The Guide to Build the Best Possible Fantasy Basketball Lineup

Nihal Garisa, Neha Konduru

Introduction

What is fantasy basketball and what is the aim of our project?

Fantasy basketball is a game where participants create virtual teams composed of real NBA players. These teams compete based on the statistical performance of the players in actual games. Each player accumulates fantasy points through various actions such as scoring, assists, rebounds, steals, and blocks. The objective is to select a lineup of players who will collectively score the most points within a week. Predicting the best possible fantasy basketball lineup involves analyzing a vast amount of data from past and current NBA games. The challenge lies in processing and interpreting information, such as player statistics, to make accurate predictions about future player performances.

Why is this important?

For fantasy basketball enthusiasts like ourselves, having a data-driven approach to selecting players can significantly enhance their chances of winning. It transforms the game from a casual hobby into a strategic and analytical competition. Fantasy basketball is a rapidly growing industry with millions of participants worldwide. Successful fantasy players can win substantial prizes like money, and platforms hosting these games benefit from higher user engagement and satisfaction. Therefore, developing accurate prediction models can have significant benefits for people and businesses involved in fantasy sports.

Beyond fantasy sports, the methodologies and insights gained from this project can contribute to the broader field of sports analytics. Teams, coaches, and analysts can use similar techniques to improve real-world strategies and performance evaluations. This project aims to leverage advanced analytical techniques to create a model that can provide fantasy basketball players with a competitive edge, contributing to both personal and professional growth in the field of data science.

Over this tutorial, we will be going through the data science lifecycle as follows:

  1. Data Collection
  2. Data Cleaning
  3. Exploratory Analysis and Data Visualization
  4. Model: Analysis, Hypothesis Testing, and ML
  5. Interpretation: Insight & Policy Decision

Part 1: Data Collection

To develop this project, we will be using the Python language and Jupyter Lab, an interactive development environment. If you are new to Jupyter Lab, you can learn more about it here. In this section, we will collect all relevant NBA player data from a trusted source using Python. We will start by importing several relevant Python libraries to use throughout this tutorial.

In [1]:
import requests
import seaborn as sns
import numpy as np
import pandas as pd
pd.set_option('display.max_columns', None)
import time
from bs4 import BeautifulSoup
import matplotlib.pyplot as plt
import statsmodels.api as sm
import statsmodels.formula.api as smf
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.model_selection import GridSearchCV
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import accuracy_score
import statsmodels.api as sm
import statsmodels.formula.api as smf
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import RandomForestRegressor
from sklearn.tree import plot_tree

One of the main libraries we will use in this project is Pandas. It is an open-source tool built on Python that makes data manipulation easy and flexible. Another library that boosts efficiency is NumPy. It allows easy computation for large datasets and provides another way to store and handle information.

Now, we will look for a dataset we can use for our topic. Since our topic is based on ESPN’s default fantasy basketball scoring system, we looked for the official NBA player data from a website called Basketball Reference, which is one of the official websites that track NBA data. We verified the legitimacy of the website as it is a popular and widely respected source for accurate basketball statistics, detailed player profiles, and historical data. Additionally, the website is often used by sports analysts, journalists, and fans for reliable information and in-depth analysis.

Specifically, we gathered HTML files containing player performance data from the 2012-13 to the 2023-24 NBA season using HTTP GET requests to the relevant HTML files from Basketball Reference. Then, we parse the saved HTML files for each season to extract the player statistics table, convert each table into a pandas dataframe, and store all these dataframes in a list. Each dataframe in the list corresponds to the player statistics for a specific NBA season.

In [2]:
years = list(range(2013,2025))
player_totals_url = "https://www.basketball-reference.com/leagues/NBA_{}_totals.html"
for yr in years:
    url = player_totals_url.format(yr)
    data = requests.get(url)
    with open("totals/{}.html".format(yr), "w+") as f:
        f.write(data.text)
In [3]:
dfs = []
for yr in years:
    with open("totals/{}.html".format(yr)) as f:
        page = f.read()
    soup = BeautifulSoup(page, "html.parser")
    soup.find('tr', class_="full_table").decompose()
    stats_table = soup.find(id="totals_stats")
    players = pd.read_html(str(stats_table))[0]
    dfs.append(players)

Data Explanation

To explain fantasy basketball’s default points-league scoring system, we referred to the article mentioned previously from ESPN’s website. Specifically, the website contains a detailed breakdown of the default point scoring system. For a more detailed breakdown of what each column variable in our dataframes mean, we referred to the glossary available above Basketball Reference’s player statistics tables.

ESPN default scoring system for fantasy basketball:

  • Point = 1
  • 3P = 1
  • FGA = -1
  • FG = 2
  • FTA = -1
  • FT = 1
  • TRB = 1
  • AST = 2
  • STL = 4
  • BLK = 4
  • TOV = -2

Glossary of basketball stats terms:

  • Rk = Rank
  • Pos = Position
  • Age = Player's age on February 1 of the season
  • Tm = Team
  • G = Games
  • GS = Games Started
  • MP = Minutes Played
  • FG = Field Goals
  • FGA = Field Goal Attempts
  • FG% = Field Goal Percentage
  • 3P = 3-Point Field Goals
  • 3PA = 3-Point Field Goal Attempts
  • 3P% = 3-Point Field Goal Percentage
  • 2P = 2-Point Field Goals
  • 2PA = 2-Point Field Goal Attempts
  • 2P% = 2-Point Field Goal Percentage
  • eFG% = Effective Field Goal Percentage
  • FT = Free Throws
  • FTA = Free Throw Attempts
  • FT% = Free Throw Percentage
  • ORB = Offensive Rebounds
  • DRB = Defensive Rebounds
  • TRB = Total Rebounds
  • AST = Assists
  • STL = Steals
  • BLK = Blocks
  • TOV = Turnovers
  • PF = Personal Fouls
  • PTS = Points

