AHL_xG_LinearModel.ipynb

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      "name": "AHL-xG-LinearModel.ipynb",
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      "authorship_tag": "ABX9TyNHMr1Ouwhg8Nmt9vbITp3X",
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      "name": "python3",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/r-wisniewski/xG-LinearModel/blob/main/AHL_xG_LinearModel.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ydtHehAMjYyR"
      },
      "source": [
        "# Acknowledgements\n",
        "\n",
        "This project is heavily based on the linear model found here: https://www.tensorflow.org/tutorials/estimator/linear"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yDoI6m4LQUll",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f073b70e-83e4-4b44-b58c-ed9439d4ddac"
      },
      "source": [
        "%tensorflow_version 2.x\r\n",
        "\r\n",
        "!pip install -q sklearn\r\n",
        "\r\n",
        "#from __future__ import absolute_import, division, print_function, unicode_literals\r\n",
        "\r\n",
        "import tensorflow as tf\r\n",
        "print(tf.version)\r\n",
        "import matplotlib.pyplot as plt # Dataset visualization.\r\n",
        "import numpy as np              # Low-level numerical Python library.\r\n",
        "import pandas as pd             # Higher-level numerical Python library.\r\n",
        "from IPython.display import clear_output"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<module 'tensorflow._api.v2.version' from '/usr/local/lib/python3.6/dist-packages/tensorflow/_api/v2/version/__init__.py'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UQ-PHCkjZpzq"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "# Import scraped data\n",
        "\n",
        "This step imports scraped event data (using ahl_scraper.py) from a csv file. Once imported, the labels and data are separated.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "evL7TpeBZ03k"
      },
      "source": [
        "#import training and test data from csv's\r\n",
        "# training data is from game id's 1017122 to 1020000\r\n",
        "xg_df_train = pd.read_csv('https://github.com/r-wisniewski/xG-LinearModel/raw/main/training.csv')\r\n",
        "# testing data is from game id's 1020001 to 1020558. 1020558 is the latest game we have data for\r\n",
        "xg_df_testing = pd.read_csv('https://github.com/r-wisniewski/xG-LinearModel/raw/main/testing.csv')\r\n",
        "\r\n",
        "# separate the labels and data\r\n",
        "y_train = xg_df_train.pop('Goal')\r\n",
        "y_testing = xg_df_testing.pop('Goal')"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ld_rsVltfW7q"
      },
      "source": [
        "### Check the imported data\n",
        "\n",
        "Let's have a quick look at what data has been imported"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nC9dQWu9fUch",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "outputId": "fdbcda92-d7aa-41f6-8cbd-d53f4cd0a478"
      },
      "source": [
        "#check the first few rows of the training panda dataframe\n",
        "xg_df_train.head()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>XLocation</th>\n",
              "      <th>YLocation</th>\n",
              "      <th>Strength</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>128</td>\n",
              "      <td>29</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>207</td>\n",
              "      <td>122</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>128</td>\n",
              "      <td>225</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>110</td>\n",
              "      <td>94</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>53</td>\n",
              "      <td>174</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            ],
            "text/plain": [
              "   XLocation  YLocation  Strength\n",
              "0        128         29         0\n",
              "1        207        122         0\n",
              "2        128        225         1\n",
              "3        110         94         1\n",
              "4         53        174         1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "72rCvQ73VXyK",
        "outputId": "82dde8a8-37e7-4941-8ee5-3e1b1f3c0e88"
      },
      "source": [
        "# Lets see how the labels are stored\n",
        "y_train.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    False\n",
              "1    False\n",
              "2    False\n",
              "3    False\n",
              "4    False\n",
              "Name: Goal, dtype: bool"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J-666rU9qZHM"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "# Let's train!\n",
