# Lecture 19 – Data 100, Fall 2020¶

by Suraj Rampure

In :
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import plotly.express as px
import plotly.graph_objs as go
from scipy.optimize import minimize
import sklearn.linear_model as lm

plt.rcParams['figure.figsize'] = (4, 4)
plt.rcParams['figure.dpi'] = 150
plt.rcParams['lines.linewidth'] = 3
sns.set()


## Thresholding in Logistic Regression¶

So far, our logistic regression model predicts probabilities. But we originally set out on a mission to create a classifier. How can we use our predicted probabilities to create classifications?

Let's get back the NBA data we had last time.

In :
df = pd.read_csv('nba.csv')
df["WON"] = df["WL"]
df["WON"] = df["WON"].replace("W", 1)
df["WON"] = df["WON"].replace("L", 0)
one_team = df.groupby("GAME_ID").first()
opponent = df.groupby("GAME_ID").last()
games = one_team.merge(opponent, left_index = True, right_index = True, suffixes = ["", "_OPP"])
games["FG_PCT_DIFF"] = games["FG_PCT"] - games["FG_PCT_OPP"]
games["PF_DIFF"] = games["PF"] - games["PF_OPP"]
games['WON'] = games['WL'].replace('L', 0).replace('W', 1)
games = games[['TEAM_NAME', 'MATCHUP', 'WON', 'FG_PCT_DIFF', 'PF_DIFF']]

In :
games.head()

Out:
TEAM_NAME MATCHUP WON FG_PCT_DIFF PF_DIFF
GAME_ID
21700001 Boston Celtics BOS @ CLE 0 -0.049 -1
21700002 Golden State Warriors GSW vs. HOU 0 0.053 9
21700003 Charlotte Hornets CHA @ DET 0 -0.030 -6
21700004 Indiana Pacers IND vs. BKN 1 0.041 0
21700005 Orlando Magic ORL vs. MIA 1 0.042 -2

Let's call this model basic_model since it only has one feature. (Eventually, we will use more features.)

It is the same model we fit in the last lecture.

In :
basic_model = lm.LogisticRegression(penalty = 'none', fit_intercept = False, solver = 'lbfgs')

In :
basic_model.fit(games[['FG_PCT_DIFF']], games['WON'])

Out:
LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=False,
intercept_scaling=1, l1_ratio=None, max_iter=100,
multi_class='warn', n_jobs=None, penalty='none',
random_state=None, solver='lbfgs', tol=0.0001, verbose=0,
warm_start=False)

As before, we can use .predict_proba to get the predicted probabilities for each class under our logistic regression model.

In :
basic_model.predict_proba(games[['FG_PCT_DIFF']])

Out:
array([[0.81733506, 0.18266494],
[0.16510648, 0.83489352],
[0.71450899, 0.28549101],
...,
[0.37288695, 0.62711305],
[0.94003495, 0.05996505],
[0.95102413, 0.04897587]])

We can plot our model, too:

In :
x_sorted = np.array(games['FG_PCT_DIFF'].sort_values()).reshape(len(games), 1)
basic_model_ps_sorted = basic_model.predict_proba(x_sorted)[:, 1]

points = go.Scatter(name = 'true observations',
x = games['FG_PCT_DIFF'],
y = games['WON'],
mode = 'markers',
marker={'opacity':0.5})

lr_line = go.Scatter(name = 'Logistic Regression model',
x = x_sorted.flatten(),
y = basic_model_ps_sorted)

fig = go.Figure([points, lr_line])
fig