Introduction
The dataset includes historical NBA game data, with Elo ratings for each team before and after the games, the outcomes of the games, and various other metrics related to the performance of the teams. These data are used to analyze team performance over time, predict future game outcomes, and provide insights into the dynamics of the NBA league. For academic references, the Elo rating system was originally developed by Arpad Elo, a Hungarian-American physics professor and chess master. It has been widely adopted in many sports and games beyond chess, including basketball, where it helps to assess team strength and performance dynamics. Web: https://projects.fivethirtyeight.com/2023-nba-predictions/
import warnings
warnings.simplefilter(action='ignore',category=FutureWarning)
warnings.simplefilter(action='ignore',category=DeprecationWarning)
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
projectdata=('nba_elo_latest.csv')
data=pd.read_csv(projectdata)
data.head()
| date | season | neutral | playoff | team1 | team2 | elo1_pre | elo2_pre | elo_prob1 | elo_prob2 | ... | carm-elo2_post | raptor1_pre | raptor2_pre | raptor_prob1 | raptor_prob2 | score1 | score2 | quality | importance | total_rating | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2022-10-18 | 2023 | 0 | NaN | BOS | PHI | 1657.639749 | 1582.247327 | 0.732950 | 0.267050 | ... | NaN | 1693.243079 | 1641.876729 | 0.670612 | 0.329388 | 126 | 117 | 96 | 13 | 55 |
| 1 | 2022-10-18 | 2023 | 0 | NaN | GSW | LAL | 1660.620307 | 1442.352444 | 0.862011 | 0.137989 | ... | NaN | 1615.718147 | 1472.173711 | 0.776502 | 0.223498 | 123 | 109 | 67 | 20 | 44 |
| 2 | 2022-10-19 | 2023 | 0 | NaN | IND | WAS | 1399.201934 | 1440.077372 | 0.584275 | 0.415725 | ... | NaN | 1462.352663 | 1472.018225 | 0.599510 | 0.400490 | 107 | 114 | 37 | 28 | 33 |
| 3 | 2022-10-19 | 2023 | 0 | NaN | DET | ORL | 1393.525172 | 1366.089249 | 0.675590 | 0.324410 | ... | NaN | 1308.969909 | 1349.865183 | 0.563270 | 0.436730 | 113 | 109 | 3 | 1 | 2 |
| 4 | 2022-10-19 | 2023 | 0 | NaN | ATL | HOU | 1535.408152 | 1351.164973 | 0.837022 | 0.162978 | ... | NaN | 1618.256817 | 1283.328356 | 0.917651 | 0.082349 | 117 | 107 | 24 | 1 | 13 |
5 rows × 27 columns
Preprocessing
In the preprocessing stage, we prepare the dataset for analysis by performing several key operations:
Type Conversions: Ensure that all data types are appropriate for the analysis. For instance, date columns should be converted to datetime format to facilitate time-based analysis. Removing Irrelevant Columns: Identify and discard columns that are not relevant to our analysis. This can include columns with excessive missing data or those that do not contribute meaningful information. Handling Missing Values: Detect and address missing data in the dataset. Depending on the nature and amount of missing data, we can either remove rows/columns with missing values or impute them based on statistical methods like mean, median, or mode. Outlier Analysis: Identify any outliers in the dataset. This step is crucial for understanding the data distribution and deciding whether any action needs to be taken regarding these outliers.
data['date'] = pd.to_datetime(data['date'])
threshold = 0.5 # Threshold for removing columns with a high percentage of missing values
columns_to_remove = data.columns[data.isnull().mean() > threshold]
data_cleaned = data.drop(columns=columns_to_remove)
data_cleaned = data_cleaned.dropna()
# Descriptive statistics for quantitative columns
quantitative_columns = data_cleaned.select_dtypes(include=['number']).columns
outlier_analysis = data_cleaned[quantitative_columns].describe()
print(outlier_analysis)
season neutral elo1_pre elo2_pre elo_prob1 \
count 1320.0 1320.000000 1320.000000 1320.000000 1320.000000
mean 2023.0 0.001515 1511.867655 1511.311315 0.627059
std 0.0 0.038910 88.962661 89.571409 0.151149
min 2023.0 0.000000 1264.103229 1257.300726 0.181341
25% 2023.0 0.000000 1461.568345 1460.866530 0.533438
50% 2023.0 0.000000 1524.876508 1523.136739 0.640681
75% 2023.0 0.000000 1576.453207 1577.825540 0.736876
max 2023.0 1.000000 1705.343075 1719.448667 0.933707
elo_prob2 elo1_post elo2_post raptor1_pre raptor2_pre \
count 1320.000000 1320.000000 1320.000000 1320.000000 1320.000000
mean 0.372941 1510.664651 1512.514319 1503.864076 1499.075101
std 0.151149 89.560581 89.306155 116.590601 116.514412
min 0.066293 1257.300726 1271.086891 955.234235 945.804075
25% 0.263124 1460.990452 1460.476484 1445.292160 1432.346974
50% 0.359319 1521.917992 1525.368845 1523.778627 1522.906299
75% 0.466562 1576.753366 1577.663170 1585.715871 1579.358239
max 0.818659 1705.343075 1719.448667 1733.775148 1728.915073
raptor_prob1 raptor_prob2 score1 score2 quality \
count 1320.000000 1320.000000 1320.000000 1320.000000 1320.000000
mean 0.603891 0.396109 115.630303 113.030303 50.511364
std 0.187301 0.187301 11.991075 12.001920 27.217232
min 0.027498 0.017256 80.000000 79.000000 0.000000
25% 0.490977 0.257375 108.000000 105.000000 29.000000
50% 0.617850 0.382150 116.000000 113.000000 52.000000
75% 0.742625 0.509023 124.000000 121.000000 73.000000
max 0.982744 0.972502 175.000000 176.000000 99.000000
importance total_rating
count 1320.000000 1320.000000
mean 32.458333 41.744697
std 29.408726 24.238657
min 0.000000 0.000000
25% 9.000000 21.000000
50% 24.000000 43.500000
75% 49.000000 57.000000
max 100.000000 100.000000
Summary data analysis
In this section, we will conduct a comprehensive summary analysis of the dataset. This includes generating statistical summaries for each column to understand the central tendency, dispersion, and shape of the dataset's distribution. We will also use graphical components like histograms and box plots to visualize the data distribution of each column.
