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def initialize_true_ratings(team_1_mean = 0.5, team_2_mean = -0.5):
    
    ## since I don't have data, I'm going to simulate using an example where team 1 > team 2
    ## example of "true" skills -> what our ratings should approach
    ## I'll use the "true" skills to generate data
    
    team_1_true_ratings = np.random.normal(team_1_mean, 1, 5)
    team_2_true_ratings = np.random.normal(team_2_mean, 1, 5)
    
    return team_1_true_ratings, team_2_true_ratings

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def play_h2h(self, result):

    """
    Initialized with player 1 and player 2 object. Uses their means, standard deviations, and the provided result to update their ratings.
    """

    ## Finding Z (purple distribution graph)
    z = self.p1.mu - self.p2.mu
    z_var = self.p1.sigma**2+self.p2.sigma**2

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def update_multiple_beta_single_game(alphas, betas, outcomes, k=1):
    assert(len(alphas)==len(betas)==len(outcomes))

    """
    This function only works one game at a time for multiple players
    
    """
    n = np.ones(len(alphas))

    # Calculate the posterior alpha and beta parameters

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alpha_dict = {
    'dOppORtg_y':0.038,
    'dORtg_y':0.019,
    'dPace_y':0.1,
    'dTReb%_y':0.02,
    # same for other team
    'dOppORtg_x':0.038,
    'dORtg_x':0.019,
    'dPace_x':0.1,
    'dTReb%_x':0.02,

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sos_cols = ['Season','TeamID','OppTeamID','Loc','ScoreDiff']
sos_df = df[sos_cols]

# here you could code "Home, Away, Neutral" location with 1, -1, and 0. I'm lazy and will include it in my one hot encoding below.

# will append season by season (prob a way to vectorize this without for loop)
sos_all = pd.DataFrame()

seasons = list(sos_df.Season.unique())

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data = pbp[['score_differential','play_type']]
data.loc[:,'play_type'] = data.play_type.copy().replace({"run":"0","pass":"1"}).astype(int)

# shuffle data 
data = data.sample(frac=1)

# let's use 10,000 observations
data = data[:10000]

plays = data.play_type.values

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## estimate pass rate
import pymc3 as pm

data = pbp[['play_type']]
data.loc[:,'play_type'] = data.play_type.copy().replace({"run":"0","pass":"1"}).astype(int)

# shuffle data 
data = data.sample(frac=1)

# only need 5000 observations

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import pymc3 as pm, theano.tensor as tt

# gamma priors for qbs
qb_a = qb_proj.shape_.values
qb_b = qb_proj.rate.values

# gamma priors for defenses
dfn_a = dfn_all.shape_.values
dfn_b = dfn_all.rate.values

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library(tidyverse)
library(tidyr)
library(dplyr)
library(na.tools)

seasons <- seq(2014, 2019);

# iteration count
i = 0
df <- NULL;

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from tqdm import tqdm

seasons = list(range(2009, 2020))

td_pg = None

for season in tqdm(seasons[-6:]):
    
    path = './data/nflscrapR/play_by_play_data/regular_season/reg_pbp_{}.csv'.format(season)
    pbp = pd.read_csv(path)