FourFactorsAnalysis.ipynb

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    "# NBA Four Factors Analysis\n",
    "\n",
    "Taking Justin Jacobs's idea in the [Squared 2020 Blog](https://squared2020.com/2017/09/05/introduction-to-olivers-four-factors/), this notebook deals with obtaining Four Factors data for the last 2020 regular seasons and see how important each of them were over the years. First, a little introduction.\n",
    "\n",
    "## Four Factors\n",
    "\n",
    "The term is based on what Dean Oliver called the *Four Factors of Basketball Success*, which are:\n",
    "\n",
    "- Shooting\n",
    "- Turnovers\n",
    "- Rebounding\n",
    "- Free Throws\n",
    "\n",
    "These are important for any team both on offense and defense, and for that reason we can think that we have 8 factors instead of 4 and they can be obtained from just the box scores. I will explain them a bit more in detail below.\n",
    "\n",
    "### Shooting\n",
    "As we all now, the team that gets more points wins basketball games. This factor is measured as the *Effective Field Goal Percentage* (EFG%):\n",
    "\n",
    "$$\n",
    "EFG\\% = \\frac{FGM + 0.5 FG3M}{FGA},\n",
    "$$\n",
    "\n",
    "where\n",
    "- FGM: Field Goals Made\n",
    "- FG3M: 3-Point Shots Made\n",
    "- FGA: Field Goal Attempts\n",
    "\n",
    "### Turnovers\n",
    "Teams need to take care of the ball to get the best out of their possessions. This factor is measured with the *Turnover Percentage* (TOV%):\n",
    "\n",
    "$$\n",
    "TOV\\% = \\frac{TOV}{POSS},\n",
    "$$\n",
    "\n",
    "where\n",
    "- TOV: Turnovers\n",
    "- POSS: Amount of Possessions in the Season\n",
    "\n",
    "### Rebounding\n",
    "An offensive rebound is another way of making the best of our possessions in case we don't shoot the ball well, taking second (or more) chances to score. The offensive rebounding factor is the *Offensive Rebound Percentage* (ORB%):\n",
    "\n",
    "$$\n",
    "ORB\\% = \\frac{ORB}{ORB + OppDRB},\n",
    "$$\n",
    "\n",
    "where\n",
    "- ORB: Offensive Rebounds\n",
    "- OppDRB. Opponents's Defensive Rebounds\n",
    "\n",
    "For the defensive rebounding factor, we can get the ORB% for the opponents (OppORB%, this is the one available in the NBA Stats Page) or the *Defensive Rebounding Percentage* (DRB%):\n",
    "\n",
    "$$\n",
    "DRB\\% = \\frac{DRB}{DRB + OppORB},\n",
    "$$\n",
    "\n",
    "where\n",
    "- DRB: Defensive Rebounds\n",
    "- OppORB. Opponents's Offensive Rebounds\n",
    "\n",
    "### Free Throws\n",
    "Lastly, one of the ways we can end a possession is by getting to the free throw line (except when getting shots because of technical or flagrant fouls). This is the relationship between the amount of free throws a team attempted (FTA) and the field goals attempted (FGA), the *Free Throw Rate* (FTRATE):\n",
    "\n",
    "$$\n",
    "FTRATE = \\frac{FTA}{FGA}\n",
    "$$\n",
    "\n",
    "## Computing NBA Four Factors Importance\n",
    "Luckily, the NBA Stats Page has these factors already computed for a lot of seaons for us to use, so we will use it to get the Four Factors for the last 20 seasons and get the importance of each of them over the years, by adjusting a linear model and try to predict the winning percentage of the teams. In this case, winning percentage might be better than amount of wins, since we had a couple of seasons with a weird number of games played (thanks to some virus).\n",
    "\n",
    "### Data Obtention"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "3dc6f8ec-718b-4967-abc9-968bd692facb",
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   "outputs": [],
   "source": [
    "# Imports\n",
    "from nba_api.stats.endpoints import leaguedashteamstats\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50d9cefc-84dc-4042-b81a-a70e5a830b10",
   "metadata": {},
   "source": [