        "Now that both the training and test data have been collected, let's train the model!\n",
        "\n",
        "Since all the data is numerical, there is no need to convert any categorical data to numerical. Newer AHL game summaries are beginning to track types of shots, when enough of those game summaries are available we could implement shot type as an additional feature."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CK3Fh8RlrIDW"
      },
      "source": [
        "### Create the input function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TyeZIbiQrNAt"
      },
      "source": [
        "# data_df = all data in table form, label_df = all associated labels in table form\n",
        "def make_input_fn(data_df, label_df, num_epochs=10, shuffle=True, batch_size=32):\n",
        "  def input_function():  # inner function, this will be returned\n",
        "    # Convert the pandas dataframe into a tf.data.Dataset object. We want to convert our pandas \"table\" to this new object type before processing.\n",
        "    ds = tf.data.Dataset.from_tensor_slices((dict(data_df), label_df))  # create tf.data.Dataset object with data and its associated label\n",
        "    if shuffle:\n",
        "      ds = ds.shuffle(1000)  # randomize order of data\n",
        "    ds = ds.batch(batch_size).repeat(num_epochs)  # split dataset into batches of 32 and repeat process for number of epochs\n",
        "    return ds  # return a batch of the dataset\n",
        "  return input_function  ####### return a function object for use ######\n",
        "\n",
        "train_input_fn = make_input_fn(xg_df_train, y_train)  # here we will call the input_function that was returned to us to get a dataset object we can feed to the model\n",
        "eval_input_fn = make_input_fn(xg_df_testing, y_testing, num_epochs=1, shuffle=False) # we aren't training it here anymore so 1 epoch and no shuffling"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xnGKwnjT37uJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c2b981e9-6f81-4ba4-e5d9-598ecbc74268"
      },
      "source": [
        "numeric_columns = ['XLocation', 'YLocation', 'Strength']\n",
        "feature_columns = []\n",
        "for feature_name in numeric_columns:\n",
        "  feature_columns.append(tf.feature_column.numeric_column(feature_name, dtype=tf.float32))\n",
        "\n",
        "# creating a crossed column to correlate \n",
        "x_y = tf.feature_column.crossed_column(['XLocation', 'YLocation'], hash_bucket_size=100)\n",
        "x_cross_y = [x_y]\n",
        "\n",
        "linear_est = tf.estimator.LinearClassifier(feature_columns=feature_columns)\n",
        "\n",
        "linear_est.train(train_input_fn)  # uses the passed function \"train_input_fn\" to grab data and train the model\n",
        "result = linear_est.evaluate(eval_input_fn)  # get model metrics/stats by running the model on testing data\n",
        "\n",
        "# lets see how accurate the model is\n",
        "print(result['accuracy'])\n",
        "print(result) # see what evaluate() returns"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "INFO:tensorflow:Using default config.\n",
            "WARNING:tensorflow:Using temporary folder as model directory: /tmp/tmpxxxhmg2i\n",
            "INFO:tensorflow:Using config: {'_model_dir': '/tmp/tmpxxxhmg2i', '_tf_random_seed': None, '_save_summary_steps': 100, '_save_checkpoints_steps': None, '_save_checkpoints_secs': 600, '_session_config': allow_soft_placement: true\n",
            "graph_options {\n",
            "  rewrite_options {\n",
            "    meta_optimizer_iterations: ONE\n",
            "  }\n",
            "}\n",
            ", '_keep_checkpoint_max': 5, '_keep_checkpoint_every_n_hours': 10000, '_log_step_count_steps': 100, '_train_distribute': None, '_device_fn': None, '_protocol': None, '_eval_distribute': None, '_experimental_distribute': None, '_experimental_max_worker_delay_secs': None, '_session_creation_timeout_secs': 7200, '_checkpoint_save_graph_def': True, '_service': None, '_cluster_spec': ClusterSpec({}), '_task_type': 'worker', '_task_id': 0, '_global_id_in_cluster': 0, '_master': '', '_evaluation_master': '', '_is_chief': True, '_num_ps_replicas': 0, '_num_worker_replicas': 1}\n",
            "INFO:tensorflow:Calling model_fn.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/tensorflow/python/keras/engine/base_layer_v1.py:1727: UserWarning: `layer.add_variable` is deprecated and will be removed in a future version. Please use `layer.add_weight` method instead.\n",
            "  warnings.warn('`layer.add_variable` is deprecated and '\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "INFO:tensorflow:Done calling model_fn.\n",
