BayesBball

I am making a dashboard in shiny that will input my free throws and update my free throw true shooting percentage using bayesian statistics.

Problem of Interest

Why are we doing this study?

define RV of interest: number of free throws made out of 10 define the parameter of interest: free throw true shooting percentage assumptions: we have to assume independence of each free throw. In reality, when you make five in a row, your confidence increases and will affect the next shots.

Define Model

  Prior Probability Distribution: $$ \pi(\theta) ~ Beta(\alpha, \beta) $$

note: LATEX doesn’t work so insert pictures instead

My best guess for theta (shooting percentage) is E(theta) = 0.7. Therefore, alpha should be bigger than beta. Because my guess is that 95% of the time I will get between 0.5 to 0.9, my standard deviation will be about 0.2 (as alpha and beta get bigger, variance decreases).

INSERT PICTURE OF BETA DISTRIBUTION WITH 95% including 0.5 to 0.9

Derive the Posterior Distribution

Apply to Problem of Interest

Make decisions baded on posterior summarize posterior dist to help