A Data Scientist for a Professional Football Club.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Data Scientist for a Professional Football Club"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split, cross_val_score\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler, PolynomialFeatures\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error\n",
    "pd.set_option('display.max_columns', 500)\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>height_cm</th>\n",
       "      <th>weight_kg</th>\n",
       "      <th>overall</th>\n",
       "      <th>pac</th>\n",
       "      <th>sho</th>\n",
       "      <th>pas</th>\n",
       "      <th>dri</th>\n",
       "      <th>def</th>\n",
       "      <th>phy</th>\n",
       "      <th>international_reputation</th>\n",
       "      <th>skill_moves</th>\n",
       "      <th>weak_foot</th>\n",
       "      <th>crossing</th>\n",
       "      <th>finishing</th>\n",
       "      <th>heading_accuracy</th>\n",
       "      <th>short_passing</th>\n",
       "      <th>volleys</th>\n",
       "      <th>dribbling</th>\n",
       "      <th>curve</th>\n",
       "      <th>free_kick_accuracy</th>\n",
       "      <th>long_passing</th>\n",
       "      <th>ball_control</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>sprint_speed</th>\n",
       "      <th>agility</th>\n",
       "      <th>reactions</th>\n",
       "      <th>balance</th>\n",
       "      <th>shot_power</th>\n",
       "      <th>jumping</th>\n",
       "      <th>stamina</th>\n",
       "      <th>strength</th>\n",
       "      <th>long_shots</th>\n",
       "      <th>aggression</th>\n",
       "      <th>interceptions</th>\n",
       "      <th>positioning</th>\n",
       "      <th>vision</th>\n",
       "      <th>penalties</th>\n",
       "      <th>composure</th>\n",
       "      <th>marking</th>\n",
       "      <th>standing_tackle</th>\n",
       "      <th>work_rate_att_Medium</th>\n",
       "      <th>work_rate_att_High</th>\n",
       "      <th>work_rate_def_Medium</th>\n",
       "      <th>work_rate_def_High</th>\n",
       "      <th>preferred_foot_Right</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>32</td>\n",
       "      <td>185.0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>94</td>\n",
       "      <td>90</td>\n",
       "      <td>93</td>\n",
       "      <td>82</td>\n",
       "      <td>90</td>\n",
       "      <td>33</td>\n",
       "      <td>80</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>85</td>\n",
       "      <td>94</td>\n",
       "      <td>88</td>\n",
       "      <td>83</td>\n",
       "      <td>88</td>\n",
       "      <td>91</td>\n",
       "      <td>81</td>\n",
       "      <td>76</td>\n",
       "      <td>77</td>\n",
       "      <td>93</td>\n",
       "      <td>89</td>\n",
       "      <td>91</td>\n",
       "      <td>89</td>\n",
       "      <td>96</td>\n",
       "      <td>63</td>\n",
       "      <td>94</td>\n",
       "      <td>95</td>\n",
       "      <td>92</td>\n",
       "      <td>80</td>\n",
       "      <td>92</td>\n",
       "      <td>63</td>\n",
       "      <td>29</td>\n",
       "      <td>95</td>\n",
       "      <td>85</td>\n",
       "      <td>85</td>\n",
       "      <td>95</td>\n",
       "      <td>22</td>\n",
       "      <td>31</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30</td>\n",
       "      <td>170.0</td>\n",
       "      <td>72.0</td>\n",
       "      <td>93</td>\n",
       "      <td>89</td>\n",
       "      <td>90</td>\n",
       "      <td>86</td>\n",
       "      <td>96</td>\n",
       "      <td>26</td>\n",
       "      <td>61</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>77</td>\n",
       "      <td>95</td>\n",
       "      <td>71</td>\n",
       "      <td>88</td>\n",
       "      <td>85</td>\n",
       "      <td>97</td>\n",
       "      <td>89</td>\n",
       "      <td>90</td>\n",
       "      <td>87</td>\n",
       "      <td>95</td>\n",
       "      <td>92</td>\n",
       "      <td>87</td>\n",
       "      <td>90</td>\n",
       "      <td>95</td>\n",
       "      <td>95</td>\n",
       "      <td>85</td>\n",
       "      <td>68</td>\n",
       "      <td>73</td>\n",
       "      <td>59</td>\n",
       "      <td>88</td>\n",
       "      <td>48</td>\n",
       "      <td>22</td>\n",
       "      <td>93</td>\n",
       "      <td>90</td>\n",
       "      <td>78</td>\n",
       "      <td>96</td>\n",
       "      <td>13</td>\n",
       "      <td>28</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>25</td>\n",