    "Let's start by getting the Four Factors data for the 20 seasons in one DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "59631176-3716-42d9-a492-bcd6a745bb85",
   "metadata": {},
   "outputs": [],
   "source": [
    "four_factors = pd.DataFrame()\n",
    "for i in range(20):\n",
    "    # Building the Season String (ie. 2020-21)\n",
    "    season_str = f\"{2001 + i}-{2 + i:02d}\"\n",
    "    # Let's make some attempts to obtain the data, since we might be doing too many requests...\n",
    "    for attempt in range(5):\n",
    "        try:\n",
    "            season_factors = leaguedashteamstats.LeagueDashTeamStats(\n",
    "                season=season_str, measure_type_detailed_defense=\"Four Factors\",\n",
    "            ).get_data_frames()[0]\n",
    "            season_factors[\"season\"] = 2002 + i\n",
    "            # Try to get the information for the season, getting only the columns we need\n",
    "            four_factors = pd.concat(\n",
    "                [four_factors, season_factors],\n",
    "                axis=0,\n",
    "            )\n",
    "        except:\n",
    "            # If we get an error we go to sleep for some time\n",
    "            time.sleep(30)\n",
    "        else:\n",
    "            # If everything's OK with the request, we continue\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "b1f1f0f7-2026-4599-a57b-1ad20e22914d",
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   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TEAM_ID</th>\n",
       "      <th>TEAM_NAME</th>\n",
       "      <th>GP</th>\n",
       "      <th>W</th>\n",
       "      <th>L</th>\n",
       "      <th>W_PCT</th>\n",
       "      <th>MIN</th>\n",
       "      <th>EFG_PCT</th>\n",
       "      <th>FTA_RATE</th>\n",
       "      <th>TM_TOV_PCT</th>\n",
       "      <th>...</th>\n",
       "      <th>FTA_RATE_RANK</th>\n",
       "      <th>TM_TOV_PCT_RANK</th>\n",
       "      <th>OREB_PCT_RANK</th>\n",
       "      <th>OPP_EFG_PCT_RANK</th>\n",
       "      <th>OPP_FTA_RATE_RANK</th>\n",
       "      <th>OPP_TOV_PCT_RANK</th>\n",
       "      <th>OPP_OREB_PCT_RANK</th>\n",
       "      <th>CFID</th>\n",
       "      <th>CFPARAMS</th>\n",
       "      <th>season</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1610612763</td>\n",
       "      <td>Memphis Grizzlies</td>\n",
       "      <td>82</td>\n",
       "      <td>28</td>\n",
       "      <td>54</td>\n",
       "      <td>0.341</td>\n",
       "      <td>3986.0</td>\n",
       "      <td>0.487</td>\n",
       "      <td>0.287</td>\n",
       "      <td>0.162</td>\n",
       "      <td>...</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>21</td>\n",
       "      <td>28</td>\n",
       "      <td>3</td>\n",
       "      <td>18</td>\n",
       "      <td>29</td>\n",
       "      <td>10</td>\n",
       "      <td>Memphis Grizzlies</td>\n",
       "      <td>2003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1610612745</td>\n",
       "      <td>Houston Rockets</td>\n",
       "      <td>82</td>\n",
       "      <td>34</td>\n",
       "      <td>48</td>\n",
       "      <td>0.415</td>\n",
       "      <td>3966.0</td>\n",
       "      <td>0.471</td>\n",
       "      <td>0.317</td>\n",
       "      <td>0.162</td>\n",
       "      <td>...</td>\n",
       "      <td>22</td>\n",
       "      <td>23</td>\n",
       "      <td>22</td>\n",
       "      <td>6</td>\n",
       "      <td>16</td>\n",
       "      <td>26</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>Houston Rockets</td>\n",
       "      <td>2006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1610612754</td>\n",
       "      <td>Indiana Pacers</td>\n",
       "      <td>82</td>\n",
       "      <td>44</td>\n",
       "      <td>38</td>\n",
       "      <td>0.537</td>\n",
       "      <td>3981.0</td>\n",
       "      <td>0.476</td>\n",
       "      <td>0.358</td>\n",