            "INFO:tensorflow:Create CheckpointSaverHook.\n",
            "INFO:tensorflow:Graph was finalized.\n",
            "INFO:tensorflow:Running local_init_op.\n",
            "INFO:tensorflow:Done running local_init_op.\n",
            "INFO:tensorflow:Calling checkpoint listeners before saving checkpoint 0...\n",
            "INFO:tensorflow:Saving checkpoints for 0 into /tmp/tmpxxxhmg2i/model.ckpt.\n",
            "INFO:tensorflow:Calling checkpoint listeners after saving checkpoint 0...\n",
            "INFO:tensorflow:loss = 0.6931472, step = 0\n",
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            "INFO:tensorflow:loss = 0.14039508, step = 50000 (0.130 sec)\n",
            "INFO:tensorflow:global_step/sec: 888.52\n",
            "INFO:tensorflow:loss = 0.37215933, step = 50100 (0.114 sec)\n",
            "INFO:tensorflow:global_step/sec: 893.401\n",
            "INFO:tensorflow:loss = 0.42823103, step = 50200 (0.112 sec)\n",
            "INFO:tensorflow:global_step/sec: 916.515\n",
            "INFO:tensorflow:loss = 0.26773256, step = 50300 (0.107 sec)\n",
            "INFO:tensorflow:global_step/sec: 866.468\n",
            "INFO:tensorflow:loss = 0.49177995, step = 50400 (0.113 sec)\n",
            "INFO:tensorflow:global_step/sec: 921.428\n",
            "INFO:tensorflow:loss = 0.4268659, step = 50500 (0.112 sec)\n",
            "INFO:tensorflow:global_step/sec: 922.026\n",
            "INFO:tensorflow:loss = 0.4487413, step = 50600 (0.107 sec)\n",
            "INFO:tensorflow:global_step/sec: 882.569\n",
            "INFO:tensorflow:loss = 0.44861972, step = 50700 (0.111 sec)\n",
            "INFO:tensorflow:Calling checkpoint listeners before saving checkpoint 50770...\n",
            "INFO:tensorflow:Saving checkpoints for 50770 into /tmp/tmpxxxhmg2i/model.ckpt.\n",
            "INFO:tensorflow:Calling checkpoint listeners after saving checkpoint 50770...\n",
            "INFO:tensorflow:Loss for final step: 0.28412005.\n",
            "INFO:tensorflow:Calling model_fn.\n",
            "INFO:tensorflow:Done calling model_fn.\n",
            "INFO:tensorflow:Starting evaluation at 2021-01-12T23:26:41Z\n",
            "INFO:tensorflow:Graph was finalized.\n",
            "INFO:tensorflow:Restoring parameters from /tmp/tmpxxxhmg2i/model.ckpt-50770\n",
            "INFO:tensorflow:Running local_init_op.\n",
            "INFO:tensorflow:Done running local_init_op.\n",
            "INFO:tensorflow:Inference Time : 1.48067s\n",
            "INFO:tensorflow:Finished evaluation at 2021-01-12-23:26:43\n",
            "INFO:tensorflow:Saving dict for global step 50770: accuracy = 0.9015764, accuracy_baseline = 0.9015764, auc = 0.6546918, auc_precision_recall = 0.15436137, average_loss = 0.30908287, global_step = 50770, label/mean = 0.09842362, loss = 0.3090817, precision = 0.0, prediction/mean = 0.09221378, recall = 0.0\n",
            "INFO:tensorflow:Saving 'checkpoint_path' summary for global step 50770: /tmp/tmpxxxhmg2i/model.ckpt-50770\n",
            "0.9015764\n",
            "{'accuracy': 0.9015764, 'accuracy_baseline': 0.9015764, 'auc': 0.6546918, 'auc_precision_recall': 0.15436137, 'average_loss': 0.30908287, 'label/mean': 0.09842362, 'loss': 0.3090817, 'precision': 0.0, 'prediction/mean': 0.09221378, 'recall': 0.0, 'global_step': 50770}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_LolecQpV8ic"
      },
      "source": [
        "We've achieved a 90.15% accuracy in estimating the events in the testing set, a set of data that is out of sample. This is data the linear model has not been trained on or has seen yet."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vuniANU4fieP"
      },
      "source": [
        "# Let's make some predictions\n",
        "\n",
        "We can predict the expected goals of an event (x,y,strength) using the `.predict()` method. Using the `.predict()` method, we'll be able to predict the expected goals and generate heat maps for each strength."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B0yHczQdf0FK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 434
        },
        "outputId": "9beb97ef-82df-4f44-adf0-defccbd5259b"
      },
      "source": [
        "def input_fn(features, batch_size=256):\n",
        "    \"\"\"An input function for prediction.\"\"\"\n",
        "    # Convert the inputs to a Dataset without labels.\n",
        "    return tf.data.Dataset.from_tensor_slices(dict(features)).batch(batch_size)\n",
        "\n",
        "#import prediction data from csv\n",
        "xg_df_predict = pd.read_csv('https://github.com/r-wisniewski/xG-LinearModel/raw/main/prediction.csv')\n",
        "\n",
        "# generate the prediction input function\n",
        "#pred_input_fn = make_input_fn(xg_df_predict, y_pred, num_epochs=1, shuffle=False)\n",
