Proposed Lesson Winrate Data Gathering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "unable-official",
   "metadata": {},
   "source": [
    "# Lesson Analysis\n",
    "\n",
    "In this notebook I will be going thorugh the proposal of a new lesson metric which aims to work similarly to ever in hand, but for lessons. To do this we will:\n",
    "\n",
    "1. Examine that the likelyhood of any lesson being drawn\n",
    "2. Show that the likelihood of any lesson being drawn is proportional to the amount of learn cards in the deck\n",
    "1. Estimate the winrate of lessons given the amount of learn cards in the deck\n",
    "1. Show that the winrate of lessons with learn in hand is comparable to winrate of decks with lessons in their sideboard."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "weighted-chess",
   "metadata": {},
   "source": [
    "## Measuring the Winrate of Situationally Good Cards\n",
    "The average winrate of a situational cards that start in your deck is currently best captured by \"Ever In Hand Winrate\" winrate metric. \"Ever In Hand Winrate\" is used over the \"Winrate When Cast\" because winrate when cast selects highly for cards that are situationally good like [Warhorn Blast](https://scryfall.com/card/khm/38/warhorn-blast) from KHM limited. [Warhorn Blast](https://scryfall.com/card/khm/38/warhorn-blast) is situationally good when you have a large board presenece/are the agressor. Players are more likely to cast it in games where you have lethal after casting it then in games where you are at parity or behind. To account for this \"Ever In Hand\" takes into account that situationally good cards should be measured when you have access to their effects and not when you cast the spell. \"Ever In Hand\" does this by only taking into account the winrate of cards that you have the opportunity to cast, not whether they were cast. This is important because it is our best guess at how good a card is on average. \"Ever In Hanhd\" estimates the average winrate of a card by taking the winrates of games where situationally good cards are good and averaging them into games where the card is either not as good, or perhaps even has no targets. The weighting of these scenarios is naturally the probability that they occur by virtue of looking at all the games where a player had access to the effect because the situations where a card is good will naturally occur at the rate they they are probable to happen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "serial-deputy",
   "metadata": {},
   "source": [
    "## Proposed Replacement for Lessons being drawn \n",
    "Currently only looking at \"Ever In Hand\" has a similar effect to \"Winrate When Cast\" because it biased towards situationally good cards. For lessons \"Ever In Hand\" is biased towards situationally good lessons because on average lessons will be fetched when they are good. When a lesson is not good a caster has the option to draw a random card over a lesson. To remedy this, we need a winrate which takes into account the situations where a lesson is good. To do this, I am proposing that we look at the winrate of lessons when a learn card is drawn. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "second-corrections",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# Get hypergeometric coefficients\n",
    "import scipy.stats as ss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "behavioral-shore",
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "Utility functions\n",
    "\n",
    "Functions that are used throughout the notebook are put here to try to reduce clutter in later analysis\n",
    "'''\n",
    "# Game data from https://www.17lands.com/public_datasets\n",
    "game_data_filename = 'game_data_public.STX.Sealed.csv'\n",
    "# STX Lessons retreived with the scryfall API\n",
    "stx_lessons = pd.read_csv(\"stx_lesson.csv\")\n",
    "# STX Cards with learn retreived with the scryfall API\n",
    "stx_learn = pd.read_csv(\"stx_learn.csv\")\n",
    "\n",
    "\n",
    "#####################################################################################################\n",
    "# Get list of card names\n",
    "#\n",