In [4]:
dfs[0].head()
Out[4]:
Rk Player Pos Age Tm G GS MP FG FGA FG% 3P 3PA 3P% 2P 2PA 2P% eFG% FT FTA FT% ORB DRB TRB AST STL BLK TOV PF PTS
0 2 Jeff Adrien PF 26 CHA 52 5 713 72 168 .429 0 2 .000 72 166 .434 .429 65 100 .650 68 128 196 36 18 27 32 80 209
1 3 Arron Afflalo SF 27 ORL 64 64 2307 397 905 .439 72 240 .300 325 665 .489 .478 191 223 .857 29 210 239 206 40 11 138 137 1057
2 4 Josh Akognon PG 26 DAL 3 0 9 2 4 .500 1 2 .500 1 2 .500 .625 0 0 NaN 0 1 1 1 0 0 0 3 5
3 5 Cole Aldrich C 24 TOT 45 0 388 44 80 .550 0 0 NaN 44 80 .550 .550 12 20 .600 30 90 120 9 5 23 23 60 100
4 5 Cole Aldrich C 24 HOU 30 0 213 23 43 .535 0 0 NaN 23 43 .535 .535 4 9 .444 12 45 57 6 3 9 14 41 50

Part 2: Data Cleaning

Now that we have collected all of our data, we need to clean and format it properly.

Formatting

First, we process the dataframes for each season by removing certain columns that are not relevant to fantasy scoring calculations. The columns we targeted for removal include the shooting percentages (e.g., FG%, 3P%), effective field goal percentage (eFG%), offensive and defensive rebounds (ORB, DRB), personal fouls (PF), and rank (Rk).

In [5]:
columns_to_drop = ['FG%', '3P%', '2P%', 'eFG%', 'ORB', 'DRB', 'PF', 'FT%', 'Rk']

for df in dfs:
    columns_to_drop_existing = [col for col in columns_to_drop if col in df.columns]
    df.drop(columns=columns_to_drop_existing, inplace=True)
In [6]:
dfs[1]
Out[6]:
Player Pos Age Tm G GS MP FG FGA 3P 3PA 2P 2PA FT FTA TRB AST STL BLK TOV PTS
0 Quincy Acy SF 23 TOR 7 0 61 6 14 2 5 4 9 5 8 15 4 4 3 2 19
1 Quincy Acy SF 23 SAC 56 0 786 60 127 2 10 58 117 30 45 201 24 19 23 28 152
2 Steven Adams C 20 OKC 81 20 1197 93 185 0 0 93 185 79 136 332 43 40 57 71 265
3 Jeff Adrien PF 27 TOT 53 12 961 143 275 0 0 143 275 76 119 306 38 24 36 39 362
4 Jeff Adrien PF 27 CHA 25 0 256 22 40 0 0 22 40 13 25 88 7 7 15 8 57
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
629 Nick Young SG 28 LAL 64 9 1810 387 889 135 350 252 539 235 285 166 95 46 12 95 1144
630 Thaddeus Young PF 25 PHI 79 78 2718 582 1283 90 292 492 991 163 229 476 182 167 36 165 1417
631 Player Pos Age Tm G GS MP FG FGA 3P 3PA 2P 2PA FT FTA TRB AST STL BLK TOV PTS
632 Cody Zeller C 21 CHA 82 3 1416 172 404 0 1 172 403 146 200 353 92 40 41 87 490
633 Tyler Zeller C 24 CLE 70 9 1049 156 290 0 1 156 289 87 121 282 36 18 38 60 399

634 rows × 21 columns

Next, to make the table more readable, we remove the rows from each dataframe where the 'Player' column contains the string 'Player', to remove misplaced header rows we received from the HTML files.

In [7]:
for i in range(len(dfs)):
    dfs[i] = dfs[i].drop(dfs[i][dfs[i]['Player'] == 'Player'].index)
In [8]:
dfs[1]
Out[8]:
Player Pos Age Tm G GS MP FG FGA 3P 3PA 2P 2PA FT FTA TRB AST STL BLK TOV PTS
0 Quincy Acy SF 23 TOR 7 0 61 6 14 2 5 4 9 5 8 15 4 4 3 2 19
1 Quincy Acy SF 23 SAC 56 0 786 60 127 2 10 58 117 30 45 201 24 19 23 28 152
2 Steven Adams C 20 OKC 81 20 1197 93 185 0 0 93 185 79 136 332 43 40 57 71 265
3 Jeff Adrien PF 27 TOT 53 12 961 143 275 0 0 143 275 76 119 306 38 24 36 39 362
4 Jeff Adrien PF 27 CHA 25 0 256 22 40 0 0 22 40 13 25 88 7 7 15 8 57
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
628 Tony Wroten PG 20 PHI 72 16 1765 345 808 40 188 305 620 209 326 228 217 78 16 204 939
629 Nick Young SG 28 LAL 64 9 1810 387 889 135 350 252 539 235 285 166 95 46 12 95 1144
630 Thaddeus Young PF 25 PHI 79 78 2718 582 1283 90 292 492 991 163 229 476 182 167 36 165 1417
632 Cody Zeller C 21 CHA 82 3 1416 172 404 0 1 172 403 146 200 353 92 40 41 87 490
633 Tyler Zeller C 24 CLE 70 9 1049 156 290 0 1 156 289 87 121 282 36 18 38 60 399

610 rows × 21 columns

It is important to note that the default data type for columns in Pandas dataframes is strings. Thus, we convert all columns supposed to be containing integer data in each dataframe from the default string type to integer type. The selected columns include various statistical categories like points scored, rebounds, assists, and other performance metrics. This conversion enhances computational efficiency for subsequent data analysis tasks.

