metrica.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "AbhishekMetricaData.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "machine_shape": "hm"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KkFlDuzYFaja",
        "colab_type": "text"
      },
      "source": [
        "Import data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rrTirNum9zsa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "away_data = pd.read_csv('https://raw.githubusercontent.com/metrica-sports/sample-data/master/data/Sample_Game_1/Sample_Game_1_RawTrackingData_Away_Team.csv', skiprows=2)\n",
        "home_data = pd.read_csv('https://raw.githubusercontent.com/metrica-sports/sample-data/master/data/Sample_Game_1/Sample_Game_1_RawTrackingData_Home_Team.csv', skiprows=2)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9S0SWVl9Fd_-",
        "colab_type": "text"
      },
      "source": [
        "Reformat into lists indexed by player, e.g. `locs_home[0]` contains locations for player 0 on home team."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KlbLZEqhG_w0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "locs_home = [np.asarray(home_data.iloc[:,range(3 + j*2,3 + j*2 +2)]) * np.array([105,68]) for j in range(14)]\n",
        "locs_away = [np.asarray(away_data.iloc[:,range(3 + j*2,3 + j*2 +2)]) * np.array([105,68]) for j in range(14)]\n",
        "locs_ball = [np.asarray(home_data.iloc[:,range(31,33)]) * np.array([105,68])]\n",
        "t = home_data['Time [s]']"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mvL6dcfO9EQZ",
        "colab_type": "code",
        "outputId": "a4c8d270-f282-4cb7-ffb9-79e101cf05da",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "np.all(np.isfinite(locs_home[0][24000:25000,:]))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C9vQbW8xFscO",
        "colab_type": "text"
      },
      "source": [
        "Influence function as defined in appendix of the paper (I've tried to keep their notation as much as possible)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2r5-59a3_oMF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def influence_function(player_index, location, time_index, home_or_away):\n",
        "  from scipy.stats import multivariate_normal as mvn\n",
        "  if home_or_away == 'h':\n",
        "    data = locs_home.copy()\n",
        "  elif home_or_away == 'a':\n",
        "    data = locs_away.copy()\n",
        "  else:\n",
        "    raise ValueError(\"Enter either 'h' or 'a'.\")\n",
        "    return\n",
        "  if np.all(np.isfinite(data[player_index][[time_index,time_index + 1],:])) & np.all(np.isfinite(locs_ball[0][time_index,:])):\n",
        "    jitter = 1e-10 ## to prevent identically zero covariance matrices when velocity is zero\n",
        "    ## compute velocity by fwd difference\n",
        "    s = np.linalg.norm(data[player_index][time_index + 1,:] - data[player_index][time_index,:] + jitter) / (t[time_index + 1] - t[time_index])\n",
        "    ## velocities in x,y directions\n",
        "    sxy = (data[player_index][time_index + 1,:] - data[player_index][time_index,:] + jitter) / (t[time_index + 1] - t[time_index])\n",
        "    ## angle between velocity vector & x-axis\n",
        "    theta = np.arccos(sxy[0] / np.linalg.norm(sxy))\n",
        "    ## rotation matrix\n",
        "    R = np.array([[np.cos(theta), -np.sin(theta)],[np.sin(theta),np.cos(theta)]])\n",
        "    mu = data[player_index][time_index,:] + sxy * 0.5\n",
        "    Srat = (s / 13) ** 2\n",
        "    Ri = np.linalg.norm(locs_ball[0][time_index,:] - data[player_index][time_index,:])\n",
        "    Ri = np.minimum(4 + Ri**3/ (18**3/6),10) ## don't think this function is specified in the paper but looks close enough to fig 9\n",
        "    S = np.array([[(1 + Srat) * Ri / 2, 0], [0, (1 - Srat) * Ri / 2]])\n",
