Created
January 22, 2019 14:35
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Elo system
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Elo Rating System" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def expectation(rank_a, rank_b):\n", | |
| " return 1 / (1 + 10 ** ((rank_b - rank_a) / 400))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Jugadores con el mismo ranking tienen igual probabilidad de ganar" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "0.5" | |
| ] | |
| }, | |
| "execution_count": 9, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "expectation(1000, 1000)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Update rule" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "> The maximum possible adjustment per game, called the K-factor, was set at K = 16 for masters and K = 32 for weaker players." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def new_rank(rank_a, rank_b, result=1):\n", | |
| " \"\"\"result: 1 => win | 0 => loss\"\"\"\n", | |
| " K = 32\n", | |
| " return rank_a + K * (result - expectation(rank_a, rank_b))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Ejemplo\n", | |
| "Un jugador fuerte `rank = 2000` vs un paquete `rank = 1500`" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "0.9467597847979775" | |
| ] | |
| }, | |
| "execution_count": 10, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "rank_a = 2000\n", | |
| "rank_b = 1500\n", | |
| "expectation(rank_a, rank_b)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "2001.7036868864648" | |
| ] | |
| }, | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "new_rank_a = new_rank(rank_a, rank_b, result = 1)\n", | |
| "new_rank_a" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "1484.0" | |
| ] | |
| }, | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "new_rank_b = new_rank(rank_b, rank_b, result = 0)\n", | |
| "new_rank_b" | |
| ] | |
| } | |
| ], | |
| "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": "3.6.6" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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