245 lines
9.1 KiB
Plaintext
245 lines
9.1 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"# read file\n",
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"Dat = pd.read_csv(\"DataLoL.csv\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Total Game played\n",
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"total_game = len(Dat['blueWins']) "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Question 1**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Probability of team blue destroyed more structure than team red, if team blue won (using Dat) is 0.06795131845841784\n",
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"Probability of team blue destroyed more structure than team red, if team blue won (using dat_blue_wins) is 0.06795131845841786\n"
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]
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}
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],
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"source": [
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"# calculate probability using Dat\n",
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"prob_blue_wins_more_structure = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueTowersDestroyed'] > Dat['redTowersDestroyed'])]) / len(Dat) # P(A ∩ B)\n",
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"prob_blue_wins = len(Dat[Dat['blueWins'] == 1]) / total_game #P(A)\n",
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"\n",
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"print(\"Probability of team blue destroyed more structure than team red, if team blue won (using Dat) is \", prob_blue_wins_more_structure / prob_blue_wins)\n",
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"\n",
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"# calculate probability using dat_blue_wins\n",
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"# filter game team blue wins\n",
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"dat_blue_wins = Dat[Dat['blueWins'] == 1]\n",
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"\n",
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"# filter game team blue win and destroyed more strcuture\n",
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"dat_blue_wins_more_structure = dat_blue_wins[dat_blue_wins['blueTowersDestroyed'] > dat_blue_wins['redTowersDestroyed']] # (A ∩ B)\n",
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"\n",
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"#Verify using dat_blue_wins\n",
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"prob_blue_wins_more_structure = len(dat_blue_wins_more_structure) / len(dat_blue_wins) # P(B|A) = P(A ∩ B) / P(A)\n",
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"print(\"Probability of team blue destroyed more structure than team red, if team blue won (using dat_blue_wins) is\", prob_blue_wins_more_structure)\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Question 2**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Probability of team blue wins, kills the dragon, kills the heralds and does the first kill is (Using chain rule) 0.037858082801903024\n",
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"Probability of team blue wins, kills the dragon, kills the heralds and does the first kill is (Using new dat set) 0.037858082801903024\n"
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]
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}
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],
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"source": [
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"# calcucate probability team blue wins\n",
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"dat_blue_wins = Dat[Dat['blueWins'] == 1]\n",
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"prob_blue_win = len(dat_blue_wins) / total_game\n",
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"\n",
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"# calculate probability team blue wins, kills the dragon\n",
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"dat_blue_wins_and_kills_dragons = dat_blue_wins[dat_blue_wins['blueDragons'] == 1]\n",
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"prob_blue_wins_and_kills_dragons = len(dat_blue_wins_and_kills_dragons) / len(dat_blue_wins) * prob_blue_win\n",
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"\n",
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"# calculate probability team blue wins, kills the dragon, kills the heralds\n",
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"dat_blue_wins_and_kills_dragons_and_heralds = dat_blue_wins_and_kills_dragons[dat_blue_wins_and_kills_dragons['blueHeralds'] == 1]\n",
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"prob_blue_wins_and_kills_dragons_and_heralds = len(dat_blue_wins_and_kills_dragons_and_heralds) / len(dat_blue_wins_and_kills_dragons) * prob_blue_wins_and_kills_dragons\n",
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"\n",
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"# calculate probability team blue wins, kills the dragon, kills the heralds and does the first kill\n",
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"dat_blue_wins_and_kills_dragons_and_heralds_and_firstblood = dat_blue_wins_and_kills_dragons_and_heralds[dat_blue_wins_and_kills_dragons_and_heralds['blueFirstBlood'] == 1]\n",
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"prob_blue_wins_and_kills_dragons_and_heralds_and_firstblood = len(dat_blue_wins_and_kills_dragons_and_heralds_and_firstblood) / len(dat_blue_wins_and_kills_dragons_and_heralds) * prob_blue_wins_and_kills_dragons_and_heralds\n",
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"\n",
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"print(\"Probability of team blue wins, kills the dragon, kills the heralds and does the first kill is (Using chain rule)\", prob_blue_wins_and_kills_dragons_and_heralds_and_firstblood)\n",
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"print(\"Probability of team blue wins, kills the dragon, kills the heralds and does the first kill is (Using new dat set)\", len(dat_blue_wins_and_kills_dragons_and_heralds_and_firstblood) / total_game)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Question 3**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [],
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"source": [
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"Dat['blueQuantileGold'] = pd.qcut(Dat['blueTotalGold'], 4, labels=False)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"P(A) calculated using Law of Total Probability = 0.4990383642069036\n",
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"P(A) is 0.4990383642069035\n"
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]