       "      <td>175.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>92</td>\n",
       "      <td>92</td>\n",
       "      <td>84</td>\n",
       "      <td>79</td>\n",
       "      <td>95</td>\n",
       "      <td>30</td>\n",
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       "      <td>5</td>\n",
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       "      <td>5</td>\n",
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       "      <td>89</td>\n",
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       "      <td>81</td>\n",
       "      <td>83</td>\n",
       "      <td>96</td>\n",
       "      <td>81</td>\n",
       "      <td>84</td>\n",
       "      <td>75</td>\n",
       "      <td>95</td>\n",
       "      <td>94</td>\n",
       "      <td>90</td>\n",
       "      <td>96</td>\n",
       "      <td>88</td>\n",
       "      <td>82</td>\n",
       "      <td>80</td>\n",
       "      <td>61</td>\n",
       "      <td>78</td>\n",
       "      <td>53</td>\n",
       "      <td>77</td>\n",
       "      <td>56</td>\n",
       "      <td>36</td>\n",
       "      <td>90</td>\n",
       "      <td>80</td>\n",
       "      <td>81</td>\n",
       "      <td>92</td>\n",
       "      <td>21</td>\n",
       "      <td>24</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>30</td>\n",
       "      <td>182.0</td>\n",
       "      <td>86.0</td>\n",
       "      <td>92</td>\n",
       "      <td>82</td>\n",
       "      <td>90</td>\n",
       "      <td>79</td>\n",
       "      <td>87</td>\n",
       "      <td>42</td>\n",
       "      <td>81</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>77</td>\n",
       "      <td>94</td>\n",
       "      <td>77</td>\n",
       "      <td>83</td>\n",
       "      <td>88</td>\n",
       "      <td>86</td>\n",
       "      <td>86</td>\n",
       "      <td>84</td>\n",
       "      <td>64</td>\n",
       "      <td>91</td>\n",
       "      <td>88</td>\n",
       "      <td>77</td>\n",
       "      <td>86</td>\n",
       "      <td>93</td>\n",
       "      <td>60</td>\n",
       "      <td>87</td>\n",
       "      <td>69</td>\n",
       "      <td>89</td>\n",
       "      <td>80</td>\n",
       "      <td>86</td>\n",
       "      <td>78</td>\n",
       "      <td>41</td>\n",
       "      <td>92</td>\n",
       "      <td>84</td>\n",
       "      <td>85</td>\n",
       "      <td>83</td>\n",
       "      <td>30</td>\n",
       "      <td>45</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>31</td>\n",
       "      <td>193.0</td>\n",
       "      <td>92.0</td>\n",
       "      <td>92</td>\n",
       "      <td>91</td>\n",
       "      <td>90</td>\n",
       "      <td>95</td>\n",
       "      <td>89</td>\n",
       "      <td>60</td>\n",
       "      <td>91</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>15</td>\n",
       "      <td>13</td>\n",
       "      <td>25</td>\n",
       "      <td>55</td>\n",
       "      <td>11</td>\n",
       "      <td>30</td>\n",
       "      <td>14</td>\n",
       "      <td>11</td>\n",
       "      <td>59</td>\n",
       "      <td>48</td>\n",
       "      <td>58</td>\n",
       "      <td>61</td>\n",
       "      <td>52</td>\n",
       "      <td>85</td>\n",
       "      <td>35</td>\n",
       "      <td>25</td>\n",
       "      <td>78</td>\n",
       "      <td>44</td>\n",
       "      <td>83</td>\n",
       "      <td>16</td>\n",
       "      <td>29</td>\n",
       "      <td>30</td>\n",
       "      <td>12</td>\n",
       "      <td>70</td>\n",
       "      <td>47</td>\n",
       "      <td>70</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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      ],
      "text/plain": [
       "   age  height_cm  weight_kg  overall  pac  sho  pas  dri  def  phy  \\\n",
       "0   32      185.0       80.0       94   90   93   82   90   33   80   \n",
       "1   30      170.0       72.0       93   89   90   86   96   26   61   \n",
       "2   25      175.0       68.0       92   92   84   79   95   30   60   \n",
       "3   30      182.0       86.0       92   82   90   79   87   42   81   \n",
       "4   31      193.0       92.0       92   91   90   95   89   60   91   \n",
       "\n",
       "   international_reputation  skill_moves  weak_foot  crossing  finishing  \\\n",
       "0                         5            5          4        85         94   \n",
       "1                         5            4          4        77         95   \n",
