This is a presentation at the ESPN Hackathon at MIT's Sloan Sports Analytics Conference 2017

1. Measuring the Basketball
Intangibles with Complex Systems
Fractals and Networks
@kpelechrinis

2. Measuring the Intangibles
• Traditional box score cannot measure things such as spacing, screens, box
outs, ball movement, team chemistry etc.
• For some of them there is not even a clear definition and/or need to be manually
measured

3. Ball movement & tracking data
• Static offenses do not generate enough movement for creating open players,
open shots, driving lanes and in general spreading the defense
• Ball movement has traditionally been one of the intangibles in basketball
• Spatial tracking systems allows to automatically track players and the ball

4. How to measure ball movement?
• Definition: A team’s ball movement is the spatial distribution of the ball’s mobility
during its offensive positions
• How can we summarize the distribution of the ball’s mobility in a concrete (ideally a single
number) way?
• While good passing game usually is thought of as good ball movement, the two are not the
same (at least under our definition)
• Key idea: Quantify the dimensionality of the court area covered from the ball
during each offensive possession

5. Dimensionality and Fractals
• Fractal dimension (FD) is a single-value descriptor that can be used to
describe the complexity of a set of points
• Contrary to the topological dimension, FD can take fractional values
• Fine-grained
• Appropriate for comparisons

6. Fractal Ball Dimensionality
• We propose to use the fractal dimensionality of the ball’s trajectory as a descriptor
of the intangible of ball movement
• Ball movement can be intuitively thought of as a self-similar process
• Evaluation? Possibly manual but time-consuming
• Indirect evaluation: good ball movement should produce successful possessions

7. FBD Evaluation
• FBD for all possessions in the data ranges between 0.3 and 1.8
• Logistic regression with DV the success (made FG) or not (missed FG, TO)
of a possession and only IV the FBD of the possession
• -.24 correlation (p-val < 0.1)

8. FBD Evaluation
• Successful possessions exhibited average FBD < 1, while non-successful had
an average FBD >1
• t-test gives a 0.2 difference in dimensionality with p-val 0.054
FBD = 0.62, Made FG2 FBD = 1.33, Missed FG

9. Future Exploration
• Add players locations in the computation of the fractal dimensionality ?
• Spatial entropy ?
• Better evaluation: what about possessions with good ball movement but did
not end up in a field goal?

10. Team Chemistry and Networks
• Why networks for chemistry of a team?
• The value of a system does not only depend on its individual components
• Pencil and diamond are both made of carbon

11. Team Chemistry and Networks
• However, the structure of carbon atoms is different!
• Network structures can lead to systems whose value is greater (or lower) than
the sum of its components
How can we define team chemistry
through networks?

12. Team Chemistry and Networks
• Team chemistry describes the ability of a team to combine the abilities of its
players in the right way
• Cohesiveness has been identified as one of the factors that are associated
with the intangible of team chemistry
• Quantify cohesiveness through passing network

13. Passing Network
• Directed, weighted network where each team player is a node and an edge
from node i to node j represents a pass made from player i to player j
• Edge weight is the number of such passes recorded
• Team chemistry ~ algebraic connectivity λ2 of the passing
network

14. Algebraic Connectivity
• The second smallest eigenvalue of L is the algebraic connectivity of the
network
• Intuition: the higher the value the more robust and coherent the network, that is, the
better the team chemistry
L = D - A
L: network Laplacian
A: adjacency matrix
D: diagonal degree matrix

15. Offense vs Defense
• The passing network of a team can provide intuition about the offensive
chemistry
• Good offensive chemistry à High algebraic connectivity of own passing network
• For defense we can use the opponent’s passing network
• Good defensive chemistry à Low algebraic connectivity of opponent’s passing network

16. Pareto Optimality
• Multi-objective ranking through
Pareto efficiency
• Pareto frontier “zones”
Illustrative data for viz

17. Charlotte @ Sacramento
λ2 = 0.5 λ2 = 0.6

18. Future Exploration
• Control for opponent strength
• Other network metrics – e.g., assortativity
• Can we use “cavity” method to identify “catalyst” and “inhibitor” players in a
team?