{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# One option vs. multi-options model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from prayas import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The one-option model is a special case of the multi-options model. This notebook demonstrates this on a simple example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a **one option model** with three variants:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "m1 = OneOptionModel([\"Red\", \"Green\", \"Blue\"], baseline=\"Red\")\n",
    "\n",
    "m1.set_result(successes=[209, 330, 408],\n",
    "              trials=[236113, 236108, 243241])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a **multi-options model** with the same setup but with only one option per variant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "m2 = MultiOptionsModel([\"Red\", \"Green\", \"Blue\"], [1, 1, 1], baseline=\"Red\")\n",
    "\n",
    "m2.set_result(successes=[[209], [330], [408]], \n",
    "              trials=[236113, 236108, 243241])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Variant</th>\n",
       "      <th>Measure</th>\n",
       "      <th>ProbabilityToBeBest</th>\n",
       "      <th>ProbabilityToBeatBaseline</th>\n",
       "      <th>UpliftFromBaseline</th>\n",
       "      <th>PotentialLossFromBaseline</th>\n",
       "      <th>MaxUplift</th>\n",
       "      <th>MaxPotentialLoss</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Blue</td>\n",
       "      <td>conversion</td>\n",
       "      <td>0.9924</td>\n",
       "      <td>1.0</td>\n",
       "      <td>89.057671</td>\n",
       "      <td>0.0</td>\n",
       "      <td>88.963086</td>\n",
       "      <td>0.017103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Green</td>\n",
       "      <td>conversion</td>\n",
       "      <td>0.0076</td>\n",
       "      <td>1.0</td>\n",
       "      <td>57.726761</td>\n",
       "      <td>0.0</td>\n",
       "      <td>57.596831</td>\n",
       "      <td>16.614105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Red</td>\n",
       "      <td>conversion</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-36.546947</td>\n",
       "      <td>47.095717</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Variant     Measure  ProbabilityToBeBest  ProbabilityToBeatBaseline  \\\n",
       "0    Blue  conversion               0.9924                        1.0   \n",
       "1   Green  conversion               0.0076                        1.0   \n",
       "2     Red  conversion               0.0000                        0.0   \n",
       "\n",
       "   UpliftFromBaseline  PotentialLossFromBaseline  MaxUplift  MaxPotentialLoss  \n",
       "0           89.057671                        0.0  88.963086          0.017103  \n",
       "1           57.726761                        0.0  57.596831         16.614105  \n",
       "2            0.000000                        0.0 -36.546947         47.095717  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1.score_baseline()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>Variant</th>\n",
       "      <th>Measure</th>\n",
       "      <th>ProbabilityToBeBest</th>\n",
       "      <th>ProbabilityToBeatBaseline</th>\n",
       "      <th>UpliftFromBaseline</th>\n",
       "      <th>PotentialLossFromBaseline</th>\n",
       "      <th>MaxUplift</th>\n",
       "      <th>MaxPotentialLoss</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Blue</td>\n",
       "      <td>conversion</td>\n",
       "      <td>0.99355</td>\n",
       "      <td>1.0</td>\n",
       "      <td>89.123055</td>\n",
       "      <td>0.0</td>\n",
       "      <td>89.117280</td>\n",
       "      <td>0.017340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Green</td>\n",
       "      <td>conversion</td>\n",
       "      <td>0.00645</td>\n",
       "      <td>1.0</td>\n",
       "      <td>57.717259</td>\n",
       "      <td>0.0</td>\n",
       "      <td>57.636056</td>\n",
       "      <td>16.714971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Red</td>\n",
       "      <td>conversion</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-36.562736</td>\n",
       "      <td>47.132823</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Variant     Measure  ProbabilityToBeBest  ProbabilityToBeatBaseline  \\\n",
       "0    Blue  conversion              0.99355                        1.0   \n",
       "1   Green  conversion              0.00645                        1.0   \n",
       "2     Red  conversion              0.00000                        0.0   \n",
       "\n",
       "   UpliftFromBaseline  PotentialLossFromBaseline  MaxUplift  MaxPotentialLoss  \n",
       "0           89.123055                        0.0  89.117280          0.017340  \n",
       "1           57.717259                        0.0  57.636056         16.714971  \n",
       "2            0.000000                        0.0 -36.562736         47.132823  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2.score_baseline()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the results are basically the same."
   ]
  }
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