       "      <td>0.160</td>\n",
       "      <td>...</td>\n",
       "      <td>4</td>\n",
       "      <td>21</td>\n",
       "      <td>28</td>\n",
       "      <td>7</td>\n",
       "      <td>23</td>\n",
       "      <td>17</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>Indiana Pacers</td>\n",
       "      <td>2005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1610612747</td>\n",
       "      <td>Los Angeles Lakers</td>\n",
       "      <td>82</td>\n",
       "      <td>37</td>\n",
       "      <td>45</td>\n",
       "      <td>0.451</td>\n",
       "      <td>3956.0</td>\n",
       "      <td>0.527</td>\n",
       "      <td>0.257</td>\n",
       "      <td>0.150</td>\n",
       "      <td>...</td>\n",
       "      <td>16</td>\n",
       "      <td>28</td>\n",
       "      <td>14</td>\n",
       "      <td>11</td>\n",
       "      <td>7</td>\n",
       "      <td>16</td>\n",
       "      <td>19</td>\n",
       "      <td>10</td>\n",
       "      <td>Los Angeles Lakers</td>\n",
       "      <td>2019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1610612762</td>\n",
       "      <td>Utah Jazz</td>\n",
       "      <td>82</td>\n",
       "      <td>41</td>\n",
       "      <td>41</td>\n",
       "      <td>0.500</td>\n",
       "      <td>3976.0</td>\n",
       "      <td>0.467</td>\n",
       "      <td>0.397</td>\n",
       "      <td>0.174</td>\n",
       "      <td>...</td>\n",
       "      <td>2</td>\n",
       "      <td>28</td>\n",
       "      <td>1</td>\n",
       "      <td>14</td>\n",
       "      <td>30</td>\n",
       "      <td>11</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>Utah Jazz</td>\n",
       "      <td>2006</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       TEAM_ID           TEAM_NAME  GP   W   L  W_PCT     MIN  EFG_PCT  \\\n",
       "12  1610612763   Memphis Grizzlies  82  28  54  0.341  3986.0    0.487   \n",
       "9   1610612745     Houston Rockets  82  34  48  0.415  3966.0    0.471   \n",
       "10  1610612754      Indiana Pacers  82  44  38  0.537  3981.0    0.476   \n",
       "13  1610612747  Los Angeles Lakers  82  37  45  0.451  3956.0    0.527   \n",
       "28  1610612762           Utah Jazz  82  41  41  0.500  3976.0    0.467   \n",
       "\n",
       "    FTA_RATE  TM_TOV_PCT  ...  FTA_RATE_RANK  TM_TOV_PCT_RANK  OREB_PCT_RANK  \\\n",
       "12     0.287       0.162  ...             18               19             21   \n",
       "9      0.317       0.162  ...             22               23             22   \n",
       "10     0.358       0.160  ...              4               21             28   \n",
       "13     0.257       0.150  ...             16               28             14   \n",
       "28     0.397       0.174  ...              2               28              1   \n",
       "\n",
       "    OPP_EFG_PCT_RANK  OPP_FTA_RATE_RANK  OPP_TOV_PCT_RANK  OPP_OREB_PCT_RANK  \\\n",
       "12                28                  3                18                 29   \n",
       "9                  6                 16                26                  8   \n",
       "10                 7                 23                17                 10   \n",
       "13                11                  7                16                 19   \n",
       "28                14                 30                11                 10   \n",
       "\n",
       "    CFID            CFPARAMS  season  \n",
       "12    10   Memphis Grizzlies    2003  \n",
       "9     10     Houston Rockets    2006  \n",
       "10    10      Indiana Pacers    2005  \n",
       "13    10  Los Angeles Lakers    2019  \n",
       "28    10           Utah Jazz    2006  \n",
       "\n",
       "[5 rows x 31 columns]"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get a random sample\n",
    "four_factors.sample(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94afc789-f173-4ded-8764-3f07690688d0",