statistical_summary = data_cleaned.describe()
print(statistical_summary)
for column in quantitative_columns:
plt.figure(figsize=(10, 6))
sns.histplot(data_cleaned[column], kde=True)
plt.title(f'Distribution of {column}')
plt.show()
plt.figure(figsize=(10, 6))
sns.boxplot(x=data_cleaned[column])
plt.title(f'Box plot of {column}')
plt.show()
date season neutral elo1_pre \
count 1320 1320.0 1320.000000 1320.000000
mean 2023-01-19 05:33:49.090909184 2023.0 0.001515 1511.867655
min 2022-10-18 00:00:00 2023.0 0.000000 1264.103229
25% 2022-12-02 00:00:00 2023.0 0.000000 1461.568345
50% 2023-01-16 00:00:00 2023.0 0.000000 1524.876508
75% 2023-03-08 00:00:00 2023.0 0.000000 1576.453207
max 2023-06-12 00:00:00 2023.0 1.000000 1705.343075
std NaN 0.0 0.038910 88.962661
elo2_pre elo_prob1 elo_prob2 elo1_post elo2_post \
count 1320.000000 1320.000000 1320.000000 1320.000000 1320.000000
mean 1511.311315 0.627059 0.372941 1510.664651 1512.514319
min 1257.300726 0.181341 0.066293 1257.300726 1271.086891
25% 1460.866530 0.533438 0.263124 1460.990452 1460.476484
50% 1523.136739 0.640681 0.359319 1521.917992 1525.368845
75% 1577.825540 0.736876 0.466562 1576.753366 1577.663170
max 1719.448667 0.933707 0.818659 1705.343075 1719.448667
std 89.571409 0.151149 0.151149 89.560581 89.306155
raptor1_pre raptor2_pre raptor_prob1 raptor_prob2 score1 \
count 1320.000000 1320.000000 1320.000000 1320.000000 1320.000000
mean 1503.864076 1499.075101 0.603891 0.396109 115.630303
min 955.234235 945.804075 0.027498 0.017256 80.000000
25% 1445.292160 1432.346974 0.490977 0.257375 108.000000
50% 1523.778627 1522.906299 0.617850 0.382150 116.000000
75% 1585.715871 1579.358239 0.742625 0.509023 124.000000
max 1733.775148 1728.915073 0.982744 0.972502 175.000000
std 116.590601 116.514412 0.187301 0.187301 11.991075
score2 quality importance total_rating
count 1320.000000 1320.000000 1320.000000 1320.000000
mean 113.030303 50.511364 32.458333 41.744697
min 79.000000 0.000000 0.000000 0.000000
25% 105.000000 29.000000 9.000000 21.000000
50% 113.000000 52.000000 24.000000 43.500000
75% 121.000000 73.000000 49.000000 57.000000
max 176.000000 99.000000 100.000000 100.000000
std 12.001920 27.217232 29.408726 24.238657
Correlation Analysis
Next, we will explore the relationships between various quantitative columns in the dataset. Understanding these correlations can provide insights into the underlying patterns and associations between different variables.
correlation_matrix = data_cleaned[quantitative_columns].corr()
plt.figure(figsize=(12, 10))
sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm')
plt.title('Correlation Matrix of Quantitative Columns')
plt.show()
# Example pairs: ('elo1_pre', 'elo2_pre'), ('score1', 'score2'), ('elo_prob1', 'elo_prob2')
pairs_to_explore = [('elo1_pre', 'elo2_pre'), ('score1', 'score2'), ('elo_prob1', 'elo_prob2')]
for x, y in pairs_to_explore:
plt.figure(figsize=(10, 6))
sns.scatterplot(data=data_cleaned, x=x, y=y)
plt.title(f'Correlation between {x} and {y}')
plt.xlabel(x)
plt.ylabel(y)
plt.show()
Discussion
Question 1.
Can the combination of home-court advantage, team ELO ratings, previous game outcomes, and player injury reports predict whether a team will win its next game?
Question 2.
How well can we predict a team's end-of-season ELO rating based on its performance metrics (points per game, rebounds, assists, turnovers) in the first half of the season?