NCAA rating formulas

rpi.py

"""
Rating percentage index (RPI).

Example taken from https://www.wikiwand.com/en/Rating_percentage_index#/Basketball_formula
"""

X = pd.DataFrame(
    data=[
        (2010, 'UConn', 64, 'Kansas', 57),
        (2010, 'UConn', 82, 'Duke', 68),
        (2010, 'Wisconsin', 71, 'UConn', 72),
        (2010, 'Kansas', 69, 'UConn', 62),
        (2010, 'Duke', 81, 'Wisconsin', 70),
        (2010, 'Wisconsin', 52, 'Kansas', 62)
    ],
    columns=['Season', 'T1', 'T1_Score', 'T2', 'T2_Score']
)

X = pd.concat([
    X[['Season', 'T1', 'T1_Score', 'T2', 'T2_Score']],
    X[['Season', 'T2', 'T2_Score', 'T1', 'T1_Score']].rename(columns={
        'T1': 'T2',
        'T2': 'T1',
        'T1_Score': 'T2_Score',
        'T2_Score': 'T1_Score'
    })
])

victory = lambda x: x['T1_Score'] > x['T2_Score']
win_rates = X.assign(victory=victory).groupby(['Season', 'T1'])['victory'].agg(['mean', 'count']).to_dict()
matchups = X.assign(victory=victory).groupby(['Season', 'T1', 'T2'])['victory'].agg(['sum', 'count']).to_dict()
n_matches = X.groupby(['Season', 'T1']).size().to_dict()
opponents = X.groupby(['Season', 'T1'])['T2'].unique().to_dict()


def update_mean(mean, count, removed_sum, removed_count):
    return (mean * count - removed_sum) / (count - removed_count)


def calc_wp(season, team):
    return win_rates['mean'][(season, team)]


def calc_owp(season, team):
    
    return 1 / n_matches[(season, team)] * sum(
        update_mean(
            mean=win_rates['mean'][(season, opponent)],
            count=win_rates['count'][(season, opponent)],
            removed_sum=matchups['sum'][(season, opponent, team)],
            removed_count=matchups['count'][(season, opponent, team)]
        ) * matchups['count'][(season, opponent, team)]
        for opponent in opponents[(season, team)]
    )


def calc_oowp(season, team, owps):
    return 1 / n_matches[(season, team)] * sum(
        owps[opponent] * matchups['count'][(season, opponent, team)]
        for opponent in opponents[(season, team)]
    )


def calc_rpi(wp, owp, oowp):
    return wp * .25 + owp * .5 + oowp * .25
    

seasons = regular['Season'].unique()

wps = {
    season: {
        team: calc_wp(season, team)
        for team in regular.query(f'Season == {season}')['T1'].unique()
    }
    for season in seasons
}

owps = {
    season: {
        team: calc_owp(season, team)
        for team in regular.query(f'Season == {season}')['T1'].unique()
    }
    for season in seasons
}

oowps = {
    season: {
        team: calc_oowp(season, team, owps[season])
        for team in regular.query(f'Season == {season}')['T1'].unique()
    }
    for season in seasons
}

rpis = {
    season: {
        team: calc_rpi(wps[season][team], owps[season][team], oowps[season][team])
        for team in regular.query(f'Season == {season}')['T1'].unique()
    }
    for season in seasons
}
rpis = pd.DataFrame.from_dict(rpis, orient='columns').stack()

srs.py

"""
Simple rating system (SRS).
"""

from scipy import optimize

X = pd.DataFrame(
    data=[
        (2010, 'UConn', 64, 'Kansas', 57),
        (2010, 'UConn', 82, 'Duke', 68),
        (2010, 'Wisconsin', 71, 'UConn', 72),
        (2010, 'Kansas', 69, 'UConn', 62),
        (2010, 'Duke', 81, 'Wisconsin', 70),
        (2010, 'Wisconsin', 52, 'Kansas', 62)
    ],
    columns=['Season', 'T1', 'T1_Score', 'T2', 'T2_Score']
)

srss = {}

for season in X['Season'].unique():
    
    season_results = regular_results.query(f'Season == {season}')
    
    teams = season_results['T1'].unique()
    
    G = pd.concat(
        [
            (
                (season_results['T1'] == team).astype(int) - \
                (season_results['T2'] == team).astype(int)
            ).rename(team)
            for team in teams
        ],
        axis='columns'
    )
    
    S = season_results['T1_Score'] - season_results['T2_Score']
    
    R = optimize.lsq_linear(G, S).x
    
    srss[season] = pd.Series(R, index=teams)
    
srss = pd.DataFrame.from_dict(srss).stack()
df = df.join(srss.rename('T1_srs'), on=['T1', 'Season'])
df = df.join(srss.rename('T2_srs'), on=['T2', 'Season'])

For the 2019 NCAA Kaggle women competition I found that the RPI I calculated this way had a 0.91 correlation with the team seeds. I didn't take into account home and away weighting.