In [9]:
for i in range(len(dfs)):
    columns_to_convert = ['Age', 'G', 'GS', 'MP', 'FG', 'FGA', '3P', '3PA', '2P', '2PA', 'FT', 'FTA', 'TRB', 'AST', 'STL', 'BLK', 'TOV', 'PTS']
    dfs[i][columns_to_convert] = dfs[i][columns_to_convert].astype(int)
In [10]:
dfs[1]
Out[10]:
Player Pos Age Tm G GS MP FG FGA 3P 3PA 2P 2PA FT FTA TRB AST STL BLK TOV PTS
0 Quincy Acy SF 23 TOR 7 0 61 6 14 2 5 4 9 5 8 15 4 4 3 2 19
1 Quincy Acy SF 23 SAC 56 0 786 60 127 2 10 58 117 30 45 201 24 19 23 28 152
2 Steven Adams C 20 OKC 81 20 1197 93 185 0 0 93 185 79 136 332 43 40 57 71 265
3 Jeff Adrien PF 27 TOT 53 12 961 143 275 0 0 143 275 76 119 306 38 24 36 39 362
4 Jeff Adrien PF 27 CHA 25 0 256 22 40 0 0 22 40 13 25 88 7 7 15 8 57
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
628 Tony Wroten PG 20 PHI 72 16 1765 345 808 40 188 305 620 209 326 228 217 78 16 204 939
629 Nick Young SG 28 LAL 64 9 1810 387 889 135 350 252 539 235 285 166 95 46 12 95 1144
630 Thaddeus Young PF 25 PHI 79 78 2718 582 1283 90 292 492 991 163 229 476 182 167 36 165 1417
632 Cody Zeller C 21 CHA 82 3 1416 172 404 0 1 172 403 146 200 353 92 40 41 87 490
633 Tyler Zeller C 24 CLE 70 9 1049 156 290 0 1 156 289 87 121 282 36 18 38 60 399

610 rows × 21 columns

Some players play on multiple teams in one season and their data is displayed in separate rows per team they played in. Thus, we aggregate player statistics for those who played for multiple teams in a single season, consolidating their data into a single row. This ensures that each player's data is represented equally on the dataframes.

In [11]:
def concat_teams(teams):
    return ','.join(sorted(set(teams)))

agg_funcs = {
    'Age': 'first',
    'Pos': 'first',
    'G': 'sum',
    'GS': 'sum',
    'MP': 'sum',
    'FG': 'sum',
    'FGA': 'sum',
    '3P': 'sum',
    '3PA': 'sum',
    '2P': 'sum',
    '2PA': 'sum',
    'FT': 'sum',
    'FTA': 'sum',
    'TRB': 'sum',
    'AST': 'sum',
    'STL': 'sum',
    'BLK': 'sum',
    'TOV': 'sum',
    'PTS': 'sum',
    'Tm': concat_teams
}

# List to hold the aggregated dataframes
df_list = []

for df in dfs:
    # Filter out rows where the team is 'TOT'
    df_filtered = df[df['Tm'] != 'TOT']
    # Group by player and apply the aggregation functions
    grouped_df = df_filtered.groupby('Player').agg(agg_funcs).reset_index()
    df_list.append(grouped_df)

Dealing with Missing Data

For each dataframe, we add back the percentage columns we previously dropped and make a case where if a player does not attempt the relevant shot variable (which causes the case where we must divide by 0), we change the default NaN (missing) values to the integer 0. Note that percentages are not part of fantasy point calculations, but will serve as an important data point to make insights later on.

In [12]:
def add_percentage_columns(df):
    df['FG%'] = df.apply(lambda row: row['FG'] / row['FGA'] if row['FGA'] > 0 else 0, axis=1)
    df['3P%'] = df.apply(lambda row: row['3P'] / row['3PA'] if row['3PA'] > 0 else 0, axis=1)
    df['2P%'] = df.apply(lambda row: row['2P'] / row['2PA'] if row['2PA'] > 0 else 0, axis=1)
    df['eFG%'] = df.apply(lambda row: (row['FG'] + 0.5 * row['3P']) / row['FGA'] if row['FGA'] > 0 else 0, axis=1)
    df['FT%'] = df.apply(lambda row: row['FT'] / row['FTA'] if row['FTA'] > 0 else 0, axis=1)
    return df
df_list = [add_percentage_columns(df) for df in df_list]

Filtering

Next, we filter out players in each dataframe who do not have the top 400 minutes played in the season, because players who do not have as many minutes played can skew the data, which can cause outliers. Thus, it is important to include players who have played for a consistent amount of time across the season.

In [13]:
def filter_top_400_by_minutes(df):
    return df.sort_values(by='MP', ascending=False).head(400)

filtered_df_list = [filter_top_400_by_minutes(df) for df in df_list]

filtered_df_list[1].head()
Out[13]:
Player Age Pos G GS MP FG FGA 3P 3PA 2P 2PA FT FTA TRB AST STL BLK TOV PTS Tm FG% 3P% 2P% eFG% FT%
265 Kevin Durant 25 SF 81 81 3122 849 1688 192 491 657 1197 703 805 598 445 103 59 285 2593 OKC 0.502962 0.391039 0.548872 0.559834 0.873292
335 Monta Ellis 28 SG 82 82 3023 576 1278 69 209 507 1069 339 430 295 471 141 23 264 1560 DAL 0.450704 0.330144 0.474275 0.477700 0.788372
111 DeMar DeRozan 24 SG 79 79 3017 604 1407 64 210 540 1197 519 630 343 313 86 28 176 1791 TOR 0.429282 0.304762 0.451128 0.452026 0.823810
65 Carmelo Anthony 29 PF 77 77 2982 743 1643 167 415 576 1228 459 541 622 242 95 51 198 2112 NYK 0.452222 0.402410 0.469055 0.503043 0.848429
237 John Wall 23 PG 82 82 2980 579 1337 108 308 471 1029 317 394 333 721 149 40 295 1583 WAS 0.433059 0.350649 0.457726 0.473448 0.804569
In [14]:
filtered_df_list[2].head()
Out[14]:
Player Age Pos G GS MP FG FGA 3P 3PA 2P 2PA FT FTA TRB AST STL BLK TOV PTS Tm FG% 3P% 2P% eFG% FT%
200 James Harden 25 SG 81 81 2981 647 1470 208 555 439 915 715 824 459 565 154 60 321 2217 HOU 0.440136 0.374775 0.479781 0.510884 0.867718
27 Andrew Wiggins 19 SF 82 82 2969 497 1137 39 126 458 1011 354 466 374 170 86 50 177 1387 MIN 0.437115 0.309524 0.453017 0.454266 0.759657
459 Trevor Ariza 29 SF 82 82 2930 366 910 194 555 172 355 122 143 459 209 152 17 141 1048 HOU 0.402198 0.349550 0.484507 0.508791 0.853147
91 Damian Lillard 24 PG 82 82 2925 590 1360 196 572 394 788 344 398 378 507 97 21 222 1720 POR 0.433824 0.342657 0.500000 0.505882 0.864322
79 Chris Paul 29 PG 82 82 2857 568 1170 139 349 429 821 289 321 376 838 156 15 190 1564 LAC 0.485470 0.398281 0.522533 0.544872 0.900312

Part 3: Exploratory Analysis & Data Visualization

In this phase of the data science life cycle, we will graph the data to enhance our understanding and perform statistical analyses to obtain mathematical evidence for any identified trends.