    "# \\param[in] df     The data you are getting the card names from\n",
    "# \\param[in] prefix An optional prefix to prepend to the card names \n",
    "#\n",
    "# \\return A list of card names\n",
    "def get_card_name_list(df, prefix=\"\"):\n",
    "    cards = [prefix+col.replace(\"deck_\",\"\") for col in df.columns if 'deck' in col]\n",
    "    return cards\n",
    "\n",
    "#####################################################################################################\n",
    "# Add columns to track the winrate of each card\n",
    "#\n",
    "# \\param[in] df The data to add a column to\n",
    "#\n",
    "# \\return The data with columns added to track the winrate of each card\n",
    "def add_col_winrate_when_in_hand(df):\n",
    "    # Generate list for new column names\n",
    "    in_hand = get_card_name_list(df,\"in_hand_\")\n",
    "    # Add the cards that are either drawn or in opening hand\n",
    "    df[in_hand] = \\\n",
    "        df[get_card_name_list(df,\"drawn_\")].to_numpy() \\\n",
    "        + df[get_card_name_list(df,\"opening_hand_\")].to_numpy()\n",
    "    # Flatten the data to only detect if the card was drawn and not care about quantity\n",
    "    df[in_hand] = df[in_hand] > 0\n",
    "    # Convert to Int\n",
    "    df[in_hand] = df[in_hand].to_numpy(dtype=int)\n",
    "    # Store win/loss for each game\n",
    "    # Storing the data in an additional column helps when we aggregate the data in a later step by\n",
    "    # accumulating it in a column as opposed to a local variable\n",
    "    ihw = get_card_name_list(df,\"ihw_\")\n",
    "    df[ihw] = df[in_hand].mul(df[\"won\"],axis=0)\n",
    "    return df\n",
    "\n",
    "#####################################################################################################\n",
    "# This function returns an iterator with a batch of data. Batching makes intermittent steps easier to\n",
    "# examine for correctness and also allows for a \"loading bar\" to post incremental progress\n",
    "#\n",
    "# \\param[in] chunksize - Size of the chunk of data to process. Optional with default 2000\n",
    "#\n",
    "# \\return dataiter - an iterator that returns data frames containing batches of cards \n",
    "def get_data_iter(chunksize = 2000):\n",
    "    data_iter = pd.read_csv(game_data_filename,chunksize=chunksize)\n",
    "    data = next(data_iter)\n",
    "    data.columns = [column.lower() for column in data.columns]\n",
    "    # Filter by columns that we are performing calculations on\n",
    "    filtered_columns = sum([ \\\n",
    "                    get_card_name_list(data,\"deck_\"),\n",
    "                    get_card_name_list(data,\"opening_hand_\"),\n",
    "                    get_card_name_list(data,\"drawn_\"),\n",
    "                    get_card_name_list(data,\"sideboard_\"),\n",
    "                    [\"won\",\"num_turns\"]\n",
    "                   ], [])\n",
    "    data = data[filtered_columns]\n",
    "    data = add_col_winrate_when_in_hand(data)\n",
    "    yield data\n",
    "    for data in data_iter:\n",
    "        data.columns = [column.lower() for column in data.columns]\n",
    "        data = data[filtered_columns]\n",
    "        data = add_col_winrate_when_in_hand(data)\n",
    "        yield data\n",
    "\n",
    "#####################################################################################################\n",
    "# Get table for expected probability for the game to end on turn N with a card in hand, given that\n",
    "# you have M copies of the card in your deck\n",
    "# \n",
    "# Acessing the table:\n",
    "# Note: turns_df has to have a column named num_games which has the relative frequency of games that\n",
    "# end on turn N\n",
    "# ---------------------------------\n",
    "# expected_drawn = get_expected_drawn_table(turns_df) \n",
    "# expected_drawn[M][N]\n",
    "# M - Number of copies in deck (from 0 to cards_in_deck)\n",
    "# N - Number of turns when the game ended (from 1 to cards_in_deck - starting_hand)\n",
    "#\n",
    "# \\param[in] turns_df      The turn data with an expected column \"num_games\" which has the\n",
    "#                          distrubtion of games which ended on turn N\n",
