A New Way to Evaluate NBA Player’s Decision Making

I have recently read a fascinating research paper on Predicting Points and Valuing Decisions in Real Time with NBA Optical Tracking Data. This blog presents an overview of it.

Let’s get started!


The result of a basketball game is an ensemble of a lot of decisions. Some decisions contribute to the winning cause, while some not so much.

As each of these decisions plays their part in determining the result of the game, there needs to be a proper mechanism to estimate their contribution to the result of the game.

Let’s discuss this in a little bit more detail…

The Problem with the Current Business Analytics

Up until now, most of the metrics employed in the game of basketball focused on the events that occur at or near the end of a possession, such as points, turnovers, and assists.
There is no metric system that provides a way to account for the decisions that players make during the course of a possession.

In simple words, up until now, there is no way to evaluate the decisions that occur when the player has possession of the ball. These include the decision to pass, dribble, shoot, or to move left and right.

The Solution

EPV (Expected Possession Value) provides a way to solve that problem.

EPV, with the help of a model, assigns a point value to every tactical option available to the player at each moment of a possession. This allows analysts to evaluate each decision that a player makes.

For example, passing to a wide open shooter in the corner is worth more EPV than to a covered player in a similar place.

Diagram of EPV as a weight average of the values of the ballcarrier’s decisions and the probability of making each decision.

EPV thus opens new doors for a multitude of opportunities for the players to get better in their respective roles.

EPV (Expected Possession Value)

EPV is defined as the number of points the offense (current decision) is expected to score by the end of the possession, given everything we know now.

Points: The currency of the NBA.
Expected: On average, with “luck” removed.
Everything: Full resolution spatial information.
Now: Any moment in time.

EPV takes help of the player-tracking data to assign a point value to each moment of a possession.

Computing EPV with a Possession Model

EPV is a conditional expectation of the number of points that the offense is expected to score, given the spatial configuration of the players and the ball at time t (d(t)).

EPV = E[points | d(t)]

By definition, the current EPV of a possession is the weighted average of the outcomes of all the future paths that the possession could take.

This requires a model that provides a probability distribution over what the ball-handler is likely to do next, given the spatial configuration of the players involved in the game.
This model is called as the Possession Model.

The possession model breaks down a player’s options into 2 categories:
1. Macro-transitions: The discrete actions that may take several seconds to complete (eg. passing or shooting).
2. Micro-transitions: The continuous actions that evolve instantaneously (eg. moving to the left or right).

Using this division, EPV can be re-written as the sum of macro and micro-transitions.

The Possession Stock Ticker

EPV can also be viewed as the share price of a publicly traded company. Because much like the share price, the EPV of a possession responds dramatically to major events (a pass or a shot attempt), while remaining steady for the rest of the time.

EPV throughout the Spurs’ final possession, with annotations of major events.

Introducing EPVmetrics

EPV derives a number of metrics that help provide precise answers to a number of fundamental basketball questions. Some of them are listed below:

1. Comparing an individual player with the league-average player

EPV can be used to collapse all of a player’s actions onto a single interpretable scale.
This value (of a particular player) can then be compared with the EPV of the league-average player, formed by combining every other player’s decision tendencies (given the same situation).

This quantification is provided by replacement-level EPV or EPVr.

2. Identifying the “selfish” shooters

EPV can also be used to quantify the value that an individual brings to a team. This can be used to segregate the players into 2 categories:

1. Players who care more about their personal point totals.
2. Players who focus more on the team’s performance.

The first category of players is labelled as “selfish” shooters.

This category of players is identified by calculating player’s shot satisfaction.

Shot Satisfaction = Σ (EPV(t) - E[points | pass in (t, t+ε], d(t)])

Thus, shot satisfaction quantifies the value of shot attempts relative to the passing options.
This is calculated by subtracting EPV conditional on a pass having happened from the EPV conditional on a shot, at every time t (when a certain player takes a shot).

That’s all about it!

If you want to dig a little deeper into the details, then feel free to read the whole paper yourself or check out other interesting papers on PapersWeLove.org.

Getting into the crypto space.