Utah Jazz: Shot Analysis

In Spring 2018, I had a class where we needed to do a group project. My teammates and I chose to do some analysis of the Utah Jazz.

Here is the results in a 3 minute video:

The work actually won best project in the class of about 60 students. You can see our names in the hall of fame in the class at http://datasciencecourse.net/2020/fame/.

Below is our winning submission report of the project, including most the code and details.

During this project we:

• Webscraped ESPN shotcharts using BeautifulSoup
• Used Regex to find the types of shots
• Utilized Pandas to wrangle the data
• Ran k-means clustering on the court
• Calculated average shot worth for each player in each cluster
• Evaluated how these differences compared using ANOVA
• Predicted the outcome of a game based on the averages

Final Submission

Jacob Brown, Avery Smith, and Kyle Salisbury

Members email uid
Jacob Brown u0729080@utah.edu u0729080
Avery Smith averyjs@gmail.com u0838931
Kyle Salisbury Kcsals@gmail.com u0711328

Primary Questions:

What are the natural groupings/clusters of shots on a basketball court?

Which combinations of player and shooting location have the highest expected value (shooting pct * points)?

Are the differences in shooting percentage statistically significant?

How does shooting pct vary at Home vs. Away?

Given only the location and shooters for a game not in our dataset, can we predict the final score of the Jazz, the amount of points each player scored, and whether or not they won?

Accomplished:

• Web scraped all data from sources and created “final” csv

• Obtained key data points using Regex

• Cleaned data and created various dataframes

• Unsupervised clustering (k-means) to divide court into 6 clusters (futher divided by 2 pointer and 3 pointer)

• Calculated expected value for each player in each court position and reported them on shot charts

• Calculated significance for shooting percentages by player and location

• Explored expected value difference for Home VS Away games

• Predicted the score of Jazz game, along with individual player totals.

Methods Used:

• Web scraping

• Regex

• Unsupervised clustering (k-means)

• Loops and logic

• Hypothesis Testing

• Visualizations (Scatter plots, heat maps)

• Predictions via pseduo-model

Programming and Methods:

``````# Import All Library Packages

from bs4 import BeautifulSoup
import requests
import urllib.request
import re
import time
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from sklearn.cluster import KMeans, AgglomerativeClustering
from sklearn import metrics
from sklearn.metrics import silhouette_samples, silhouette_score
import math
import scipy as sc
from scipy.stats import norm

# Develop some color maps
seven_colors = ListedColormap(["#e41a1c","#984ea3","#a65628","#377eb8","#ffff33","#4daf4a","#ff7f00"])
cmap_bold = ListedColormap(['#FF0000', '#00FF00'])

# Load in the court picture
``````

Data Aquisition Process

(This may take quite a while to run. It also saves local htmls so it is suggested, if running the code, to start later at Exploratory Analysis section)

We scraped shot charts for the Utah Jazz from http://www.espn.com . We used the hyperlinks on the Jazz schedule page to find all the Jazz games for the entire season. We saved each page as a .html file so we could interact with them without having to scrape them over and over again.

``````# Function to get soups for a given URL
def getWebsiteAsSoup(url):
"""
Retrieve a website and return it as a BeautifulSoup object.
"""

req = urllib.request.Request(url)
with urllib.request.urlopen(req) as response:

class_soup = BeautifulSoup(classlist_html, 'html.parser')
with open('class_list.html', 'w') as new_file:
new_file.write(str(class_soup))

return class_soup
``````
``````# url for the jazz schedule
schedule_url = "http://www.espn.com/nba/team/schedule/_/name/utah/utah-jazz"
schedule_soup = getWebsiteAsSoup(schedule_url)
base_url = "http://www.espn.com/nba/game?gameId="  # append url_endings to this
url_endings = []
regex = '//www.espn.com/nba/recap/_/id/(\d+)"'
for a_element in schedule_soup.find_all('a'):  # find all elements of type 'a'
ending = re.findall(regex, str(a_element))
if ending != []:  # many of these elements won't contain the regular expression--skip them
url_endings.append(ending[0])

print('Number of Jazz Games:')
print(len(url_endings))  # shows how many games the Jazz have played so far
``````
``````# Function to save html for a given URL
def saveWebsiteToLocal(url, number):
"""
Retrieve a website and save it locally as an html.
"""

req = urllib.request.Request(url)
with urllib.request.urlopen(req) as response:

# print(classlist_html)

class_soup = BeautifulSoup(classlist_html, 'html.parser')
with open('html/game_' + str(number) + '.html', 'w') as new_file:
new_file.write(str(class_soup))

return
``````
``````# download all the games to a local copy
i = 1
for game in url_endings:
saveWebsiteToLocal(base_url+url_endings[i-1], i)
i+=1
time.sleep(10)
``````

