The Problem of Shot Selection in Basketball

  title={The Problem of Shot Selection in Basketball},
  author={Brian Skinner},
  journal={PLoS ONE},
In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this article, I explore the question of when a team should shoot and when they should pass up the shot by considering a simple theoretical model of the shot selection process, in which the quality of shot opportunities generated by the offense is assumed to fall randomly within a uniform distribution. Within this model I derive an answer to the question… 

Figures from this paper

Towards a Decision Quality Model for Shot Selection in Basketball: an Exploratory Study

Light is cast on the actual weights (validities) of the different cues involved in predicting outcomes of shooting decisions in basketball to help coaches provide objective feedback about players’ shooting performance beyond hit percentages.

Optimizing the best play in basketball using deep learning

Deep learning was applied to optimize the best offensive play in a game scenario for a given set of features to predict the highest probability of a made shot in a close game of basketball.

Crunch time in the NBA – The effectiveness of different play types in the endgame of close matches in professional basketball

In professional basketball, the final few possessions often determine the result of a game. The coach’s decision on tactics may be critical to a team’s win or loss. This study investigated offense

A Bayesian marked spatial point processes model for basketball shot chart

A Bayesian joint model for the mark and the intensity of marked point processes, where the intensity is incorporated in the mark model as a covariate is proposed, which suggests that the field goal percentage and the shot intensity are positively associated for a majority of the players.

Star Players in the NBA - Decoys or Game-Changers?

In the National Basketball Association (NBA), when an attacking team is trailing by a small margin in the last seconds of a game, the coach has to make a critical decision: should he or she design a

Transition Tensor Markov Decision Processes: Analyzing Shot Policies in Professional Basketball

This paper derives the dynamics of the team-average process such that the expected transition count for an arbitrary state-pair is equal to the weighted sum of the expected counts of the separate lineup-specific MDPs using a novel transition weighting scheme.

A Bayesian Joint Model for Spatial Point Processes with Application to Basketball Shot Chart

The success rate of a basketball shot may be higher at locations where a player makes more shots. In a marked spatial point process model, this means that the marks are dependent on the intensity of

Optimal Strategy in Basketball

This book chapter reviews some of the major principles associated with optimal strategy in basketball. In particular, we consider the principles of allocative efficiency (optimal allocation of shots

Markov decision processes with dynamic transition probabilities: An analysis of shooting strategies in basketball

This paper combines lineup-specific non-stationary Markov decision processes into team-average MDPs using a novel transition weighting scheme to enable computational feasibility and discusses the game-theoretic ramifications of testing alternative decision policies.


In this paper we model basketball plays as episodes from teamspecific non-stationary Markov decision processes (MDPs) with shot clock dependent transition probabilities. Bayesian hierarchical models



The hot hand in basketball: On the misperception of random sequences

Generality of the matching law as a descriptor of shot selection in basketball.

Shot-selection matching varied systematically for players who were members of successful versus unsuccessful teams, competed at different levels of collegiate play, and served as regulars versus substitutes, suggesting that the matching law is a robust descriptor of basketball shot selection, although the mechanism that produces matching is unknown.

The Price of Anarchy in Basketball

Optimizing the performance of a basketball offense may be viewed as a network problem, wherein each play represents a “pathway" through which the ball and players may move from origin (the in-bounds

The hot hand exists in volleyball and is used for allocation decisions.

It is concluded that for volleyball the hot hand exists, coaches and playmaker are able to detect it, and playmakers tend to use it "adaptively," which results in more hits for a team.

Allocative and Dynamic Efficiency in NBA Decision Making

This paper examines the optimality of the shooting decisions of National Basketball Association (NBA) players using a rich data set of shot outcomes. The decision to shoot is a complex problem that

A Starting Point for Analyzing Basketball Statistics

The aim of this paper is to bring to a peer-reviewed journal the generally accepted basics of the analysis of basketball, thereby providing a common starting point for future research in basketball.

Understanding baseball team standings and streaks

Can one understand the statistics of wins and losses of baseball teams? Are their consecutive-game winning and losing streaks self-reinforcing or can they be described statistically? We apply the

Basketball on Paper: Rules and Tools for Performance Analysis

Journey "inside the numbers" for an exceptional set of statistical tools and rules that can help explain the winning, or losing, ways of a basketball team. Basketball on Paper doesn't diagram plays

Reinforcement learning in professional basketball players

Using the sequences of field goal attempts made by professional basketball players, it is shown that the outcome of even a single field goal attempt has a considerable effect on the rate of subsequent 3 point shot attempts, in line with standard models of reinforcement learning.

Quantifying the Performance of Individual Players in a Team Activity

A network approach is developed that provides a powerful quantification of the contributions of individual players and of overall team performance in the European Cup 2008 soccer tournament.