{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8a3dd9d5-c209-4106-9eb3-1ee0be86aece",
   "metadata": {},
   "source": [
    "# Implied Odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "458a0dff-511a-4a5b-946a-d670016c438c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import penaltyblog as pb\n",
    "import numpy as np\n",
    "from pprint import pprint"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8cc0277-a96b-4a77-bd0d-028cde0c7fc3",
   "metadata": {},
   "source": [
    "### Example starting odds (including overround)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cb194f91-26c0-40cb-864f-f0d5f6ddac81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.0324257063387499)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds = [2.7, 2.3, 4.4]\n",
    "\n",
    "np.sum(1 / np.array(odds))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e23c1a8-0d4f-41e8-9549-9e6b712831cb",
   "metadata": {},
   "source": [
    "### Remove the overround using basic multiplicative method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6b1aa169-90fb-4515-ac67-317194b30f46",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'implied_probabilities': array([0.35873804, 0.42112726, 0.2201347 ]),\n",
      " 'margin': np.float64(0.03242570633874986),\n",
      " 'method': 'multiplicative'}\n"
     ]
    }
   ],
   "source": [
    "normalised = pb.implied.multiplicative(odds)\n",
    "pprint(normalised)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c7717524-5e27-4fdd-bdd6-2ea30a0321c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.9999999999999999)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(normalised[\"implied_probabilities\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b41420a2-054a-4f7d-ab5e-316886873eb1",
   "metadata": {},
   "source": [
    "### Remove the overround using additive method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3b9ff93c-4652-44d4-bba8-10f25605d21b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'implied_probabilities': array([0.3595618 , 0.42397404, 0.21646416]),\n",
       " 'method': 'additive',\n",
       " 'margin': np.float64(0.03242570633874986)}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normalised = pb.implied.additive(odds)\n",
    "normalised"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ee0b2a33-550e-4d6d-8ab8-4e124f14ee44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.0)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(normalised[\"implied_probabilities\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c977bcf6-3af3-411a-82d8-40322b3856ee",
   "metadata": {},
   "source": [
    "### Remove the overround using power method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "008c5e72-74ff-4447-af9a-8a2c461bf0bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'implied_probabilities': array([0.3591711 , 0.42373075, 0.21709815]),\n",
       " 'method': 'power',\n",
       " 'k': 1.0309132393169356,\n",
       " 'margin': np.float64(0.03242570633874986)}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normalised = pb.implied.power(odds)\n",
    "normalised"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0eda96dd-b9ac-4758-9538-290f1ee9519e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.9999999999989682)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(normalised[\"implied_probabilities\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19a7c0f0-b2a5-4a77-b250-c6c5c9df5ac4",
   "metadata": {},
   "source": [
    "### Remove the overround using Shin's method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3e2c7b78-cd7d-484c-9551-9a328a58d3ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'implied_probabilities': array([0.35934392, 0.42324385, 0.21741223]),\n",
       " 'method': 'shin',\n",
       " 'z': 0.016236442857291165,\n",
       " 'margin': np.float64(0.03242570633874986)}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normalised = pb.implied.shin(odds)\n",
    "normalised"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "36f7924b-a9da-400f-9b2e-f54554727b23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.9999999999990125)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(normalised[\"implied_probabilities\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73920fe5-9ba7-4fe8-b1d5-eeaa35d88222",
   "metadata": {},
   "source": [
    "### Remove the overround using Joseph Buchdahl's margin weights proportional to the odds approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "faa40081-7ec3-4389-9524-e7c40eb6bd81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'implied_probabilities': array([0.3595618 , 0.42397404, 0.21646416]),\n",
       " 'method': 'differential_margin_weighting',\n",
       " 'margin': np.float64(0.03242570633874986)}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normalised = pb.implied.differential_margin_weighting(odds)\n",
    "normalised"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d0fbccdb-0af8-4867-bc70-b4e5edadad08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.9999999999999998)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(normalised[\"implied_probabilities\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb578272-4157-482d-8821-e1214e80bfb2",
   "metadata": {},
   "source": [
    "### Remove the overround using Keith Cheung's odds ratio approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e05a8f3e-5126-4796-8d4d-1f44f8e9410b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'implied_probabilities': array([0.35881036, 0.42256142, 0.21862822]),\n",
       " 'method': 'odds_ratio',\n",
       " 'c': 1.05116912729218,\n",
       " 'margin': np.float64(0.03242570633874986)}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normalised = pb.implied.odds_ratio(odds)\n",
    "normalised"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "02965066-0c24-4b29-a531-f3aa892e0b35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.000000000000595)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(normalised[\"implied_probabilities\"])"
   ]
  }
 ],
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