       "2                         5            5          5        75         89   \n",
       "3                         5            4          4        77         94   \n",
       "4                         5            1          4        15         13   \n",
       "\n",
       "   heading_accuracy  short_passing  volleys  dribbling  curve  \\\n",
       "0                88             83       88         91     81   \n",
       "1                71             88       85         97     89   \n",
       "2                62             81       83         96     81   \n",
       "3                77             83       88         86     86   \n",
       "4                25             55       11         30     14   \n",
       "\n",
       "   free_kick_accuracy  long_passing  ball_control  acceleration  sprint_speed  \\\n",
       "0                  76            77            93            89            91   \n",
       "1                  90            87            95            92            87   \n",
       "2                  84            75            95            94            90   \n",
       "3                  84            64            91            88            77   \n",
       "4                  11            59            48            58            61   \n",
       "\n",
       "   agility  reactions  balance  shot_power  jumping  stamina  strength  \\\n",
       "0       89         96       63          94       95       92        80   \n",
       "1       90         95       95          85       68       73        59   \n",
       "2       96         88       82          80       61       78        53   \n",
       "3       86         93       60          87       69       89        80   \n",
       "4       52         85       35          25       78       44        83   \n",
       "\n",
       "   long_shots  aggression  interceptions  positioning  vision  penalties  \\\n",
       "0          92          63             29           95      85         85   \n",
       "1          88          48             22           93      90         78   \n",
       "2          77          56             36           90      80         81   \n",
       "3          86          78             41           92      84         85   \n",
       "4          16          29             30           12      70         47   \n",
       "\n",
       "   composure  marking  standing_tackle  work_rate_att_Medium  \\\n",
       "0         95       22               31                     0   \n",
       "1         96       13               28                     1   \n",
       "2         92       21               24                     0   \n",
       "3         83       30               45                     0   \n",
       "4         70       10               10                     1   \n",
       "\n",
       "   work_rate_att_High  work_rate_def_Medium  work_rate_def_High  \\\n",
       "0                   1                     0                   0   \n",
       "1                   0                     1                   0   \n",
       "2                   1                     1                   0   \n",
       "3                   1                     1                   0   \n",
       "4                   0                     1                   0   \n",
       "\n",
       "   preferred_foot_Right  \n",
       "0                     1  \n",
       "1                     0  \n",
       "2                     1  \n",
       "3                     1  \n",
       "4                     1  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('footballer_data.csv')\n",
    "\n",
    "model_data = df.drop(['ID','club','club_logo','flag', 'nationality','photo','potential', 'birth_date'], axis = 'columns')\n",
    "\n",
    "model_data['work_rate_att'] = pd.Categorical(model_data.work_rate_att, categories=['Low','Medium','High'])\n",
    "model_data['work_rate_def'] = pd.Categorical(model_data.work_rate_def, categories=['Low','Medium','High'])\n",
    "model_data['preferred_foot'] = pd.Categorical(model_data.preferred_foot, categories = ['Left','Right'])\n",
    "\n",
    "model_data = pd.get_dummies(model_data, drop_first=True)\n",
    "model_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\mezzati\\AppData\\Local\\Continuum\\anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.491330443481161\n",
      "4.2620046165876735\n"
     ]
    },
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "losses = abs(model_data.overall - model_data.overall.median())\n",
    "sns.distplot(losses)\n",