    "# \\param[in] cards_in_deck The number of cards in a deck. Default 40.\n",
    "# \\param[in] starting_hand The number of cards in your starting hand. Default 7.\n",
    "#\n",
    "# \\return An expected probability table with columns labeled with the number of copies of a card in\n",
    "#         the deck and the rows labeled with the number of turns\n",
    "def get_expected_drawn_table(turns_df, cards_in_deck=40, starting_hand=7):\n",
    "    # Game ends when you draw your deck on average\n",
    "    max_turns = cards_in_deck - starting_hand\n",
    "    # Game ends when you \n",
    "    max_copies = cards_in_deck\n",
    "    turn_dist = pd.DataFrame(np.zeros(max_turns), index=range(1,max_turns+1), columns=[\"turn_dist\"])\n",
    "    turn_dist[\"turn_dist\"] = turn_dist[\"turn_dist\"].add(turns_df[\"num_games\"], fill_value=0)\n",
    "    turn_dist = turn_dist[\"turn_dist\"]/sum(turn_dist[\"turn_dist\"])\n",
    "    expected_drawn = pd.DataFrame()\n",
    "    # Set to zero to zero to compensate for floating point error with calculations\n",
    "    expected_drawn[0] = turn_dist*np.zeros(max_turns)\n",
    "    # Coefficients of the hypergeometric distribution\n",
    "    # Hypergeometric distribution is the likelyhood you draw\n",
    "    # N copies of a card with M chances\n",
    "    # Iterate over copies and turns\n",
    "    for copies in range(1, max_copies+1):\n",
    "        expected_drawn_N_copies = []\n",
    "        for turns in range(1,max_turns+1):\n",
    "            # We are assuming that on average cards drawn on turn M is M + starting_hand\n",
    "            cards_drawn = turns + starting_hand\n",
    "            hgd = ss.hypergeom(cards_in_deck,  copies, cards_drawn)\n",
    "            # The probability of drawing any copies is one minus the probability of drawing zero\n",
    "            expected_drawn_N_copies.append(1-hgd.pmf(0))\n",
    "        expected_drawn_N_copies = turn_dist*expected_drawn_N_copies\n",
    "        expected_drawn_N_copies = expected_drawn_N_copies/sum(expected_drawn_N_copies)\n",
    "        expected_drawn[copies] = expected_drawn_N_copies\n",
    "    return expected_drawn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "provincial-analyst",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "'''\n",
    "Raw Calculations\n",
    "\n",
    "Calculate the likelyhood of drawing a card with learn. \n",
    "Calculate the likelyhoood of drawing a lesson.\n",
    "'''\n",
    "# Group the data by number of turns\n",
    "# Add a num_games column to track the number of games that took a particular length\n",
    "def group_num_turns(df):\n",
    "    df[\"num_games\"] = 1\n",
    "    df = df.groupby(by=\"num_turns\").sum()\n",
    "    return df\n",
    "\n",
    "data_iter = get_data_iter()\n",
    "data_grouped_by_turn_count = next(data_iter)\n",
    "data_grouped_by_turn_count = group_num_turns(data_grouped_by_turn_count)\n",
    "# Used to track progress\n",
    "counter = 0\n",
    "for batch in data_iter:\n",
    "    print(counter,end=\" \")\n",
    "    batch = group_num_turns(batch)\n",
    "    data_grouped_by_turn_count = data_grouped_by_turn_count.add(batch,fill_value=0)\n",
    "    counter += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "pretty-jefferson",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data_grouped_by_turn_count[\"num_games\"])\n",
    "plt.xlabel('Turn Number Game Ended On')\n",
    "plt.ylabel('Total Number of Games')\n",
    "plt.title(\"Number of Turns in a Game Frequency Plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "american-separate",
   "metadata": {},
   "source": [
    "# Showing The Likelyhood of drawing a lesson\n",
    "We theorize that the likelyhood of drawing a lesson is similar to the likelyhood of drawing any card with learn because you use learn cards to search for a lesson. To show this we are going to plot the sampled likelyhood of drawing a lesson for games that end on turn N with the sampled lieklyhood that you drew a learn card for games that ended on turn N."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "needed-johnston",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Expected Turn Frequency of data\n",