Data Processing

The following image was screenshotted from the url http://www.espn.com/nba/game?gameId=400975701 . Each of the dots is an element of type ‘li’ which can be scraped.

We used beautiful soup to identify the html element for each shot, and used regular expressions to extract the interesting data from each shot. This is what the HTML looks like. We were mostly interested in data-text, data-homeaway, data-shooter, and left and top positions.

``````# regular expressions to obtain key data
utah_regex = 'utah.png'
period_regex = r'data-period="(\d)"'
shooter_regex = r'data-shooter="(\d+)"'
blocks_regex = r'blocks'
blocks_shooter_name_regex = r"blocks (\w+ \w+)"
shooter_name_regex = r'data-text="(\w+ \w+)'
distance_regex = r' (\d+-foot)'
type_regex = r'foot ([\w ]+)[ "]'
alt_type_regex = r'e*s ([\w ]+)["\(]'
assist_regex = r'\((\w+ \w+) assists\)'
left_regex = r'left:(\d+.\d+)%'
top_regex = r'top:(\d+.\d+)%'
three_regex = r'three'
``````
``````# Obtaining key words from scraping
start = time.clock()
array = []
tot_games = 80
for i in range(1, tot_games+1):
GameWebsite = BeautifulSoup(open("html/game_" + str(i) + ".html"), "html.parser")
court_symbol = GameWebsite.select('.shot-chart > .team-logo')
home_team = re.findall(utah_regex, str(court_symbol))
if home_team:
AllJazzShots = GameWebsite.find_all(class_="shots home-team")[0]
homeaway = 1
else:
AllJazzShots = GameWebsite.find_all(class_="shots away-team")[0]
homeaway = 0
for j in range(0, 300):
Shot = AllJazzShots.find(id="shot" + str(j))
if Shot == None:
continue
game = i
shot = j
else:
period = re.findall(period_regex, str(Shot))[0]
shooter =  re.findall(shooter_regex, str(Shot))[0]
block = re.findall(blocks_regex, str(Shot))
shooter_name = re.findall(shooter_name_regex, str(Shot))
if block:
shooter_name = re.findall(blocks_shooter_name_regex, str(Shot))[0]
elif shooter_name == []:
shooter_name = None
else:
shooter_name = shooter_name[0]
distance = re.findall(distance_regex, str(Shot))
if distance == []:
distance = None
else:
distance = distance[0]
shot_type = re.findall(type_regex, str(Shot))
if shot_type == []:
shot_type = re.findall(alt_type_regex, str(Shot))
#if shot_type == []:
#    shot_type = "deviant"
shot_type = shot_type[0]
# clears out some problems associated with greedy regex
start = shot_type.find("makes ") + len("makes ")
if start >= len("makes "):
shot_type = shot_type[start:]
start = shot_type.find("misses ") + len("misses ")
if start >= len("misses "):
shot_type = shot_type[start:]
assist = re.findall(assist_regex, str(Shot))
if assist == []:
assist = None
else:
assist = assist[0]
left = float(re.findall(left_regex, str(Shot))[0])
# one axis needs to be flipped depending on if it is home or away
if (homeaway == 0):
left = 100-left
#print('away')
top = float(re.findall(top_regex, str(Shot))[0])
if homeaway:
top = 100-top
three = re.findall(three_regex, shot_type)
if three == []:
three = 0
else:
three = 1
game_array = [game, shot, homeaway, made_missed, period, shooter, shooter_name, distance, shot_type,
assist, left, top, three]
array.append(game_array)
end = time.clock()
print("This took " + str(end-start) + " seconds to run")
``````
``````This took 44.585532 seconds to run
``````
``````columns = ["game", "shot", "home/away", "made/missed", "period", "shooter", "shooter_name",
"distance", "shot_type", "assist", "left", "top", "ThreePt"]
print('Total Number of Shots: ' + str(len(array)))  # total number of shots
print('Average Shots Per Game: ' + str(len(array)/tot_games))  # avg shots per game
``````
``````Total Number of Shots: 6614
Average Shots Per Game: 82.675
``````
``````panda_dataframe = pd.DataFrame(array, columns=columns)
``````
game shot home/away made/missed period shooter shooter_name distance shot_type assist left top ThreePt
0 1 0 1 1 1 4257 Derrick Favors 6-foot jumper Joe Ingles 91.333333 60.0 0
1 1 1 1 0 1 4257 Derrick Favors 12-foot jumper None 86.888889 70.0 0
2 1 2 1 1 1 3032976 Rudy Gobert 3-foot dunk Joe Ingles 90.222222 48.0 0
3 1 5 1 0 1 3908809 Donovan Mitchell 8-foot pullup jump shot None 84.666667 58.0 0
4 1 6 1 0 1 4011 Ricky Rubio 18-foot pullup jump shot None 74.666667 62.0 0
``````panda_dataframe.to_csv("shots_dataframe_final.csv")
``````

