NBA Court Real Estate

The Value of Positioning and Spacing

Dan Cervone
New York University
dcervone@nyu.edu

JSM 2016
Chicago, IL
August 3, 2016

The basketball court is a real estate market

Space is a valuable commodity in basketball.

During a possession:

  • Players own (occupy) different court space.
  • Players compete for space.
  • Through movement, players exchange space.

The basketball court is a real estate market

How do we quantify:

  • Which space is most important? And to whom?
  • Who has the upper hand in the battle over floor space?
  • How do different teams/players value space differently?
  • Impact of personnel, matchups on court spacing.

nyc_map

NBA optical tracking data

NBA Optical Tracking Data

SportVu player-tracking data:

  • In all 29 arenas since 2013.
  • 2D locations of all players, 3D location of the ball at 25Hz.
  • Event annotations (passes, shots, fouls, etc.).
  • Each season is about a billion spatiotemporal observations.

Who's got the most valuable property?


Player's real estate investment portfolio value:

  • Who the player is
  • Where he is
  • How open he is, what space he controls

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What space does a player control?

“Weighted Voronoi” model for real estate portfolios:

  • Players own their exact location
  • “Invested” in other areas they're close to
  • No investment in areas another player is closer to

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Weighted Voronoi details

Specifically: divide the court into \( M \) equally sized cells

  • \( w^i_j(t) = \text{dist}(\text{player } i, \text{cell } j)^2 \) at time \( t \).

  • \( x_j^i(t) \) gives player \( i \)'s investiment in cell \( j \) at time \( t \):

    \[ x^i_j(t) = \begin{cases} \frac{1}{1 + w^i_j(t)} & i = \text{argmin}_h w^h_j(t) \\ 0 & \text{otherwise} \end{cases} \]

  • \( \beta \in \mathbb{R}^M \), where \( \beta_j \) is price/value of region \( j \)

  • \( X^i(t) \) row vector, entry \( j \) is \( x^i_j(t) \).

  • \( X^i(t) \beta \) is the total property value of player \( i \) at time \( t \)

Dominant regions

“Dominant regions” generalize Voronoi partitions

  • \( s^i_j(t) = \) minimum possible time for player \( i \) to reach cell \( j \) at time \( t \).
  • calculated using inferred dynamics data and physical motion assumptions
  • computationally expensive.

Nakanishi, R. et al. “An Approximate Computation of the Dominant Region Diagram for the Real-Time Analysis of Group Behaviors.” RoboCup 2009, from Lecture Notes in Computer Science, 2010.

Inferring court property values


Idea: Passes move the ball to more valuable real estate

  • Player C passes to player A
  • Player A's portfolio value \( > \) player C's
  • We can infer value of every piece of court space using passing data


vor2

Inferring court property values


Idea: Passes move the ball to more valuable real estate

  • Player C passes to player A
  • Player A's portfolio value \( > \) player C's
  • We can infer value of every piece of court space using passing data
Massey, C., and Thaler, R. “The Loser’s curse: overconfidence vs. market efficiency in the national football league draft.” NBER Working Paper W11270, 2006.


wvor2

Inferring court property values

\( \beta \) is estimated using a penalized Plackett-Luce model.

  • \( P(i \rightarrow j | i \rightarrow j \text{ or } j \rightarrow i) \propto \exp(X^j(t)\beta) \)
  • \[ \begin{align} L_{\lambda}(\beta) =& \Bigg[ \sum_{i, j} \sum_{t : \text{pass } i \rightarrow j} X^j(t)\beta - \log\Big( \exp \big(X^i(t)\beta \big) + \exp \big( X^j(t)\beta \big) \Big) \Bigg] \\ & \hspace{4cm} - \frac{1}{2}\lambda ||\beta||_2^2 \\ & \text{subject to } \beta_m \geq 0 \text{ for all } m. \end{align} \]
  • Easy and fast inference using R's glmnet.
Friedman, J. et al. “glmnet: Lasso and elastic-net regularized generalized linear models.” R package version 1, 2009.

Inferring court property values

Player- (team-) specific property values (\( \beta + \alpha^i \))

\[ \begin{align} L_{\lambda_1, \lambda_2}(\beta, \alpha^1, \ldots, \alpha^K) = & \\ & \hspace{-6cm} \Bigg[ \sum_{i, j} \sum_{t : \text{pass } i \rightarrow j} X^j(t)(\beta + \alpha^j) - \log\Big( \exp \big(X^i(t)(\beta + \alpha^i) \big) + \exp \big( X^j(t)(\beta + \alpha^j) \big) \Big) \Bigg] \nonumber \\ & \hspace{2cm} - \frac{1}{2}\lambda_1 ||\beta||_2^2 - \frac{1}{2}\lambda_2 \sum_i ||\alpha^i||_2^2 \\ & \text{ subject to } \beta_k \geq 0, \: k=1, \ldots, M. \nonumber \end{align} \]

  • \( \alpha^i, i = 1, \ldots K \) represent player or team effects.

Real estate value maps

Team real estate value maps

Player real estate maps

Possession views

NBA Optical Tracking Data



The more red/blue an offensive/defensive player's cell is, the higher the value of his court space portfolio.

Spacing metrics

Warriors 2014-15

Player Player PV on-ball Player PV off-ball Teammate PV on-ball
Marreese Speights 2.46 2.29 8.51
David Lee 2.07 1.97 8.42
Andrew Bogut 1.91 1.95 8.56
Draymond Green 1.89 1.89 8.55
Harrison Barnes 1.87 2.46 8.34
Klay Thompson 1.81 2.36 8.50
Leandro Barbosa 1.52 2.24 8.38
Shaun Livingston 1.47 1.91 8.51
Andre Iguodala 1.41 2.30 8.50
Stephen Curry 1.03 1.78 8.54
  • Player PV on-ball: Players' average portfolio value when ballcarrier.
  • Player PV off-ball: Players' avg. portfolio value when NOT ballcarrier.
  • Teammate PV on-ball: Teammates' avg. portfolio value when player is ballcarrier.

Spacing metrics

Cavaliers 2014-15

Player Player PV on-ball Player PV off-ball Teammate PV on-ball
Kevin Love 2.46 2.34 8.65
Timofey Mozgov 2.33 2.22 8.71
Shawn Marion 2.06 2.39 8.72
Tristan Thompson 2.03 2.05 8.76
J.R. Smith 1.89 2.42 8.66
Dion Waiters 1.85 2.50 8.65
LeBron James 1.80 1.99 8.73
Iman Shumpert 1.69 2.46 8.65
Kyrie Irving 1.38 2.01 8.84
Matthew Dellavedova 1.25 2.06 8.59
  • Player PV on-ball: Players' average portfolio value when ballcarrier.
  • Player PV off-ball: Players' avg. portfolio value when NOT ballcarrier.
  • Teammate PV on-ball: Teammates' avg. portfolio value when player is ballcarrier.

Thank you

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  • Andrew Miller
  • Luke Bornn
  • Alex Franks
  • Alex D'Amour
  • Kirk Goldsberry
     
  • Moore/Sloan foundations