    "print(losses.mean())\n",
    "print(losses.std())\n",
    "\n",
    "x = np.random.normal(10,2,size = 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(16831, 45) (1163, 45)\n"
     ]
    }
   ],
   "source": [
    "test_size = round(((2*losses.std())/0.25)**2)\n",
    "\n",
    "y = model_data.overall\n",
    "X = model_data.drop('overall', axis = 'columns')\n",
    "\n",
    "Xtrain, Xtest, ytrain, ytest = train_test_split(X,\n",
    "                                                y, \n",
    "                                                test_size = test_size, \n",
    "                                                random_state = 0)\n",
    "\n",
    "print(Xtrain.shape,Xtest.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_pipeline = Pipeline([\n",
    "    ('linear_regression', LinearRegression())\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9055815330889487\n"
     ]
    }
   ],
   "source": [
    "cv_score = cross_val_score(model_pipeline, Xtrain, ytrain, cv=5, scoring='neg_mean_absolute_error')\n",
    "\n",
    "cv_score_mean = -cv_score.mean()\n",
    "print(cv_score_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8872662605202266\n"
     ]
    }
   ],
   "source": [
    "y_quad = model_data.overall\n",
    "X_quad = model_data.assign(age2 = lambda x: x.age**2).drop('overall', axis = 'columns')\n",
    "\n",
    "X_quad_train, X_quad_test, y_quad_train, y_quad_test = train_test_split(X_quad, y_quad, \n",
    "                                                                        test_size = test_size, \n",
    "                                                                        random_state = 0)\n",
    "\n",
    "quadratic_model_pipeline = Pipeline([\n",
    "    ('linear_regression', LinearRegression())\n",
    "])\n",
    "\n",
    "quad_cv_score = cross_val_score(quadratic_model_pipeline, \n",
    "                                X_quad_train, \n",
    "                                y_quad_train, \n",
    "                                cv = 5, \n",
    "                                scoring = 'neg_mean_absolute_error')\n",
    "\n",
    "quad_cv_score_mean = -quad_cv_score.mean()\n",
    "print(quad_cv_score_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 7\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8861587663410997\n"
     ]
    }
   ],
   "source": [
    "model_pipeline_intxn = Pipeline([\n",
    "    ('poly', PolynomialFeatures(include_bias = False)),\n",
    "    ('linear_regression', LinearRegression())\n",
    "])\n",
    "\n",
    "cv_score = cross_val_score(model_pipeline_intxn, \n",
    "                           Xtrain, \n",
    "                           ytrain, \n",
    "                           cv = 5, \n",
    "                           scoring = 'neg_mean_absolute_error')\n",
    "\n",
    "print(-cv_score.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 8\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding cubic terms will attain more powerful but also more complicated model with too many parameters which will also make it more prone to overfitting. Because the model will correspond too closely to training data and therefore it may fail to fit validation data and more importantly test data. In this case, the generalization error will be more than expected (in comarison with training error). So it can not predict future observation reliably."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 9\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8685278142596833\n",
      "[0.80099928 0.93605635]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_pipeline_intxn.fit(Xtrain, ytrain)\n",
    "\n",
    "ypred = model_pipeline_intxn.predict(Xtest)\n",
    "\n",
    "test_errors = ytest - ypred\n",
    "\n",
    "generalization_error = mean_absolute_error(ytest, ypred)\n",
    "\n",
    "test_ci = generalization_error + 1.96 * np.std(test_errors) / np.sqrt(len(test_errors)) * np.array([-1, 1])\n",
    "\n",
    "sns.distplot(abs(test_errors))\n",
    "\n",
    "print(generalization_error)\n",
    "print(test_ci)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test error is close to the CV error of the model which is a good thing. Because it depicts we could avoid overfitting by using a cross-validation technique. If we had used the training data to find the error of the models and choose the best one based on that, it would have probably posed the problem of overfitting and in that case the generalization error would be more."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}