   "metadata": {},
   "source": [
    "### Adjusting our Linear Models\n",
    "For each season, we will adjust a linear model without intercept (using Scikit Learn) that depends on our 8 factors to the **Win Percentage (W%)** of each team. We will just focus on the offensive factors' importance then, and we will store that data in a new DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "77e5ad6a-9d1a-4096-8898-635e619d15e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "four_factors_models = pd.DataFrame(columns=[\"EFG_PCT\", \"FTA_RATE\", \"TM_TOV_PCT\", \"OREB_PCT\"])\n",
    "for i in range(20):\n",
    "    # For each season, we will fit a linear model, trying to adjust it to the win percentage\n",
    "    season = 2002 + i\n",
    "    season_factors = four_factors.loc[\n",
    "        four_factors[\"season\"] == season,\n",
    "        [\"EFG_PCT\", \"FTA_RATE\", \"TM_TOV_PCT\", \"OREB_PCT\", \"OPP_EFG_PCT\", \"OPP_FTA_RATE\", \"OPP_TOV_PCT\", \"OPP_OREB_PCT\"],\n",
    "    ]\n",
    "    model = LinearRegression(fit_intercept=False)\n",
    "    model.fit(\n",
    "        X=season_factors,\n",
    "        y=four_factors.loc[four_factors[\"season\"] == season, \"W_PCT\"],\n",
    "    )\n",
    "    season = 2002 + i\n",
    "    # Put the 4 first factors (offensive)\n",
    "    four_factors_models.loc[season] = np.abs(model.coef_[:4]) / np.sum(np.abs(model.coef_[:4]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "7e3279cf-8009-431d-bc50-08b5e673778b",
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   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>EFG_PCT</th>\n",
       "      <th>FTA_RATE</th>\n",
       "      <th>TM_TOV_PCT</th>\n",
       "      <th>OREB_PCT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2002</th>\n",
       "      <td>0.408893</td>\n",
       "      <td>0.063766</td>\n",
       "      <td>0.409220</td>\n",
       "      <td>0.118122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003</th>\n",
       "      <td>0.518899</td>\n",
       "      <td>0.040976</td>\n",
       "      <td>0.307262</td>\n",
       "      <td>0.132864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004</th>\n",
       "      <td>0.432751</td>\n",
       "      <td>0.048626</td>\n",
       "      <td>0.317373</td>\n",
       "      <td>0.201250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005</th>\n",
       "      <td>0.445683</td>\n",
       "      <td>0.046723</td>\n",
       "      <td>0.340023</td>\n",
       "      <td>0.167571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006</th>\n",
       "      <td>0.414419</td>\n",
       "      <td>0.042803</td>\n",
       "      <td>0.310623</td>\n",
       "      <td>0.232155</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       EFG_PCT  FTA_RATE  TM_TOV_PCT  OREB_PCT\n",
       "2002  0.408893  0.063766    0.409220  0.118122\n",
       "2003  0.518899  0.040976    0.307262  0.132864\n",
       "2004  0.432751  0.048626    0.317373  0.201250\n",
       "2005  0.445683  0.046723    0.340023  0.167571\n",
       "2006  0.414419  0.042803    0.310623  0.232155"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "four_factors_models.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ff5e416-e519-419c-b776-f2d3e7001194",
   "metadata": {},
   "source": [
    "### Plot and Analysis\n",
    "\n",
    "We can represent the relative importance of each factor as years go on as a stacked box plot, since our factor importance sums 1 for every year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "1844b081-e551-4637-973d-cb8803d19c8b",
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   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "four_factors_models.plot.bar(\n",
    "    stacked=True, cmap=\"coolwarm\",\n",
    "    figsize=(14, 7),\n",
    "    title=\"Four Factors Importance Over 20 Seasons\",\n",