Using the ESPN default scoring key, mentioned in the previous section, we added the total points accumulated for each category and put this data in a new column called ‘FP_TOTAL’. For clarity, we also included the total points accumulated for each category in separate columns to visualize before totaling the final fantasy score in ‘FP_TOTAL’ for each player.

In [15]:
def add_fantasy_columns(df):
    df['FP_PTS'] = df.apply(lambda row: row['PTS'], axis=1)
    df['FP_3P'] = df.apply(lambda row: row['3P'], axis=1)
    df['FP_FGA'] = df.apply(lambda row: row['FGA'] * -1, axis=1)
    df['FP_FG'] = df.apply(lambda row: row['FG'] * 2, axis=1)
    df['FP_FTA'] = df.apply(lambda row: row['FTA']* -1, axis=1)
    df['FP_FT'] = df.apply(lambda row: row['FT'], axis=1)
    df['FP_TRB'] = df.apply(lambda row: row['TRB'], axis=1)
    df['FP_AST'] = df.apply(lambda row: row['AST'] * 2, axis=1)
    df['FP_STL'] = df.apply(lambda row: row['STL'] * 4, axis=1)
    df['FP_BLK'] = df.apply(lambda row: row['BLK'] * 4, axis=1)
    df['FP_TOV'] = df.apply(lambda row: row['TOV'] * -2, axis=1)
    return df
filtered_df_list = [add_fantasy_columns(df) for df in filtered_df_list]
In [16]:
filtered_df_list[4].head()
Out[16]:
Player Age Pos G GS MP FG FGA 3P 3PA 2P 2PA FT FTA TRB AST STL BLK TOV PTS Tm FG% 3P% 2P% eFG% FT% FP_PTS FP_3P FP_FGA FP_FG FP_FTA FP_FT FP_TRB FP_AST FP_STL FP_BLK FP_TOV
24 Andrew Wiggins 21 SF 82 82 3048 709 1570 103 289 606 1281 412 542 328 189 82 30 187 1933 MIN 0.451592 0.356401 0.473068 0.484395 0.760148 1933 103 -1570 1418 -542 412 328 378 328 120 -374
257 Karl-Anthony Towns 21 C 82 82 3030 802 1480 101 275 701 1205 356 428 1007 220 56 103 212 2061 MIN 0.541892 0.367273 0.581743 0.576014 0.831776 2061 101 -1480 1604 -428 356 1007 440 224 412 -424
193 James Harden 27 PG 81 81 2947 674 1533 262 756 412 777 746 881 659 907 121 38 464 2356 HOU 0.439661 0.346561 0.530245 0.525114 0.846765 2356 262 -1533 1348 -881 746 659 1814 484 152 -928
159 Giannis Antetokounmpo 22 SF 80 80 2845 656 1259 49 180 607 1079 471 612 700 434 131 151 234 1832 MIL 0.521048 0.272222 0.562558 0.540508 0.769608 1832 49 -1259 1312 -612 471 700 868 524 604 -468
230 John Wall 26 PG 78 78 2836 647 1435 89 272 558 1163 422 527 326 831 157 49 322 1805 WAS 0.450871 0.327206 0.479794 0.481882 0.800759 1805 89 -1435 1294 -527 422 326 1662 628 196 -644
In [17]:
def get_total_fp(df):
    df['FP_Total'] = df.apply(lambda row: row['FP_PTS'] + row['FP_3P'] + row['FP_FGA'] + row['FP_FG'] + row['FP_FTA'] + row['FP_FT'] + row['FP_TRB'] + row['FP_AST'] + row['FP_STL'] + row['FP_BLK'] + row['FP_TOV'], axis=1)
    return df
filtered_df_list = [get_total_fp(df) for df in filtered_df_list]
In [18]:
filtered_df_list[5].head()
Out[18]:
Player Age Pos G GS MP FG FGA 3P 3PA 2P 2PA FT FTA TRB AST STL BLK TOV PTS Tm FG% 3P% 2P% eFG% FT% FP_PTS FP_3P FP_FGA FP_FG FP_FTA FP_FT FP_TRB FP_AST FP_STL FP_BLK FP_TOV FP_Total
324 LeBron James 33 PF 82 82 3026 857 1580 149 406 708 1174 388 531 709 747 116 71 347 2251 CLE 0.542405 0.366995 0.603066 0.589557 0.730697 2251 149 -1580 1714 -531 388 709 1494 464 284 -694 4648
303 Khris Middleton 26 SF 82 82 2982 593 1272 146 407 447 865 320 362 429 328 119 21 191 1652 MIL 0.466195 0.358722 0.516763 0.523585 0.883978 1652 146 -1272 1186 -362 320 429 656 476 84 -382 2933
25 Andrew Wiggins 22 SF 82 82 2979 569 1300 112 338 457 962 202 314 358 160 91 51 138 1452 MIN 0.437692 0.331361 0.475052 0.480769 0.643312 1452 112 -1300 1138 -314 202 358 320 364 204 -276 2260
47 Bradley Beal 24 SG 82 82 2977 683 1484 199 530 484 954 292 369 363 373 96 36 214 1857 WAS 0.460243 0.375472 0.507338 0.527291 0.791328 1857 199 -1484 1366 -369 292 363 746 384 144 -428 3070
278 Jrue Holiday 27 SG 81 81 2927 615 1244 120 356 495 888 187 238 365 486 123 64 213 1537 NOP 0.494373 0.337079 0.557432 0.542605 0.785714 1537 120 -1244 1230 -238 187 365 972 492 256 -426 3251

In the rest of this section, we will leverage visualization! Throughout this tutorial, we will mainly use the Matplotlib and Seaborn libraries. If you are new to these libraries, feel free to learn more about them through the provided links, as they are incredibly valuable tools for data visualization.

First, we visualize the overall fantasy data across a different number of seasons using bar graphs.