    "turn_freq = data_grouped_by_turn_count[\"num_games\"]\n",
    "turn_freq = turn_freq/(turn_freq.sum())\n",
    "\n",
    "# plot draw rates of lessons\n",
    "lessons = data_grouped_by_turn_count[\"in_hand_\"+stx_lessons[\"name\"]]\n",
    "lessons = lessons.sum(axis=1)\n",
    "lessons = lessons/turn_freq # Scale based on frequency of games ending on turn N\n",
    "lessons_plot = plt.plot(lessons, label='lessons')\n",
    "\n",
    "# plot draw rates of learn cards\n",
    "learn = data_grouped_by_turn_count[\"in_hand_\"+stx_learn[\"name\"]]\n",
    "learn = learn.sum(axis=1)\n",
    "learn = learn/turn_freq #Scale based on frequency of games ending on turn N\n",
    "learn_plot = plt.plot(learn, label='learn')\n",
    "\n",
    "plt.xlabel('Turn')\n",
    "plt.ylabel('Total Count in Hand')\n",
    "plt.title(\"Learn/Lesson Frequency Plot\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "single-designation",
   "metadata": {},
   "source": [
    "# Compare \"Learn Drawn \"to \"Lessons Drawn\"\n",
    "Now that we have the rate at which lessons and learn occur in games, we will plot the error of the estimate below. What we can see is that \"learn drawn\" slightly over represents \"lessons drawn\" in the early game, but as the number of turns increases the error gets smaller. This is because learn cards draw a lesson when they are cast. The underestimation of lessons by learn in the late game is probably due to lessons in deck or recursion in the format, but is <0.2% difference by inspection with the caviat that there is less data from games >20 turns so the variance is wider."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "municipal-literature",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "num_turns\n",
       "1     0.954545\n",
       "2     0.750000\n",
       "3     0.529412\n",
       "4     0.514706\n",
       "5     0.455319\n",
       "6     0.349733\n",
       "7     0.243183\n",
       "8     0.149787\n",
       "9     0.089831\n",
       "10    0.035977\n",
       "11    0.017675\n",
       "12   -0.013975\n",
       "13   -0.029329\n",
       "14   -0.057320\n",
       "15   -0.075479\n",
       "16   -0.068267\n",
       "17   -0.090983\n",
       "18   -0.104418\n",
       "19   -0.100145\n",
       "20   -0.144578\n",
       "21   -0.046272\n",
       "22   -0.103139\n",
       "23   -0.071429\n",
       "24   -0.144144\n",
       "25   -0.158730\n",
       "26   -0.142857\n",
       "27   -0.111111\n",
       "28    0.062500\n",
       "29   -0.285714\n",
       "30   -0.187500\n",
       "31    0.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot difference\n",
    "compare = (learn-lessons)/(learn)\n",
    "plt.plot(compare)\n",
    "plt.plot(np.zeros(len(compare)))\n",
    "\n",
    "plt.xlabel('Turn Number')\n",
    "plt.ylabel('Percent Error')\n",
    "plt.title(\"Percent learn cards Overrepresent Lessons Drawn\")\n",
    "plt.show()\n",
    "compare"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "complimentary-buffer",
   "metadata": {},
   "source": [
    "# Estimate the winrate of lessons\n",
    "In this section we will estimate the winrate of each lesson by looking at the winrate of decks with the lesson in the sideboard which drew a card with learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "agricultural-tracker",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Table of expected rate of drawing a card given you have n copies of the card and it's turn n\n",
    "expected_drawn = get_expected_drawn_table(data_grouped_by_turn_count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "immune-selection",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 "
     ]
    }
   ],
   "source": [
    "'''\n",
    "Raw Calculations\n",
    "\n",
    "Calculate the likelyhood of winning with a card in sideboard\n",
    "Calculate the likelyhoood of winning with a card in sideboard, weighting it based on the number of learn cards in deck\n",
    "'''\n",
    "def add_lessons_columns(df): \n",
    "    # Add column for winrate given the lesson was in the sb\n",
    "    df[\"lesson_sb_\"+stx_lessons[\"name\"]] = (df[\"sideboard_\" + stx_lessons[\"name\"]]>0).to_numpy(dtype=int)\n",