    ").legend(loc='center left',bbox_to_anchor=(1.0, 0.5));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b25a03c1-6989-435d-984c-39edaf5ae410",
   "metadata": {},
   "source": [
    "In the past, Dean Oliver assigned the following importance to the offensive factors:\n",
    "\n",
    "- Shooting (40%)\n",
    "- Turnovers (25%)\n",
    "- Rebounding (20%)\n",
    "- Free Throws (15%)\n",
    "\n",
    "Let's see which of these 20 years is closer to that distribution according to our models (using Euclidean distance)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "70852273-1be4-4c7e-8c2f-1de7298f971f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EFG_PCT       0.429392\n",
       "FTA_RATE      0.095517\n",
       "TM_TOV_PCT    0.295126\n",
       "OREB_PCT      0.179964\n",
       "Name: 2012, dtype: float64"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the argument for the closest row to the distribution above.\n",
    "argmin = np.argmin(np.linalg.norm((four_factors_models - np.array([0.4, 0.15, 0.25, 0.20])), axis=1))\n",
    "# Show the Series corresponding to that argument.\n",
    "four_factors_models.iloc[argmin]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c880509d-1ce1-4be9-a532-1322838b44d0",
   "metadata": {},
   "source": [
    "As we can see, the closest season to that distribution was the **2011-12** Season, where we experienced the last lockout, and [Chris Paul was held hostage by the NBA](https://www.nytimes.com/2011/12/10/sports/basketball/nba-basketball-roundup.html?_r=1&ref=basketball&pagewanted=all).\n",
    "\n",
    "The Heat (with Lebron, Wade and Bosh) won the championship after defeating the Durant, Westbrook and Harden led Thunder. This season had 66 games and is the one where FTRATE was at its max.\n",
    "\n",
    "The Four Factors can give us a good estimation of what it takes to win NBA games, and can be useful for teams to figure out what they may be lacking, in order to get in the best shape for the next season. Thanks to the NBA Stats API we can put all this data into a DataFrame and get even more insights. For example, now we know that taking care of the ball is really important for teams, we can figure out which were the 5 worse ones on that aspect last season."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "71fd3834-dfb2-40e6-a29d-e38d707cbd36",
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TEAM_NAME</th>\n",
       "      <th>TM_TOV_PCT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Oklahoma City Thunder</td>\n",
       "      <td>0.158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Cleveland Cavaliers</td>\n",
       "      <td>0.157</td>\n",
       "    </tr>\n",
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       "      <th>13</th>\n",
       "      <td>Los Angeles Lakers</td>\n",
       "      <td>0.152</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Chicago Bulls</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Detroit Pistons</td>\n",
       "      <td>0.151</td>\n",
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       "                TEAM_NAME  TM_TOV_PCT\n",
       "20  Oklahoma City Thunder       0.158\n",
       "5     Cleveland Cavaliers       0.157\n",
       "13     Los Angeles Lakers       0.152\n",
       "4           Chicago Bulls       0.151\n",
       "8         Detroit Pistons       0.151"
      ]
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   "source": [
    "four_factors.loc[four_factors[\"season\"] == 2021].sort_values(by=\"TM_TOV_PCT\", ascending=False)[[\"TEAM_NAME\", \"TM_TOV_PCT\"]].head(5)"
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    "Maybe this is the reason why the [Lakers are desperately looking for a Point Guard](https://247sports.com/Article/Los-Angeles-Lakers-trade-free-agency-All-Star-point-guard-Chris-Paul-Russell-Westbrook-168220327/) for next season!"
   ]
  }
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