We start by graphing average fantasy points per player position across all seasons. To clarify the abbreviations for the positions:

  • PG = Point Guard
  • C = Center
  • PF = Power Forward
  • SG = Shooting Guard
  • SF = Small Forward

Why this matters? According to ESPN, the default setting roster for a fantasy basketball system includes one point guard (PG), one shooting guard (SG), one small forward (SF), one power forward (PF), one center (C), one SG/PG, one forward SF/PF, three of any position, and three backup spots of any position.

In [19]:
combined_df = pd.concat(filtered_df_list, ignore_index=True)

average_fp_per_pos = combined_df.groupby('Pos')['FP_Total'].mean().reset_index()

average_fp_per_pos = average_fp_per_pos.sort_values('FP_Total', ascending=False)

plt.figure(figsize=(10, 6))
sns.barplot(x='Pos', y='FP_Total', data=average_fp_per_pos, palette='viridis')
plt.title('Average Fantasy Points per Player Position (Overall)')
plt.xlabel('Player Position')
plt.ylabel('Average Fantasy Points')
plt.show()

As you can see, the average fantasy points for point guards (PG) across all seasons were the highest among all the other positions, while small forwards (SF) had the least average fantasy points. We think this is because in the earlier seasons, point guards had the ball the most, which caused them to generate the most statistics.

Next, we graph the average fantasy points per player position from last year’s season (2022-23).

In [20]:
last_5_dfs = filtered_df_list[-1:]
combined_df = pd.concat(last_5_dfs, ignore_index=True)
average_fp_per_pos = combined_df.groupby('Pos')['FP_Total'].mean().reset_index()
average_fp_per_pos = average_fp_per_pos.sort_values('FP_Total', ascending=False)
plt.figure(figsize=(10, 6))
sns.barplot(x='Pos', y='FP_Total', data=average_fp_per_pos, palette='viridis')
plt.title('Average Fantasy Points per Player Position (Last 1 Year)')
plt.xlabel('Player Position')
plt.ylabel('Average Fantasy Points')
plt.show()

Here, we see that the average fantasy points for centers (C) from last season were the highest among all the other positions, while small forwards (SF) still had the least average fantasy points. We think this is because gameplans today have evolved to have playmaking and scoring through centers. This evolution took place as centers started developing a similar skill set as point guards, but centers are taller than point guards, which gives them a further advantage. In the earlier seasons, centers were not as skilled as point guards in scoring and playmaking, so they were kept from generating as many fantasy points, which explains the outcomes of both of our plots.

These trends are further analyzed in the website below: https://sportsanalytics.studentorg.berkeley.edu/articles/point-centers.html

Now, we visualize the relationship between percentage data and fantasy points using scatter plots.

Here, we try to determine if there is a relationship between field goal percentage and fantasy points for each player.

In [21]:
combined_df = pd.concat(filtered_df_list, ignore_index=True)
X = combined_df['FG%']
y = combined_df['FP_Total']
X = sm.add_constant(X)
model = sm.OLS(y, X).fit()
intercept, slope = model.params
plt.figure(figsize=(10, 6))
sns.scatterplot(x='FG%', y='FP_Total', data=combined_df, s=100)
plt.plot(combined_df['FG%'], slope * combined_df['FG%'] + intercept, color='red')
plt.title('Effect of Field Goal Percentage on Fantasy Points')
plt.xlabel('Field Goal Percentage')
plt.ylabel('Fantasy Points')
plt.show()
print(model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               FP_Total   R-squared:                       0.072
Model:                            OLS   Adj. R-squared:                  0.072
Method:                 Least Squares   F-statistic:                     372.8
Date:                Sat, 18 May 2024   Prob (F-statistic):           4.62e-80
Time:                        23:35:36   Log-Likelihood:                -38828.
No. Observations:                4800   AIC:                         7.766e+04
Df Residuals:                    4798   BIC:                         7.767e+04
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const       -154.7550     75.960     -2.037      0.042    -303.672      -5.838
FG%         3162.7308    163.799     19.309      0.000    2841.610    3483.852
==============================================================================
Omnibus:                      447.779   Durbin-Watson:                   0.336
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              583.826
Skew:                           0.805   Prob(JB):                    1.67e-127
Kurtosis:                       3.572   Cond. No.                         17.4
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

As you may see, there is a strong correlation between the field goal percentage and each player’s fantasy points, because the line is steep (has a relatively large slope). This means the higher the field goal percentage, the more likely each player scores more fantasy points.

Next, we try to determine if there is a relationship between three-point percentage and fantasy points for each player.

In [22]:
X = combined_df['3P%']
y = combined_df['FP_Total']
X = sm.add_constant(X)
model = sm.OLS(y, X).fit()
intercept, slope = model.params
plt.figure(figsize=(10, 6))
sns.scatterplot(x='3P%', y='FP_Total', data=combined_df, s=100)
plt.plot(combined_df['3P%'], slope * combined_df['3P%'] + intercept, color='red')
plt.title('Effect of Three Point Percentage on Fantasy Points')
plt.xlabel('Three Point Percentage')
plt.ylabel('Fantasy Points')
plt.show()
print(model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               FP_Total   R-squared:                       0.012
Model:                            OLS   Adj. R-squared:                  0.012
Method:                 Least Squares   F-statistic:                     60.00
Date:                Sat, 18 May 2024   Prob (F-statistic):           1.15e-14
Time:                        23:35:37   Log-Likelihood:                -38978.
No. Observations:                4800   AIC:                         7.796e+04
Df Residuals:                    4798   BIC:                         7.797e+04
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const       1086.4137     29.422     36.926      0.000    1028.734    1144.094
3P%          687.2690     88.725      7.746      0.000     513.327     861.211
==============================================================================
Omnibus:                      501.808   Durbin-Watson:                   0.388
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              670.437
Skew:                           0.876   Prob(JB):                    2.61e-146
Kurtosis:                       3.535   Cond. No.                         8.26
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Here, we see that there is not a strong correlation between three-point percentage and fantasy points for each player as the linear regression line looks fairly horizontal. This goes to show that having a high three-point percentage does not necessarily indicate that a player will receive a high number of fantasy points. Therefore, this shows that the player’s overall ability to score is more important than scoring three-pointers.

