Basketball Free Throw Percentage App

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

See this link: shinyapps.io/BayesBball

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

Likelihood: f(x|theta) ~ Binomial

Derive the Posterior Distribution

Posterior: pi(theta|x) ~ Beta(x + alpha, n - x + beta)

Apply to Problem of Interest

Make decisions baded on posterior summarize posterior dist to help