Exploratory Analysis

Data can be read from here without having to run the top half of the notebook - (which could take a while)

``````# data can be read from here without having to run the top half of the notebook
# (which could take a while)
``````
``````# Describe Data Set
ShotsPD.describe()
``````
Unnamed: 0 game shot home/away made/missed period shooter left top ThreePt
count 6793.000000 6793.000000 6793.000000 6793.000000 6793.000000 6793.000000 6.793000e+03 6793.000000 6793.000000 6793.000000
mean 3396.000000 41.636096 49.889445 0.496688 0.462093 2.474901 1.736174e+06 83.788835 50.669071 0.342264
std 1961.114522 23.667811 30.681017 0.500026 0.498598 1.129431 1.664691e+06 10.165391 21.980889 0.474502
min 0.000000 1.000000 0.000000 0.000000 0.000000 1.000000 1.007000e+03 48.000000 2.000000 0.000000
25% 1698.000000 21.000000 23.000000 0.000000 0.000000 1.000000 4.257000e+03 74.666667 44.000000 0.000000
50% 3396.000000 42.000000 49.000000 0.000000 0.000000 2.000000 2.581177e+06 87.777778 50.000000 0.000000
75% 5094.000000 62.000000 75.000000 1.000000 1.000000 3.000000 3.032976e+06 92.444444 60.000000 1.000000
max 6792.000000 82.000000 133.000000 1.000000 1.000000 5.000000 4.065673e+06 98.888889 98.000000 1.000000
``````print('Number of Shots Taken by Each Player:')
print('----------------------------------------')
print(ShotsPD['shooter_name'].value_counts(), '\n')
``````
``````Number of Shots Taken by Each Player:
----------------------------------------
Donovan Mitchell    1361
Ricky Rubio          827
Joe Ingles           718
Derrick Favors       702
Rodney Hood          552
Rudy Gobert          442
Alec Burks           413
Jonas Jerebko        341
Jae Crowder          295
Royce O              285
Thabo Sefolosha      240
Joe Johnson          226
Raul Neto            151
Ekpe Udoh            119
Dante Exum            87
Georges Niang         11
Nate Wolters           6
David Stockton         3
Erik McCree            2
Naz Mitrou             1
Name: shooter_name, dtype: int64
``````
``````ShotsPD = ShotsPD.replace("Royce O", "Royce O'Neale")

# filter out any shooter with less than 100 shots for the season
ShotsPD = ShotsPD[ShotsPD["shooter_name"]!="Dante Exum"]
ShotsPD = ShotsPD[ShotsPD["shooter_name"]!="Nate Wolters"]
ShotsPD = ShotsPD[ShotsPD["shooter_name"]!="David Stockton"]
ShotsPD = ShotsPD[ShotsPD["shooter_name"]!="Georges Niang"]
ShotsPD = ShotsPD[ShotsPD["shooter_name"]!="Erik McCree"]
ShotsPD = ShotsPD[ShotsPD["shooter_name"]!="Naz Mitrou"]
``````
``````print('Types of Shots Taken:')
print('----------------------------------------')
print(ShotsPD['shot_type'].value_counts(), '\n')
``````
``````Types of Shots Taken:
----------------------------------------
three point jumper              2004
two point shot                   901
driving layup                    590
jumper                           533
pullup jump shot                 490
layup                            371
dunk                             235
step back jumpshot               190
layup                            185
driving floating jump shot       141
three point pullup jump shot     135
dunk                             131
tip shot                         118
driving layup                    103
two point shot                    90
three pointer                     84
hook shot                         70
three point jumper                55
jump bank shot                    36
driving dunk                      34
alley oop dunk shot               28
alley oop layup                   26
alley oop dunk shot               26
jumper                            21
three point shot                  20
alley oop layup                   10
finger roll layup                 10
driving dunk                       9
running pullup jump shot           9
finger roll layup                  4
pullup jump shot                   4
shot                               3
hook shot                          3
jump bank shot                     1
step back jumpshot                 1
driving floating jump shot         1
Name: shot_type, dtype: int64
``````