Next, we try to determine if there is a relationship between effective three-point percentage and fantasy points for each player. Effective field goal percentage takes into account both two-pointer and three-pointer shots, where three-pointers provide additional weight: EFFECTIVE FIELD GOAL PERCENTAGE FORMULA: (FG + 0.5 * 3P) / FGA

In [23]:
combined_df = pd.concat(filtered_df_list, ignore_index=True)
X = combined_df['eFG%']
y = combined_df['FP_Total']
X = sm.add_constant(X)
model = sm.OLS(y, X).fit()
intercept, slope = model.params
plt.figure(figsize=(10, 6))
sns.scatterplot(x='eFG%', y='FP_Total', data=combined_df, s=100)
plt.plot(combined_df['eFG%'], slope * combined_df['eFG%'] + intercept, color='red')
plt.title('Effect of Effective Field Goal Percentage on Fantasy Points')
plt.xlabel('Effective Field Goal Percentage')
plt.ylabel('Fantasy Points')
plt.show()
print(model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               FP_Total   R-squared:                       0.068
Model:                            OLS   Adj. R-squared:                  0.068
Method:                 Least Squares   F-statistic:                     351.0
Date:                Sat, 18 May 2024   Prob (F-statistic):           1.20e-75
Time:                        23:35:38   Log-Likelihood:                -38838.
No. Observations:                4800   AIC:                         7.768e+04
Df Residuals:                    4798   BIC:                         7.769e+04
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const       -570.9918    100.267     -5.695      0.000    -767.561    -374.423
eFG%        3601.2584    192.215     18.736      0.000    3224.430    3978.087
==============================================================================
Omnibus:                      490.114   Durbin-Watson:                   0.383
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              653.471
Skew:                           0.853   Prob(JB):                    1.26e-142
Kurtosis:                       3.599   Cond. No.                         21.4
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Here, we see that there is a strong correlation between effective field goal percentage and fantasy points for each player, because the line is steeper (has a greater slope). This means the higher the effective field goal percentage, the more likely each player scores more fantasy points. Therefore, players with more versatile scoring ability likely get awarded more fantasy points.

Lastly, we try to determine if there is a relationship between free throw percentage and fantasy points for each player.

In [24]:
combined_df = pd.concat(filtered_df_list, ignore_index=True)
X = combined_df['FT%']
y = combined_df['FP_Total']
X = sm.add_constant(X)
model = sm.OLS(y, X).fit()
intercept, slope = model.params
plt.figure(figsize=(10, 6))
sns.scatterplot(x='FT%', y='FP_Total', data=combined_df, s=100)
plt.plot(combined_df['FT%'], slope * combined_df['FT%'] + intercept, color='red')
plt.title('Effect of Free Throw Percentage on Fantasy Points')
plt.xlabel('Field Throw Percentage')
plt.ylabel('Fantasy Points')
plt.show()
print(model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               FP_Total   R-squared:                       0.047
Model:                            OLS   Adj. R-squared:                  0.047
Method:                 Least Squares   F-statistic:                     235.1
Date:                Sat, 18 May 2024   Prob (F-statistic):           7.53e-52
Time:                        23:35:39   Log-Likelihood:                -38893.
No. Observations:                4800   AIC:                         7.779e+04
Df Residuals:                    4798   BIC:                         7.780e+04
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const         71.8411     80.621      0.891      0.373     -86.212     229.894
FT%         1626.2832    106.056     15.334      0.000    1418.365    1834.201
==============================================================================
Omnibus:                      473.797   Durbin-Watson:                   0.450
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              625.994
Skew:                           0.835   Prob(JB):                    1.17e-136
Kurtosis:                       3.582   Cond. No.                         14.4
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Here, we can see there is a strong correlation between the free throw percentage and each player’s fantasy points, because the line is steep (has a relatively large slope). This means the higher the free throw percentage, the more likely each player scores more fantasy points.

Now, we visualize the relationship between age and average fantasy points across all seasons using a bar graph.

In [25]:
combined_df = pd.concat(filtered_df_list, ignore_index=True)
average_fp_per_age = combined_df.groupby('Age')['FP_Total'].mean().reset_index()
average_fp_per_age = average_fp_per_age.sort_values('Age')

plt.figure(figsize=(10, 6))
sns.barplot(x='Age', y='FP_Total', data=average_fp_per_age, palette='viridis')
plt.title('Average Fantasy Points per Age')
plt.xlabel('Age')
plt.ylabel('Average Fantasy Points')
plt.show()

From this graph, we can see that players in their high 20s and early 30s generally have the highest number of fantasy points, while players in their late 30s and 40s generally have the lowest number of fantasy points.

Next, we visualize the relationship between a player who switched teams between seasons and average fantasy points using a bar graph.

In [26]:
last_season_df = filtered_df_list[-1]
second_last_season_df = filtered_df_list[-2]

merged_df = pd.merge(last_season_df, second_last_season_df, on='Player', suffixes=('_last', '_prev'))

merged_df['Team_Switch'] = merged_df['Tm_last'] != merged_df['Tm_prev']

switched_teams_df = merged_df[merged_df['Team_Switch']]

average_fp_last_season = switched_teams_df['FP_Total_last'].mean()
average_fp_prev_season = switched_teams_df['FP_Total_prev'].mean()

average_fp_diff = average_fp_last_season - average_fp_prev_season

plot_data = pd.DataFrame({
    'Season': ['Previous Season', 'Last Season'],
    'Average_FP': [average_fp_prev_season, average_fp_last_season]
})

plt.figure(figsize=(10, 6))
sns.barplot(x='Season', y='Average_FP', data=plot_data, palette='viridis')
plt.title('Average Fantasy Points for Players Who Switched Teams')
plt.xlabel('Season')
plt.ylabel('Average Fantasy Points')
plt.show()

From this graph, we can see that players who switch teams between seasons generally have fewer average fantasy points in their current season. We think this is because players are getting used to adjusting to their new team for the current season, which may hinder their performance.

Now, we visualize the distribution of scoring metric weightages in total fantasy points using pie charts.