        "\n",
        "predictions = linear_est.predict(\n",
        "    input_fn=lambda: input_fn(xg_df_predict))\n",
        "\n",
        "pred_dicts = list(predictions)\n",
        "\n",
        "# cast the predict return to a list. If not casted use next(pred_xxxx)\n",
        "#pred_dicts = list(linear_est.predict(pred_input_fn)) # this returns a predictions array (whether or not the event is a goal) for EACH input test data \n",
        "probs = pd.Series([pred['probabilities'][1] for pred in pred_dicts]) # take each prediction array and strip off the 2nd element ([1]) which is the chance of this event being a goal. Add to a pd.series.\n",
        "\n",
        "probs.plot(kind='hist', bins=20, title='predicted probabilities') # plot all probabilities"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "INFO:tensorflow:Calling model_fn.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/tensorflow/python/keras/engine/base_layer_v1.py:1727: UserWarning: `layer.add_variable` is deprecated and will be removed in a future version. Please use `layer.add_weight` method instead.\n",
            "  warnings.warn('`layer.add_variable` is deprecated and '\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "INFO:tensorflow:Done calling model_fn.\n",
            "INFO:tensorflow:Graph was finalized.\n",
            "INFO:tensorflow:Restoring parameters from /tmp/tmpxxxhmg2i/model.ckpt-50770\n",
            "INFO:tensorflow:Running local_init_op.\n",
            "INFO:tensorflow:Done running local_init_op.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fba4f0b7ba8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k8aTubp8eBNu"
      },
      "source": [
        "# Check the xG\r\n",
        "\r\n",
        "Let's check some x,y,strength combinations and see the expected goals."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ru1HGb0DeAhY",
        "outputId": "c94fcf55-6712-4933-f426-fd8b0089389d"
      },
      "source": [
        "print(xg_df_predict.loc[122122])\r\n",
        "print(pred_dicts[122122]['probabilities'])"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "XLocation    108\n",
            "YLocation    217\n",
            "Strength      -1\n",
            "Name: 122122, dtype: int64\n",
            "[0.9366285  0.06337146]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xJRJuHNHevRH"
      },
      "source": [
        "This arbitrarily chosen row (122122) is location 108,217 on the ice at a strength of -1 which means its either 4v5 or 3v4 (for the shooter). The returned prediction array for a particular run was `[0.94418013 0.05581985]` means there is a 94.4% chance a shot from this x,y,strength combination will not result in a goal and a 5.5% chance it will result in a goal."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "exxH4sQBgE6o"
      },
      "source": [
        "# Generate heat maps\r\n",
        "\r\n",
        "Now we are able to generate heat maps for each strength."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "vyppB7Alx8cQ",
        "outputId": "8ae65af7-f4a5-44d7-fa2d-c0ce86e3fe00"
      },
      "source": [
        "num_indexes = int((xg_df_predict.size)/3)\r\n",
        "indexes_per_strength = int(num_indexes/5)\r\n",
        "\r\n",
        "for i in range(-2,3):\r\n",
        "    #Create numpy array that will be populated by our records\r\n",
        "    #shape = (rows,columns) in our case rows are the y's and columns are the x's\r\n",
        "    rows = 297\r\n",
        "    cols = 301\r\n",
        "    A = np.ndarray(shape=(rows,cols), dtype=float)\r\n",
        "\r\n",
        "    for n in range(indexes_per_strength):\r\n",
        "        row_num = indexes_per_strength*(i+2) + n\r\n",
        "        x = xg_df_predict.loc[row_num, 'XLocation']\r\n",
        "        y = xg_df_predict.loc[row_num, 'YLocation']\r\n",
        "        #A[x][y] = xG\r\n",
        "        A[x,y] = pred_dicts[row_num]['probabilities'][1]\r\n",
        "        \r\n",
        "    plt.xlabel('Distance between the boards')\r\n",
        "    plt.ylabel('Distance from net')\r\n",
        "    title = 'xGF for AHL shots at Strength %s' % i\r\n",
        "    plt.title(title)\r\n",
        "    im = plt.imshow(A, cmap='hot')\r\n",
        "    plt.colorbar(im)\r\n",
        "    plt.show()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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": "0O3tIm4inttI"
      },
      "source": [
        "# Compare predicted xG versus actual game scores\n",
        "\n",
        "## In sample accuracy\n",
        "\n",
        "TBD\n",
        "\n",
        "\n",
        "## Out of sample accuracy\n",
        "\n",
        "TBD"
      ]
    }
  ]
}