Unsupervised clustering via kmeans to find natural clusters of the shots

We ultimately wanted to group the shots into different clusters for further analysis as groups. We wanted to try an unsupervised clustering algorithm to give us some insight into how the computer might see the court. We used kmeans because it was easy to implement, and because we were interested only in x and y location as our variables, so kmeans seemed like it would naturally lend itself to our analysis.

We used kmeans to cluster the basketball shots based on their X and Y locations on the court. We chose to use 6 different clusters, because that lead to results that were the most easily idenfifiable by humans. We were quite happy with our results. One group was right by the rim in the area called the key/paint/post. There were 5 other regions spanning the court that included both 2 pointers and 3 pointers. These zones correlated quite nicely with what we would naturally identify as the left and right corners, wings, and the middle of the court. Further dividing the groups into two-pointers and three-pointers gives us 11 separate clusters for further analysis.

``````# Show the Natural Clusterings on the court with colors
X = np.zeros( (len(ShotsPD), 2) )
X[:, 0] = ShotsPD['left']
X[:, 1] = ShotsPD['top']
y_pred = KMeans(n_clusters=6, n_init=10, init='random', max_iter=300).fit_predict(X)

# Saves these locations to the dataframe
ShotsPD['LocationCluster'] = y_pred
ShotsPD.to_csv("location_dataframe_final.csv")

# Redistribute the left data to be on scale of 0-100 (to plot on court pic)
xNorm = 100*(ShotsPD['left'] - min(ShotsPD['left'])) / (max(ShotsPD['left']) - min(ShotsPD['left']))

plt.scatter(xNorm[:], X[:, 1], c=ShotsPD['LocationCluster'],  marker="o", cmap=seven_colors);
plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.grid(False)
plt.show()
``````

These clusters are interesting. They naturally appear to match what we would identify as the key, the left and right corners, the wings, and the middle of the court. We added these groupings to our dataset

We created shot charts for the team as a whole, and for each individual player

``````# unsupervised clustering can give different labels

# Redistribute the left data to be on scale of 0-100
xNorm = 100*(ShotsPD['left'] - min(ShotsPD['left'])) / (max(ShotsPD['left']) - min(ShotsPD['left']))
ShotsPD['left'] = xNorm
``````
``````# Entire shots by Jazz by location, makes and misses
# greens are makes, reds are misses
cmap_bold = ListedColormap(['#FF0000', '#00FF00'])
plt.colorbar()
plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.title('2017-18 Season Shot Chart for Entire Jazz Team')
plt.grid(False)
plt.show()
``````

Individual players
``````# shot chart for every player on the Jazz
# greens are makes, reds are misses
for shooter_name in ShotsPD['shooter_name'].unique():
shooter_shots = ShotsPD[ShotsPD['shooter_name'] == shooter_name]
plt.title(str(shooter_name))
plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.grid(False)
plt.show()
``````

We can use simple data frame masking and math to compute some simple statistics for individual players

``````mitchell_shots = ShotsPD[ShotsPD["shooter_name"]=="Donovan Mitchell"]
print('Number of Shots Mitchell has shot: ' + str(len(mitchell_shots)))
print('Number of Shots Mitchell has made: ' + str(len(mitchell_makes)))
print('Number of Shots Mitchell has missed: ' + str(len(mitchell_misses)))
print('Mitchell Field Goal Percentage: ' + str(len(mitchell_makes)/len(mitchell_shots)))  # Mitchell field goal shooting pct
``````
``````Number of Shots Mitchell has shot: 1361
Number of Shots Mitchell has made: 595
Number of Shots Mitchell has missed: 766
Mitchell Field Goal Percentage: 0.4371785451873622
``````
``````mitchell_threes = mitchell_shots[mitchell_shots["ThreePt"]==1]
mitchell_twos = mitchell_shots[mitchell_shots["ThreePt"]==0]
print("Mitchell's two point percentage is: " + str(round(two_pt_pct*100, 2)) + " %")
print("Mitchell's three point percentage is: " + str(round(three_pt_pct*100, 2)) + " %")
``````
``````Mitchell's two point percentage is: 49.71 %
Mitchell's three point percentage is: 33.79 %
``````

We try to get an idea of which regions have the highest expected value (for the team as a whole). We’ll plot them later as well. This shows the expected values for 3 pointers and then two pointers

``````## Team Stats -- 3 Pointers
# 3 pointers
NumShots = []
ExpectedValue3 =[]
AvLeft3 = []
AvTop3 =[]
PtVal = 3
for i in range(0,6):
Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==1)]
if NumShots[i] > 1:
else:

AvLeft3.append(np.mean(Location['left']))
AvTop3.append(np.mean(Location['top']))

print('---- 3 Pointers ----')
print('Percentages')
print('---------------------')
print('Expected Values')
print(ExpectedValue3)
``````
``````---- 3 Pointers ----
Percentages
[0, 0.3986636971046771, 0.4009111617312073, 0.35555555555555557, 0.31875, 0.3536231884057971]
---------------------
Expected Values
[0, 1.1959910913140313, 1.2027334851936218, 1.0666666666666667, 0.9562499999999999, 1.0608695652173914]
``````
``````## Team Stats -- 2 Pointers
# 2 pointers
NumShots = []
ExpectedValue2 =[]
PtVal = 2
AvLeft2 = []
AvTop2 =[]

for i in range(0,6):
Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==0)]

AvLeft2.append(np.mean(Location['left']))
AvTop2.append(np.mean(Location['top']))

print('---- 2 Pointers ----')
print('Percentages')
print('---------------------')
print('Expected Values')
print(ExpectedValue2)
``````
``````---- 2 Pointers ----
Percentages
[0.5643629217163446, 0.43023255813953487, 0.3561643835616438, 0.4018264840182648, 0.3465909090909091, 0.44086021505376344]
---------------------
Expected Values
[1.1287258434326892, 0.8604651162790697, 0.7123287671232876, 0.8036529680365296, 0.6931818181818182, 0.8817204301075269]
``````
``````## Delete some parts mostly because the paint (key) cluster won't have a 3, only a 2.
xx = np.isnan(AvLeft3)
for i in range(0, len(AvLeft3)):
if  xx[i] == True:
DeleteVar = i
DeleteVar
del AvLeft3[DeleteVar]
del AvTop3[DeleteVar]
``````
``````# Show where each cluster is located on the court (the means!)
import seaborn as sns

df = pd.DataFrame({
'x': AvLeft3 + AvLeft2,
'y': AvTop3 + AvTop2,
'group': ['0','1', '2','3','4','5','6','7','8','9','10']
})

p1=sns.regplot(data=df, x="x", y="y", fit_reg=False, marker="o", color="skyblue", scatter_kws={'s':400})
for line in range(0,df.shape[0]):
p1.text(df.x[line]+0.2, df.y[line], df.group[line], horizontalalignment='left', size='medium',
color='black', weight='semibold')

plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.grid(False)
plt.show()

