C. Armero i Cervera, G. Calvo, C. Armero, L. Spezia
A basketball player or team has a hot hand when they perform better than expected over a given period of time or have a streak of consecutive made shots.
We present a Bayesian longitudinal hidden Markov model that examines that phenomenon in a team's performance across different games of a season. The modelling includes a hidden and an observable process in each match. The hidden part is a hidden Markov chain with two states, cold and hot. The observable process uses a longitudinal Bernoulli model to evaluate the success or failure of shots at the basket. Probabilities of the success of each shot depending on the state (cold or hot) of the team are modelled via a mixed logistic regression model.
This model is applied to the matches of the Miami Heat team of the 2005-06 NBA season. Posterior distribution for sojourn times, occupancy times, transition probabilities, the stationary probability of being in a cold of hot state, or the probability of making a shot are discussed.
Keywords: Bayesian logistic regression mixed models; Discrete Markov chains; US National Basketball Association
Scheduled
Bayesian Methods I
November 8, 2023 4:00 PM
HC4: Sacristía Room