    "    df[\"lesson_sb_won_\"+stx_lessons[\"name\"]] = df[\"lesson_sb_\"+stx_lessons[\"name\"]].mul(df[\"won\"],axis=0)\n",
    "    # Add columns for winrate given the lesson was in the sideboard and you drew the card with learn\n",
    "    # Column for ever drew a learn card\n",
    "    learn= df[\"in_hand_\"+stx_learn[\"name\"]]\n",
    "    df[\"learn_drawn\"] = (learn.sum(axis=1) > 0).to_numpy(dtype=int)\n",
    "    # Column for total count of learn cards in deck\n",
    "    learn_deck = df[\"deck_\"+stx_learn[\"name\"]]\n",
    "    df[\"learn_deck\"] = learn_deck.sum(axis=1)\n",
    "    # Weight each sample based on the likelyhood that the game ended on turn N given that you had \"learn_drawn\"\n",
    "    # number of learn cards using hypergeomteric distribution and the sampled turn length data\n",
    "    df[\"learn_weight\"] = [expected_drawn[x][y] for x,y in zip(df[\"learn_deck\"],df[\"num_turns\"])]\n",
    "    # Weight games where a learn card was not drawn as 0\n",
    "    df[\"learn_weight\"] = df[\"learn_weight\"]*df[\"learn_drawn\"]\n",
    "    # Only count games where \n",
    "    df[\"learned_weighted_N_\" +stx_lessons[\"name\"]] = (df[\"lesson_sb_\"+stx_lessons[\"name\"]].mul(df[\"learn_drawn\"],axis=0) > 0).to_numpy(dtype=int)\n",
    "    df[\"lessons_weighted_\" + stx_lessons[\"name\"]] =  df[\"lesson_sb_\"+stx_lessons[\"name\"]].mul(df[\"learn_weight\"],axis=0)\n",
    "    df[\"lessons_weighted_won_\" + stx_lessons[\"name\"]] = df[\"lessons_weighted_\" + stx_lessons[\"name\"]].mul(df[\"won\"],axis=0)\n",
    "    return df\n",
    "\n",
    "\n",
    "data_iter = get_data_iter()\n",
    "lesson_winrate = next(data_iter)\n",
    "lesson_winrate = add_lessons_columns(lesson_winrate)\n",
    "lesson_winrate = lesson_winrate.sum()\n",
    "counter = 0\n",
    "for batch in data_iter:\n",
    "    print(counter,end=\" \")\n",
    "    batch = add_lessons_columns(batch)\n",
    "    batch = batch.sum()\n",
    "    lesson_winrate = lesson_winrate.add(batch, fill_value=0)\n",
    "    counter += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "focal-volleyball",
   "metadata": {},
   "source": [
    "# Correlation of \"Lesson in Sideboard\" to \"Ever Drawn Learn Card\" for Lessons\n",
    "Here we show that the winrate of decks with a particular lesson in the sideboard is correlated to the winrate of decks with the same lesson cards in the sideboard which drew a learn card. This is a strong indication that our proposed metric is correct since sideboard winrate is unbiased towards cards that are situationally good."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "announced-building",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "first_cn = \"environmental sciences\"\n",
    "last_cn = \"basic conjuration\"\n",
    "\n",
    "# Calculate the winrate of cards of decks with lesson cards in the sideboard\n",
    "sb_played = lesson_winrate.loc[\"lesson_sb_\"+first_cn:\"lesson_sb_\"+last_cn].to_numpy()\n",
    "sb_won = lesson_winrate.loc[\"lesson_sb_won_\"+first_cn:\"lesson_sb_won_\"+last_cn].to_numpy()\n",
    "sb_winrate = sb_won/(sb_played + 0.0000001) # DEBUG: Divide by Zero Error\n",
    "\n",
    "# Calculate the winrate of games where a learn card was drawn and there was a lesson in the sb\n",
    "weighted_played = lesson_winrate.loc[\"lessons_weighted_\"+first_cn:\"lessons_weighted_\"+last_cn].to_numpy()\n",
    "weighted_won = lesson_winrate.loc[\"lessons_weighted_won_\"+first_cn:\"lessons_weighted_won_\"+last_cn].to_numpy()\n",
    "weighted_winrate = weighted_won/(weighted_played + 0.0000001) # DEBUG: Divide by Zero Error\n",
    "\n",
    "plt.scatter(sb_winrate, weighted_winrate)\n",
    "# Y=X For reference\n",
    "plt.plot(np.linspace(0.5,0.7,200),np.linspace(0.5,0.7,200), color='green' )\n",
    "plt.xlabel('Card In Sideboard Winrate')\n",
    "plt.ylabel('Learn Drawn Winrate')\n",
    "plt.title(\"Correlation of SB Winrate To Learn Drawn Winrate For Lessons\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "material-roller",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\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>sb_winrate</th>\n",
       "      <th>weighted_winrate</th>\n",
