{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_rating = 400\n",
    "k = 100\n",
    "\n",
    "things = ['Malted Milk','Rich Tea','Hobnob','Digestive']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Elo Algos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_win(r1, r2):\n",
    "    \"\"\"\n",
    "    Expected probability of player 1 beating player 2\n",
    "    if player 1 has rating 1 (r1) and player 2 has rating 2 (r2)\n",
    "    \"\"\"\n",
    "    return 1.0 / (1 + math.pow(10, (r2-r1)/400))\n",
    "\n",
    "def update_rating(R, k, P, d):\n",
    "    \"\"\"\n",
    "    d = 1 = WIN\n",
    "    d = 0 = LOSS\n",
    "    \"\"\"\n",
    "    return R + k*(d-P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "def elo(Ra, Rb, k, d):\n",
    "    \"\"\"\n",
    "    d = 1 when player A wins\n",
    "    d = 0 when player B wins\n",
    "    \"\"\"\n",
    "    \n",
    "    Pa = expected_win(Ra, Rb)\n",
    "    Pb = expected_win(Rb, Ra)\n",
    "    \n",
    "    # update if A wins\n",
    "    if d == 1:\n",
    "        Ra = update_rating(Ra, k, Pa, d)\n",
    "        Rb = update_rating(Rb, k, Pb, d-1)\n",
    "    \n",
    "    # update if B wins\n",
    "    elif d == 0:\n",
    "        Ra = update_rating(Ra, k, Pa, d)\n",
    "        Rb = update_rating(Rb, k, Pb, d+1)\n",
    "    \n",
    "    return Pa, Pb, Ra, Rb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "def elo_sequence(things, initial_rating, k, results):\n",
    "    \"\"\"\n",
    "    Initialises score dictionary, and runs through sequence of pairwise results, returning final dictionary of Elo rankings\n",
    "    \"\"\"\n",
    "\n",
    "    dic_scores = {i:initial_rating for i in things}\n",
    "\n",
    "    for result in results:\n",
    "\n",
    "        winner, loser = result\n",
    "        Ra, Rb = dic_scores[winner], dic_scores[loser]\n",
    "        _, _, newRa, newRb = elo(Ra, Rb, k, 1)\n",
    "        dic_scores[winner], dic_scores[loser] = newRa, newRb\n",
    "\n",
    "    return dic_scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean Elo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mElo(things, initial_rating, k, results, numEpochs):\n",
    "    \"\"\"\n",
    "    Randomises the sequence of the pairwise comparisons, running the Elo sequence in a random\n",
    "    sequence for a number of epochs\n",
    "    \n",
    "    Returns the mean Elo ratings over the randomised epoch sequences\n",
    "    \"\"\"\n",
    "    \n",
    "    lst_outcomes = []\n",
    "    \n",
    "    for i in np.arange(numEpochs):\n",
    "        np.random.shuffle(results)\n",
    "        lst_outcomes.append(elo_sequence(things, initial_rating, k, results))\n",
    "        \n",
    "    return pd.DataFrame(lst_outcomes).mean().sort_values(ascending=False)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pairwise Outcomes from Christian's Taste Test\n",
    "\n",
    "> **Format** (Winner, Loser)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = np.array([('Malted Milk','Rich Tea'),('Malted Milk','Digestive'),('Malted Milk','Hobnob')\\\n",
    "            ,('Hobnob','Rich Tea'),('Hobnob','Digestive'),('Digestive','Rich Tea')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "jenResults = np.array([('Rich Tea','Malted Milk'),('Digestive','Malted Milk'),('Hobnob','Malted Milk')\\\n",
    "            ,('Hobnob','Rich Tea'),('Hobnob','Digestive'),('Digestive','Rich Tea')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Hobnob         529.617095\n",
       "Digestive      442.809668\n",
       "Rich Tea       356.925713\n",
       "Malted Milk    270.647524\n",
       "dtype: float64"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mElo(things, initial_rating, k, jenResults, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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