In [27]:
scoring_metrics = ['FP_PTS', 'FP_3P', 'FP_FG', 'FP_FT', 'FP_TRB', 'FP_AST', 'FP_STL', 'FP_BLK']
combined_df = pd.concat(filtered_df_list, ignore_index=True)

scoring_sums = combined_df[scoring_metrics].sum()

scoring_percentage = (scoring_sums / scoring_sums.sum()) * 100

plt.figure(figsize=(10, 8))
plt.pie(scoring_percentage, labels=scoring_percentage.index, autopct='%1.1f%%', startangle=140)
plt.title('Weightage of Positive Scoring Metrics in Total Fantasy Points')
plt.axis('equal')
plt.show()

This pie chart shows the distribution of fantasy scoring metric weightage where players can gain points (which is what we mean by positive) to make up the average percentage of a player's gained fantasy points.

In [28]:
scoring_metrics = ['FP_PTS', 'FP_3P', 'FP_FG', 'FP_FT', 'FP_TRB', 'FP_AST', 'FP_STL', 'FP_BLK']
combined_df = pd.concat(filtered_df_list, ignore_index=True)

positions = combined_df['Pos'].unique()

fig, axes = plt.subplots(2, len(positions) // 2 + len(positions) % 2, figsize=(20, 10), subplot_kw=dict(aspect="equal"))
axes = axes.flatten()

for i, pos in enumerate(positions):
    pos_df = combined_df[combined_df['Pos'] == pos]
    correlations = pos_df[scoring_metrics + ['FP_Total']].corr()['FP_Total'].drop('FP_Total')
    absolute_correlations = correlations.abs()
    wedges, texts, autotexts = axes[i].pie(absolute_correlations, autopct='%1.1f%%', startangle=140)
    axes[i].set_title(f'Influence on FP_Total for {pos}')
    axes[i].legend(wedges, absolute_correlations.index, title="Metrics", loc="center left", bbox_to_anchor=(1, 0, 0.5, 1))

for j in range(i + 1, len(axes)):
    fig.delaxes(axes[j])

plt.tight_layout()
plt.show()

The above pie charts show the distribution of default fantasy scoring metrics that have positive weightage that make up each player position’s total fantasy points. Each pie chart has relatively similar distributions.

In [29]:
combined_df = pd.concat(filtered_df_list, ignore_index=True)

negative_metrics = ['FP_FGA', 'FP_FTA', 'FP_TOV']

average_losses = combined_df[negative_metrics].mean().abs()

plt.figure(figsize=(10, 8))
wedges, texts, autotexts = plt.pie(average_losses, labels=average_losses.index, autopct='%1.1f%%', startangle=140)
plt.title('Weightage of Negative Scoring Metrics in Total Fantasy Points')
plt.axis('equal')
plt.legend(wedges, average_losses.index, title="Metrics", loc="center left", bbox_to_anchor=(1, 0, 0.5, 1))
plt.show()

This pie chart shows the distribution of fantasy scoring metric weightage where players can lose points (which is what we mean by negative) to make up the average percentage of a player's lost fantasy points.

In [30]:
combined_df = pd.concat(filtered_df_list, ignore_index=True)
negative_metrics = ['FP_FGA', 'FP_FTA', 'FP_TOV']
positions = combined_df['Pos'].unique()
fig, axes = plt.subplots(2, len(positions) // 2 + len(positions) % 2, figsize=(20, 10), subplot_kw=dict(aspect="equal"))
axes = axes.flatten()

for i, pos in enumerate(positions):
    pos_df = combined_df[combined_df['Pos'] == pos]
    average_losses = pos_df[negative_metrics].mean().abs()
    
    wedges, texts, autotexts = axes[i].pie(average_losses, autopct='%1.1f%%', startangle=140)
    axes[i].set_title(f'Average Fantasy Points Loss for {pos}')
    
    axes[i].legend(wedges, average_losses.index, title="Metrics", loc="center left", bbox_to_anchor=(1, 0, 0.5, 1))

for j in range(i + 1, len(axes)):
    fig.delaxes(axes[j])

plt.tight_layout()
plt.show()

The following pie charts show the distribution of default fantasy scoring metrics that have negative weightage that make up each player position’s total fantasy points. Here we can see that centers lose more fantasy points from free throw attempts, since they gain more negative weightage for free throw attempts. Point Guards lose more points from turnovers, since gain more negative weightage for turnovers.

Part 4: Model: Analysis, Hypothesis Testing, and ML

Hypothesis Test regarding the relationship between Minutes and Games Played

We believe that volume is a large aspect of fantasy points scoring, so minutes and games played can be important factors

Here are our null and alternate hypotheses:

H0: There is no relationship between minutes and games played on fantasy point scoring.

H1: There is a relationship minutes and games played on fantasy point scoring

Running a least squares regression to examine the effects of multiple variables on fantasy basketball scoring

In [31]:
model = smf.ols(formula='FP_Total ~ Age + G + Q("3P%") + GS + Q("eFG%") + Q("FG%") + Q("FT%") + Q("2P%")', data=combined_df).fit()
print(model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               FP_Total   R-squared:                       0.755
Model:                            OLS   Adj. R-squared:                  0.755
Method:                 Least Squares   F-statistic:                     1848.
Date:                Sat, 18 May 2024   Prob (F-statistic):               0.00
Time:                        23:35:47   Log-Likelihood:                -35630.
No. Observations:                4800   AIC:                         7.128e+04
Df Residuals:                    4791   BIC:                         7.134e+04
Df Model:                           8                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept  -1717.6257     76.216    -22.536      0.000   -1867.044   -1568.207
Age            2.0903      1.396      1.497      0.134      -0.647       4.827
G             15.1789      0.410     37.040      0.000      14.375      15.982
Q("3P%")     619.8662     58.410     10.612      0.000     505.355     734.377
GS            17.3570      0.248     69.936      0.000      16.870      17.844
Q("eFG%")  -1888.2648    226.474     -8.338      0.000   -2332.257   -1444.273
Q("FG%")    3000.0200    203.162     14.767      0.000    2601.730    3398.310
Q("FT%")     925.5394     61.534     15.041      0.000     804.904    1046.175
Q("2P%")     494.2475    158.791      3.113      0.002     182.944     805.551
==============================================================================
Omnibus:                      616.065   Durbin-Watson:                   1.751
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1598.945
Skew:                           0.719   Prob(JB):                         0.00
Kurtosis:                       5.435   Cond. No.                     3.57e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.57e+03. This might indicate that there are
strong multicollinearity or other numerical problems.
In [32]:
features = ['Age', 'G', 'GS', 'MP', '3P%', 'FT%', 'FG%','2P%', 'eFG%']
target = 'FP_Total'
X = combined_df[features]
y = combined_df[target]
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.05)
model = LinearRegression()
model.fit(X_train, y_train)
y_pred = model.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print(f"Mean Squared Error: {mse}")
print("Coefficients:", model.coef_)
print("Intercept:", model.intercept_)

