Pathway Analytics
  • Introduction
  • Blog
    • MMM Showdown: Google Meridian vs. PyMC Marketing
    • Drop Line Charts - Use Process Behavior Charts Instead!
    • Create a GitBook Data Science Portfolio
    • 5 Reasons I Chose Johns Hopkins Online AI Masters Program
  • Statistics
    • Google Lightweight MMM
    • Propensity Score Matching
    • Thompson Sampling
    • Basketball Free Throw Percentage App
  • Deep Learning
    • Classifying Medical Abstract Sentences
    • Predicting Bitcoin Prices
    • Food Image Classifying
  • Supervised Learning
    • Waiter Tips Multivariate Regression
    • Sleep Cycle - Analyzing My Own Sleep Data
  • Unsupervised Learning
    • Customer Segmentation using KMeans
    • Time Series Clustering
  • Dashboards, Reports, and Visualizations
    • Shiny Useful Code
    • R Markdown Reports
  • Mini Notes
    • Useful SQL Code
    • Testing Code
    • Correlation Plots
    • Docker - Jupyter Lab and R Studio Setup
    • Tensorflow GPU Setup
    • Object Oriented Programming
    • R and Python Together using Reticulate
    • Random Forests are Versatile
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On this page
  • Problem of Interest
  • Define Model
  • Derive the Posterior Distribution
  • Apply to Problem of Interest
  1. Statistics

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

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Last updated 3 years ago