        "    Sigma = np.matmul(R,S)\n",
        "    Sigma = np.matmul(Sigma,S)\n",
        "    Sigma = np.matmul(Sigma,np.linalg.inv(R)) ## this is not efficient, forgive me.\n",
        "    out = mvn.pdf(location,mu,Sigma) / mvn.pdf(data[player_index][time_index,:],mu,Sigma)\n",
        "  else:\n",
        "    out = np.zeros(location.shape[0])\n",
        "  return out"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kaQV0iezUye-",
        "colab_type": "text"
      },
      "source": [
        "Here's a plot of the pitch control at the 24000th timepoint. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GB-Lxt5O7B1S",
        "colab_type": "code",
        "outputId": "cdc15c11-ea64-4f02-d86d-814466c214dc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "xx,yy = np.meshgrid(np.linspace(0,105,200),np.linspace(0,68,200))\n",
        "Zh = np.zeros(40000)\n",
        "Za = np.zeros(40000)\n",
        "\n",
        "for k in range(11):\n",
        "  Zh += influence_function(k,np.c_[xx.flatten(),yy.flatten()],24000,'h')\n",
        "  Za += influence_function(k,np.c_[xx.flatten(),yy.flatten()],24000,'a')\n",
        "Zh = Zh.reshape((200,200))\n",
        "Za = Za.reshape((200,200))\n",
        "plt.contourf(xx,yy,1 / (1 + np.exp(-Za + Zh)))\n",
        "for k in range(11):\n",
        "  plt.scatter(locs_home[k][24000,0],locs_home[k][24000,1],color='darkgray')\n",
        "  plt.scatter(locs_away[k][24000,0],locs_away[k][24000,1],color='black')\n",
        "plt.scatter(locs_ball[0][24000,0],locs_ball[0][24000,1],color = 'red')\n",
        "plt.colorbar()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.colorbar.Colorbar at 0x7f4f476c2358>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RzIWl28bVALP",
        "colab_type": "text"
      },
      "source": [
        "And, for reference, the locations of the home players (grey), away players (black) & the ball (red). \n",
        "\n",
        "Seems sensible, I think, but quite possibly some mistakes on my end. Guess we'll see what Javi produces over next few days :)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p_5FIBX93MWi",
        "colab_type": "code",
        "outputId": "d91033a9-717e-4dfb-884b-5889c2987637",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 557
        }
      },
      "source": [
        "from IPython.display import HTML\n",
        "import matplotlib.animation as animation\n",
        "\n",
        "fig,ax = plt.subplots()\n",
        "ims= []\n",
        "xx,yy = np.meshgrid(np.linspace(0,105,200),np.linspace(0,68,200))\n",
        "\n",
        "def animate(i):\n",
        "  fr = 23000 + i\n",
        "  Zh = np.zeros(40000)\n",
        "  Za = np.zeros(40000)\n",
        "  for k in range(11):\n",
        "    Zh += influence_function(k,np.c_[xx.flatten(),yy.flatten()],fr,'h')\n",
        "    Za += influence_function(k,np.c_[xx.flatten(),yy.flatten()],fr,'a')\n",
        "  Zh = Zh.reshape((200,200))\n",
        "  Za = Za.reshape((200,200))\n",
        "  im = plt.contourf(xx,yy,1 / (1 + np.exp(-Za + Zh)))\n",
        "\n",
        "  for k in range(11):\n",
        "    plt.scatter(locs_home[k][fr,0],locs_home[k][fr,1],color='darkgray')\n",
        "    plt.scatter(locs_away[k][fr,0],locs_away[k][fr,1],color='black')\n",
        "  plt.scatter(locs_ball[0][fr,0],locs_ball[0][fr,1],color = 'red')\n",
        "\n",
        "HTML(animation.FuncAnimation(fig, animate, frames=1000, interval = 40,repeat=False).to_html5_video())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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          "metadata": {
            "tags": []
          },
          "execution_count": 46
        },
        {
          "output_type": "display_data",
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}