Mean Squared Error: 69486.39354592712
Coefficients: [ 1.96775973e+00 -9.92737027e+00  5.12621897e-01  1.18749422e+00
  2.50653080e+02  3.46327930e+02  2.93248928e+03  4.91634053e+02
 -1.61604972e+03]
Intercept: -955.7387567713192
In [33]:
X = combined_df[['Age', 'G', 'GS', 'MP', '3P%', 'FT%', 'FG%','2P%', 'eFG%']].values
y = combined_df['FP_Total'].values
X = (X - X.mean(axis=0)) / X.std(axis=0)
X = np.c_[np.ones(X.shape[0]), X]
theta = np.zeros(X.shape[1])
iterations = 1000
alpha = 0.01
def hypothesis(X, theta):
    return np.dot(X, theta)
def cost_function(X, y, theta):
    m = len(y)
    return (1 / (2 * m)) * np.sum((hypothesis(X, theta) - y) ** 2)

def gradient_descent(X, y, theta, alpha, iterations):
    m = len(y)
    cost_history = np.zeros(iterations)

    for iteration in range(iterations):
        error = hypothesis(X, theta) - y
        gradient = (1 / m) * np.dot(X.T, error)
        theta -= alpha * gradient
        cost_history[iteration] = cost_function(X, y, theta)
    
    return theta, cost_history

final_theta, cost_history = gradient_descent(X, y, theta, alpha, iterations)

print("Final theta:", final_theta)

plt.plot(range(iterations), cost_history)
plt.xlabel('Iterations')
plt.ylabel('Cost')
plt.title('Cost vs. Iterations')
plt.show()

Final theta: [1295.30949413    5.42380823  -21.4595378   181.03334471  562.84756762
   28.98779362   51.41053839  148.42640373   35.58089283  -52.91286839]
In [34]:
X = combined_df[['Age', 'G', 'GS', 'MP', '3P%', 'FT%', 'FG%', '2P%', 'eFG%']]

filter_condition = (X['Age'] != 0) & (X['G'] != 0) & (X['GS'] != 0) & (X['MP'] != 0) & (X['3P%'] != 0) & (X['FT%'] != 0) & (X['FG%'] != 0) & (X['2P%'] != 0) & (X['eFG%'] != 0)
X = X[filter_condition]
y = combined_df.loc[filter_condition, 'FP_Total']  # Adjust 'Total_FP' based on your actual target variable name

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1, random_state=1)

model_decisiontree = DecisionTreeRegressor(random_state=50)
model_decisiontree.fit(X_train, y_train)
Out[34]:
DecisionTreeRegressor(random_state=50)
In [35]:
y_pred = model_decisiontree.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print("MSE:", mse)

MSE: 157483.8811369509
In [36]:
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1, random_state=1)

model_randomforest = RandomForestRegressor(random_state=1)

model_randomforest.fit(X_train, y_train)

y_pred = model_randomforest.predict(X_test)

mse = mean_squared_error(y_test, y_pred)
print("Mean Squared Error (MSE) for Random Forest:", mse)

feature_importance = model_randomforest.feature_importances_
sorted_idx = np.argsort(feature_importance)

plt.figure(figsize=(10, 6))
plt.barh(range(len(sorted_idx)), feature_importance[sorted_idx], align='center')
plt.yticks(range(len(sorted_idx)), np.array(X.columns)[sorted_idx])
plt.xlabel('Feature Importance')
plt.title('Random Forest Feature Importance')
plt.show()

Mean Squared Error (MSE) for Random Forest: 61888.61990077519

Part 5: Interpretation - Insight and Policy Decision

The purpose of this analysis was to test the hypothesis regarding the relationship between minutes played, games played, and fantasy point scoring in fantasy basketball. We posited that volume metrics, such as minutes and games played, are significant factors in determining fantasy points scored by a player.

Hypotheses: Null Hypothesis (H0): There is no relationship between minutes played and games played on fantasy point scoring. Alternate Hypothesis (H1): There is a relationship between minutes played and games played on fantasy point scoring. To investigate this, we conducted a least squares regression analysis to assess the impact of multiple variables, including minutes played and games played, on fantasy basketball scoring.

Key Findings: Regression Analysis: The results from the least squares regression provided insights into the significance of various predictors on fantasy points.

Significance of Variables: Both minutes played and games played were found to be significant predictors of fantasy point scoring. This indicates that players who spend more time on the court and participate in more games tend to accumulate higher fantasy points. Volume Metrics: The positive coefficients for minutes played and games played suggest that as these variables increase, the fantasy points scored by a player also increase. This supports the notion that volume is a critical aspect of fantasy point scoring.

Conclusion: Based on the regression analysis, we reject the null hypothesis (H0) and accept the alternate hypothesis (H1). There is a statistically significant relationship between minutes played, games played, and fantasy point scoring. This finding aligns with our belief that volume metrics, such as the amount of time a player is on the court and the number of games they play, are important factors in determining their fantasy basketball performance.

Implications: For fantasy basketball managers, this analysis highlights the importance of considering players' minutes and games played when making roster decisions. Players who consistently play more minutes and participate in more games are likely to be more valuable in terms of fantasy points, making them strategic picks for a successful fantasy basketball season.

References

https://www.basketball-reference.com/
https://www.basketball-reference.com/leagues/NBA_2024_totals.html https://www.espn.com/fantasy/basketball/story/_/id/30296896/espn-fantasy-default-points-league-scoring-explained https://www.espn.com/fantasy/basketball/story/_/id/20800285/adjusting-settings https://sportsanalytics.studentorg.berkeley.edu/articles/point-centers.html

In [ ]: