{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(putting_workflow)=\n", "# Model building and expansion for golf putting\n", "\n", ":::{post} Apr 2, 2022\n", ":tags: Bayesian workflow, model expansion, sports \n", ":category: intermediate, how-to\n", ":author: Colin Carroll, Marco Gorelli, Oriol Abril-Pla\n", ":::\n", "\n", "**This uses and closely follows [the case study from Andrew Gelman](https://mc-stan.org/users/documentation/case-studies/golf.html), written in Stan. There are some new visualizations and we steered away from using improper priors, but much credit to him and to the Stan group for the wonderful case study and software.**\n", "\n", "We use a data set from \"Statistics: A Bayesian Perspective\" {cite:p}berry1996statistics. The dataset describes the outcome of professional golfers putting from a number of distances, and is small enough that we can just print and load it inline, instead of doing any special csv reading.\n", "\n", ":::{include} ../extra_installs.md\n", ":::" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import io\n", "\n", "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import pymc as pm\n", "import pytensor.tensor as pt\n", "import scipy\n", "import scipy.stats as st\n", "import xarray as xr\n", "\n", "from xarray_einstats.stats import XrContinuousRV" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "RANDOM_SEED = 8927\n", "az.style.use(\"arviz-darkgrid\")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# golf putting data from berry (1996)\n", "golf_data = \"\"\"distance tries successes\n", "2 1443 1346\n", "3 694 577\n", "4 455 337\n", "5 353 208\n", "6 272 149\n", "7 256 136\n", "8 240 111\n", "9 217 69\n", "10 200 67\n", "11 237 75\n", "12 202 52\n", "13 192 46\n", "14 174 54\n", "15 167 28\n", "16 201 27\n", "17 195 31\n", "18 191 33\n", "19 147 20\n", "20 152 24\"\"\"\n", "\n", "\n", "golf_data = pd.read_csv(io.StringIO(golf_data), sep=\" \", dtype={\"distance\": \"float\"})\n", "\n", "BALL_RADIUS = (1.68 / 2) / 12\n", "CUP_RADIUS = (4.25 / 2) / 12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start plotting the data to get a better idea of how it looks. The hidden cell contains the plotting code" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "def plot_golf_data(golf_data, ax=None, color=\"C0\"):\n", " \"\"\"Utility function to standardize a pretty plotting of the golf data.\"\"\"\n", " if ax is None:\n", " _, ax = plt.subplots()\n", " bg_color = ax.get_facecolor()\n", " rv = st.beta(golf_data.successes, golf_data.tries - golf_data.successes)\n", " ax.vlines(golf_data.distance, *rv.interval(0.68), label=None, color=color)\n", " ax.plot(\n", " golf_data.distance,\n", " golf_data.successes / golf_data.tries,\n", " \"o\",\n", " mec=color,\n", " mfc=bg_color,\n", " label=None,\n", " )\n", "\n", " ax.set_xlabel(\"Distance from hole\")\n", " ax.set_ylabel(\"Percent of putts made\")\n", " ax.set_ylim(bottom=0, top=1)\n", "\n", " ax.set_xlim(left=0)\n", " ax.grid(True, axis=\"y\", alpha=0.7)\n", " return ax" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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