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}
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],
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"source": [
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"# filter data to each quantiles\n",
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"dat_quantile_1 = Dat[Dat['blueQuantileGold'] == 0]\n",
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"dat_quantile_2 = Dat[Dat['blueQuantileGold'] == 1]\n",
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"dat_quantile_3 = Dat[Dat['blueQuantileGold'] == 2]\n",
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"dat_quantile_4 = Dat[Dat['blueQuantileGold'] == 3]\n",
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"\n",
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"# calculate a proportion of game in each quantiles\n",
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"quantile_1_prob = len(dat_quantile_1) / total_game\n",
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"quantile_2_prob = len(dat_quantile_2) / total_game\n",
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"quantile_3_prob = len(dat_quantile_3) / total_game\n",
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"quantile_4_prob = len(dat_quantile_4) / total_game\n",
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"\n",
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"# calculate team blue win rate in each quantiles\n",
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"quantile_1_win_rate = len(dat_quantile_1[dat_quantile_1['blueWins'] == 1]) / len(dat_quantile_1)\n",
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"quantile_2_win_rate = len(dat_quantile_2[dat_quantile_2['blueWins'] == 1]) / len(dat_quantile_2)\n",
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"quantile_3_win_rate = len(dat_quantile_3[dat_quantile_3['blueWins'] == 1]) / len(dat_quantile_3)\n",
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"quantile_4_win_rate = len(dat_quantile_4[dat_quantile_4['blueWins'] == 1]) / len(dat_quantile_4)\n",
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"\n",
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"#calculate probability team blue wins using law of total probability\n",
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"prob_a = (quantile_1_prob * quantile_1_win_rate) + (quantile_2_prob * quantile_2_win_rate) + (quantile_3_prob * quantile_3_win_rate) + (quantile_4_prob * quantile_4_win_rate)\n",
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"print(\"P(A) calculated using Law of Total Probability = \", prob_a)\n",
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"\n",
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"#Verify\n",
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"prob_blue_wins = len(Dat[Dat['blueWins'] == 1]) / total_game # calculate probability (event/sample space)\n",
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"print(\"P(A) is\", prob_blue_wins)\n",
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"\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Question 4**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Probability of team blue wins given that it destroyed more structure than team red (using Bayes's theorem) is 0.7596371882086167\n",
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"Probability of team blue wins given that it destroyed more structure than team red (using Dat) is 0.7596371882086167\n"
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]
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}
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],
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"source": [
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"# calculate probability used in Bayes's theorem\n",
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"\n",
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"# P(A)\n",
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"prob_blue_wins = len(Dat[Dat['blueWins'] == 1]) / total_game\n",
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"\n",
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"# P(B)\n",
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"prob_blue_more_structure = len(Dat[Dat['blueTowersDestroyed'] > Dat['redTowersDestroyed']]) / total_game\n",
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"\n",
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"# P(A ∩ B)\n",
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"dat_blue_more_structure = Dat[Dat['blueTowersDestroyed'] > Dat['redTowersDestroyed']]\n",
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"prob_blue_wins_more_structure = len(dat_blue_more_structure[dat_blue_more_structure['blueWins'] == 1]) / total_game\n",
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"\n",
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"# P(B|A)\n",
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"prob_blue_more_structure_if_blue_wins = prob_blue_wins_more_structure / prob_blue_wins\n",
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"\n",
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"# calculate P(A|B) using Bayes's theorem\n",
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"print(\"Probability of team blue wins given that it destroyed more structure than team red (using Bayes's theorem) is \", prob_blue_more_structure_if_blue_wins * prob_blue_wins / prob_blue_more_structure)\n",
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"\n",
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"\n",
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"#Verify using Dat\n",
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"\n",
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"# P(A ∩ B)\n",
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"prob_blue_wins_more_structure = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueTowersDestroyed'] > Dat['redTowersDestroyed'])]) / total_game \n",
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"\n",
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"# P(B)\n",
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"prob_blue_more_structure = len(Dat[Dat['blueTowersDestroyed'] > Dat['redTowersDestroyed']]) / total_game\n",
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"\n",
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"# calculate P(A|B) using Dat\n",
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"print(\"Probability of team blue wins given that it destroyed more structure than team red (using Dat) is \", prob_blue_wins_more_structure / prob_blue_more_structure)\n",
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"\n",
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"\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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