This is a review of the NBA research conducted by Joseph Kuehn applying event tree models and conditional probability.
A key to the success of any NBA team is the ability to put together a lineup of players who work well together. Success depends on the whole being better than the parts. In this research, a framework is developed to determine the value an individual player contributes to a particular lineup as well as which players help their teammates’ production and which hurt their production.
Play-by-play data incorporated included the 250 players with the greatest number of possessions from the 2014-2015 NBA season, including all 10 players on the court and a detailed result of the possession. A basketball game is modeled as a series of possessions with each possession being a series of events, which have the potential to gain points for the offensive team. Each possession is represented on an event tree model. The event tree model uses probabilities for each action taken by each of the offensive players on the court to calculate the expected number of points associated with each action and the expected number of points for each possession. This demonstrates how the probabilities of particular actions taken by a team affect the expected number of points per possession.
Conditional probability is used to model individual players taking into account the player, his teammates, opposing players, and the particular event. In the first step, the maximum possibility is used to map observed probabilities into three player scores, which measure the player’s tendency to accomplish an event, the player’s effect on teammates’ abilities to accomplish an event and the player’s defensive effect on his opponents. A least-square approach is used to match the scores created in step one with a player’s rating is utilized in the second step.
Substitute players can be inserted in a lineup using the above probabilities to determine what effect that player has on the lineup. Different strategies can also be substituted for other plays to determine the effect that has on the expected outcome of the possession.
The player model also provides information to let coaches and analysts know which actions players have a tendency to fall back on in any given situation, the probability they make or miss a shot from a particular location and the probability they get an offensive rebound from a missed shot from a particular location. Defensive player ratings tell coaches how a player affects the probability of the actions taken by the opponent in these situations.
Coaches can use this information in putting together lineups of teammates who complement each other, increasing their effectiveness both offensively and defensively. Players that are not as highly skilled as others often play to a higher level when put on lines that work to their strengths. Highly skilled players can play below their capabilities when paired with non-complement teammates. This knowledge enables coaches to put together the strongest line-ups possible, building on their players’ strengths and minimizing weaknesses. Coaches and analysts, when evaluating individual players, can also use this information. It is important to assess the individual for their own abilities and not those gained while working with their teammates. The abilities of the individual player will be transferred to a new team while skills gained from working with particular teammates will not be transferable. Players can be evaluated as to whether they increase or decrease their teammates’ expected points. All of this allows better trade and draft decisions.
Analytics Used: Event Tree Model, Conditional Probability, Least Squares
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