       "      <th>num_samples</th>\n",
       "      <th>margin_of_error</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mascot exhibition</th>\n",
       "      <td>0.624158</td>\n",
       "      <td>0.658790</td>\n",
       "      <td>1712.0</td>\n",
       "      <td>0.012084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>teachings of the archaics</th>\n",
       "      <td>0.551987</td>\n",
       "      <td>0.586216</td>\n",
       "      <td>2873.0</td>\n",
       "      <td>0.009328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>environmental sciences</th>\n",
       "      <td>0.557820</td>\n",
       "      <td>0.582098</td>\n",
       "      <td>20779.0</td>\n",
       "      <td>0.003469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>expanded anatomy</th>\n",
       "      <td>0.551147</td>\n",
       "      <td>0.576085</td>\n",
       "      <td>21353.0</td>\n",
       "      <td>0.003422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>introduction to annihilation</th>\n",
       "      <td>0.552426</td>\n",
       "      <td>0.575579</td>\n",
       "      <td>21591.0</td>\n",
       "      <td>0.003403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fractal summoning</th>\n",
       "      <td>0.554258</td>\n",
       "      <td>0.575010</td>\n",
       "      <td>21221.0</td>\n",
       "      <td>0.003432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>inkling summoning</th>\n",
       "      <td>0.553384</td>\n",
       "      <td>0.574742</td>\n",
       "      <td>20899.0</td>\n",
       "      <td>0.003459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>spirit summoning</th>\n",
       "      <td>0.552007</td>\n",
       "      <td>0.573728</td>\n",
       "      <td>20881.0</td>\n",
       "      <td>0.003460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pest summoning</th>\n",
       "      <td>0.552110</td>\n",
       "      <td>0.573383</td>\n",
       "      <td>20516.0</td>\n",
       "      <td>0.003491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>introduction to prophecy</th>\n",
       "      <td>0.551160</td>\n",
       "      <td>0.572025</td>\n",
       "      <td>21336.0</td>\n",
       "      <td>0.003423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>necrotic fumes</th>\n",
       "      <td>0.552570</td>\n",
       "      <td>0.571663</td>\n",
       "      <td>7525.0</td>\n",
       "      <td>0.005764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mercurial transformation</th>\n",
       "      <td>0.548585</td>\n",
       "      <td>0.571249</td>\n",
       "      <td>7794.0</td>\n",
       "      <td>0.005664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>illuminate history</th>\n",
       "      <td>0.548528</td>\n",
       "      <td>0.570429</td>\n",
       "      <td>3142.0</td>\n",
       "      <td>0.008920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>confront the past</th>\n",
       "      <td>0.540735</td>\n",
       "      <td>0.570120</td>\n",
       "      <td>2990.0</td>\n",
       "      <td>0.009144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>reduce to memory</th>\n",
       "      <td>0.548583</td>\n",
       "      <td>0.568702</td>\n",
       "      <td>7520.0</td>\n",
       "      <td>0.005766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>elemental summoning</th>\n",
       "      <td>0.549649</td>\n",
       "      <td>0.567927</td>\n",
       "      <td>21480.0</td>\n",
       "      <td>0.003412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>start from scratch</th>\n",
       "      <td>0.544238</td>\n",
       "      <td>0.566529</td>\n",
       "      <td>7686.0</td>\n",
       "      <td>0.005703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>basic conjuration</th>\n",
       "      <td>0.539007</td>\n",
       "      <td>0.560251</td>\n",
       "      <td>2792.0</td>\n",
       "      <td>0.009463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>containment breach</th>\n",
       "      <td>0.533482</td>\n",
       "      <td>0.553233</td>\n",
       "      <td>7423.0</td>\n",
       "      <td>0.005803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>academic probation</th>\n",
