The “Pseudo ROC” method (i)
• ˜X(˜t): set of measurements obtained from X(t) by aggregating t at a
frequency of 1 second (˜t)
• Y (˜t): variable assuming value 1 if, according to the video report, the
game is active at second ˜t, 0 otherwise
• for a given ¯Smin
and ¯Tspd
combination, ˆY (˜t): variable assuming
value 1 in ˜t if the majority of the observations xt corresponding to
that ˜t was labelled as active by our procedure, 0 otherwise
• we define, accordingly, true positives - TP(˜t), true negatives - TN(˜t),
false positives - FP(˜t), false negatives - FN(˜t).
sensitivity and specificity are computed, respectively, as:
W = ˜t
TP(˜t)
˜t
TP(˜t)+
˜t
FN(˜t)
; Z = ˜t
TN(˜t)
˜t
TN(˜t)+
˜t
FP(˜t)
we measure the performance of our procedure by evaluating the Area under
the curve (AUC) in terms of W and Z varying at different ¯Smin
and ¯Tspd
values used as thresholds.

14. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
The “Pseudo ROC” method (ii)
For a given ¯Smin
,
• PROC¯Tspd |¯Smin
: the ROC curve
• PAUC¯Tspd |¯Smin
: the corresponding AUC computed for ¯Tspd
varying at
a sequence of threshold values in [0,20].
PAUC¯Tspd |¯Smin
is computed for the ¯Smin
in a sequence of values in [0,20].
1 We let ς be the value of ¯Smin
such that
ς = argmax
¯Smin
(PAUC¯Tspd |¯Smin
)
2 Adopting the Youden index criteria (Fluss et al., 2005), for the
chosen ς, we let τ be the value of ¯Tspd
such that
τ = argmax
¯Tspd
Φ(ς, ¯Tspd
)
where Φ = W − 1 + Z

15. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Find ¯Smin
0.500.600.700.80
S^min
PAUC_T^spd|S^min
0.25 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.75 12 13 14 15 16 17 18 19 20
Figure: Pattern of PAUC¯Tspd |¯Smin
as a function of ¯Smin
. CS1 (solid
line), CS2 (dotted line) and CS3 (longdash line).
Examples of PROC curves for some selected values of ¯Smin

16. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Find ¯Tspd
0.20.30.40.5
T^spd
W−1+Z
0.25 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.75 12 13 14 15 16 17 18 19 20
Figure: Pattern of Φ(ς, ¯Tspd
) as a function of ¯Tspd
. CS1 (ς= 9.25,
solid line), CS2 (ς= 8.5, dotted line) and CS3 (ς= 8.5, longdash line).

17. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Conclusions
• When the information on breaks and pauses during the game is
missing, analysts need for an automatic procedure to filter out
inactive moments.
• The proposed tuning strategy benefits from the usage of a “ground
truth” coming from a video analysis and from the development of a
performance evaluation method similar to Receiving Operation
Characteristic curves.
• The identified values for the parameters has been found to be
consistent along different case studies.
• The procedure, along with the identified values may helps basketball
experts who want to analyse tracked data without watching the
video of the game.
• Future works aims to develop a similar automatic procedure to split
the game in offensive and defensive actions using the same sensor
tracked data.

18. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
Acknowledgements
Big & Open Data Innovation (BODaI) laboratory BODaI
Big Data analytics in Sports (BDS) laboratory BDS

19. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
The Context
Data &
Methods
Results
Conclusions
Acknowledgm.
& References
References
1 D’Amour, A., Cervone, D., Bornn, L. & Goldsberry, K. (2015), Move or die: How ball movement
creates open shots in the nba, MIT Sloan Sports Analytics Conference
2 Fluss, R., Faraggi, D. & Reiser, B. (2005), Estimation of the youden index and its associated cutoff
point, Biometrical Journal: Journal of Mathematical Methods in Biosciences 47(4), 458-472
3 Franks, A., Miller, A., Bornn, L., & Goldsberry, K. (2015), Counterpoints: Advanced defensive
metrics for nba basketball. In 9th Annual MIT Sloan Sports Analytics Conference, Boston, MA.
4 Krzanowski, W. J. & Hand, D. J. (2009), ROC curves for continuous data, Chapman and Hall/CRC
5 Kubatko, J., Oliver, D., Pelton, K., & Rosenbaum, D. T. (2007), A starting point for analyzing
basketball statistics. Journal of Quantitative Analysis in Sports, vol. 3(3)
6 Metulini, R. (2017) Filtering procedures for sensor data in basketball. Statistics&Applications 15(2).
7 Metulini, R. (2018), Players movements and team shooting performance: a data mining approach for
basketball, in 49th Scientific meeting of the Italian Statistical Society SIS2018 proceedings
8 Metulini, R., Manisera, M. & Zuccolotto, P. (2018), Modelling the dynamic pattern of surface area
in basketball and its effects on team performance, Journal of Quantitative Analysis in Sports 14(3),
117-130.
9 Miller, A. C. & Bornn, L. (2017), Possession sketches: Mapping NBA strategies, MIT Sloan Sports
Analytics Conference 2017
10 Oliver, D. (2004), Basketball on paper: rules and tools for performance analysis. Potomac Books,
Inc.
11 Wu, S. & Bornn, L. (2017), Modeling offensive player movement in professional basketball, The
American Statistician 72(1), 72-79.
12 Zuccolotto, P., Manisera, M., & Sandri (2018), M. Big data analytics for modeling scoring
probability in basketball: The effect of shooting under high-pressure conditions. International Journal
of Sports Science & Coaching, vol. 13(4), pp. 569-589.

20. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
Supplemental
Criterion A
if |ζt | = 5 − > label xt as inactive
else − > label xt as active, where | · | denotes cardinality.
Criterion B
if ∃i ∈ ζt : Pi (t) ∈ Cr & Tft
i (t) ≥ ¯Tft
− > label xt as inactive
else − > label xt as active
where Tft
i (t) =
0 if Pi (t) ∈ Cr
∞
j=1
Ii (t − j) + Ii (t + j) if Pi (t) ∈ Cr ;
Ii (t − j) =
T(t − j + 1) - T(t − j) if Pi (t − j) ∈ Cr &
j
h=1
Ii (t − h) = T(t) - T(t − j)
0 otherwise;
Ii (t + j) =
T(t + j) - T(t + j − 1) if Pi (t + j) ∈ Cr &
j
h=1
Ii (t + h) = T(t + j) - T(t)
0 otherwise.
Criterion C
if ∀i ∈ ζt Si (t) ≤ ¯Smin
& T
spd
i
(t) ≥ ¯Tspd
− > label xt as inactive
else − > label xt as active
where T
spd
i
(t) =
0 if Si (t) > ¯Smin
∞
j=1
Ii (t − j) + Ii (t + j) if Si (t) ≤ ¯Smin
;
Ii (t − j) =
T(t − j + 1) - T(t − j) if Si (t − j) ≤ ¯Smin
&
j
h=1
Ii (t − h) = T(t) - T(t − j)
0 otherwise;
Ii (t + j) =
T(t + j) - T(t + j − 1) if Si (t + j) ≤ ¯Smin
&
j
h=1
Ii (t + h) = T(t + j) - T(t)
0 otherwise.
Back to Filtering Procedure

21. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
Supplemental
Figure: PROC¯Tspd |¯Smin
for selected values
of ¯Smin
. ¯Smin
=0.25, 5, 9.25 and 15 (dashed
line, dotted line, solid line and dotdash line,
respectively). CS1.
Figure: PROC¯Tspd |¯Smin
for selected values
of ¯Smin
. ¯Smin
=0.25, 5, 8.5 and 15 (dashed line,
dotted line, solid line and dotdash line,
respectively). CS2.
Figure: PROC¯Tspd |¯Smin
for selected values
of ¯Smin
. ¯Smin
=0.25, 5, 8.5 and 15 (dashed line,
dotted line, solid line and dotdash line,
respectively). CS3.
Back to Find ¯Smin

22. Detecting
moments
using sensor
tracked data
Metulini,
Facchinetti,
Zuccolotto
Supplemental
(0,0)
(-15,-8)
(15,8)
X
Y
(-9.2,0) (9.2,0)
r=1.8
Figure: International Basketball Federation (FIBA) court with
relevant measures annotated.
Back to Filtering procedure