       "      <td>0.536339</td>\n",
       "      <td>0.549287</td>\n",
       "      <td>3074.0</td>\n",
       "      <td>0.009018</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              sb_winrate  weighted_winrate  num_samples  \\\n",
       "name                                                                      \n",
       "mascot exhibition               0.624158          0.658790       1712.0   \n",
       "teachings of the archaics       0.551987          0.586216       2873.0   \n",
       "environmental sciences          0.557820          0.582098      20779.0   \n",
       "expanded anatomy                0.551147          0.576085      21353.0   \n",
       "introduction to annihilation    0.552426          0.575579      21591.0   \n",
       "fractal summoning               0.554258          0.575010      21221.0   \n",
       "inkling summoning               0.553384          0.574742      20899.0   \n",
       "spirit summoning                0.552007          0.573728      20881.0   \n",
       "pest summoning                  0.552110          0.573383      20516.0   \n",
       "introduction to prophecy        0.551160          0.572025      21336.0   \n",
       "necrotic fumes                  0.552570          0.571663       7525.0   \n",
       "mercurial transformation        0.548585          0.571249       7794.0   \n",
       "illuminate history              0.548528          0.570429       3142.0   \n",
       "confront the past               0.540735          0.570120       2990.0   \n",
       "reduce to memory                0.548583          0.568702       7520.0   \n",
       "elemental summoning             0.549649          0.567927      21480.0   \n",
       "start from scratch              0.544238          0.566529       7686.0   \n",
       "basic conjuration               0.539007          0.560251       2792.0   \n",
       "containment breach              0.533482          0.553233       7423.0   \n",
       "academic probation              0.536339          0.549287       3074.0   \n",
       "\n",
       "                              margin_of_error  \n",
       "name                                           \n",
       "mascot exhibition                    0.012084  \n",
       "teachings of the archaics            0.009328  \n",
       "environmental sciences               0.003469  \n",
       "expanded anatomy                     0.003422  \n",
       "introduction to annihilation         0.003403  \n",
       "fractal summoning                    0.003432  \n",
       "inkling summoning                    0.003459  \n",
       "spirit summoning                     0.003460  \n",
       "pest summoning                       0.003491  \n",
       "introduction to prophecy             0.003423  \n",
       "necrotic fumes                       0.005764  \n",
       "mercurial transformation             0.005664  \n",
       "illuminate history                   0.008920  \n",
       "confront the past                    0.009144  \n",
       "reduce to memory                     0.005766  \n",
       "elemental summoning                  0.003412  \n",
       "start from scratch                   0.005703  \n",
       "basic conjuration                    0.009463  \n",
       "containment breach                   0.005803  \n",
       "academic probation                   0.009018  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show the data in a table\n",
    "weighted_n = lesson_winrate.loc[\"learned_weighted_N_\"+first_cn:\"learned_weighted_N_\"+last_cn].to_numpy()\n",
    "error = 0.5/np.sqrt(weighted_n)\n",
    "a = np.array([sb_winrate, weighted_winrate, weighted_n,error])\n",
    "winrates = pd.DataFrame( \n",
    "                        data=a.T,\n",
    "                        columns=[\"sb_winrate\", \"weighted_winrate\",\"num_samples\", \"margin_of_error\"],\n",
    "                        index=stx_lessons[\"name\"])\n",
    "winrates = winrates.sort_values(\"weighted_winrate\",ascending=False)\n",
    "winrates\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "metallic-board",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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