``````

``````## Delete the 3's for the parents of cluster 5
for i in range(0,len(ExpectedValue3)):
if ExpectedValue3[i] == 0:
Extra = i
del ExpectedValue3[Extra]

# Create expected values and round it for simplicity
ExpectedValue = ExpectedValue3 + ExpectedValue2
ExpectedValueRound = np.round_(ExpectedValue, decimals=2)
``````

Analysis

Plot the expected values for the team

``````## Team chart with expected values
ExpectedValue = ExpectedValue3 + ExpectedValue2
df = pd.DataFrame({
'x': AvLeft3 + AvLeft2,
'y': AvTop3 + AvTop2,
'group': [str(ExpectedValueRound[0]),str(ExpectedValueRound[1]),str(ExpectedValueRound[2]),
str(ExpectedValueRound[3]),str(ExpectedValueRound[4]),str(ExpectedValueRound[5]),
str(ExpectedValueRound[6]),str(ExpectedValueRound[7]),str(ExpectedValueRound[8]),
str(ExpectedValueRound[9]),str(ExpectedValueRound[10])]
})

p1=sns.regplot(data=df, x="x", y="y", fit_reg=False, marker="o", color="skyblue", scatter_kws={'s':400})
for line in range(0,df.shape[0]):
p1.text(df.x[line]+0.2, df.y[line], df.group[line], horizontalalignment='left',
size='medium', color='black', weight='semibold')

plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.grid(False)
sns.plt.show()
``````

Heat map for the team with color scale

``````x = AvLeft3 + AvLeft2
y = AvTop3 + AvTop2
B = ExpectedValueRound
low = np.min(B)
high = np.max(B)
cs = plt.scatter(x,y,c=B,cmap=plt.cm.bwr,vmin=low,vmax=high)

plt.colorbar(cs)
plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.grid(False)
plt.show()
# red is hot--high expected value.  blue is cool--low expected value
``````

As we can see, corner threes and twos in they key are the most efficient shots for the Jazz team overall. The longer jumper two’s are the worst shot the Jazz can shoot as a team. Hence, from this plot we can take it that shooting a two pointer isn’t really worth it, unless it is inside the paint.

Using masking and loops with added logic, we are able to look at all the expected values on the court for each player. We will also print out the values and player name

``````# 3 pointers
PlayerIDs = np.unique(ShotsPD['shooter'])
PlayerNames = np.unique(ShotsPD['shooter_name'])
NumOPlayers = len(PlayerNames)
for Name in range(0,NumOPlayers):
NumShots = []
ExpectedValue3 =[]
AvLeft3 = []
AvTop3 =[]
PtVal3 = 3
PtVal2 = 2
NumShots3 = []
NumShots2 = []
ExpectedValue2 =[]
ExpectedValueRound = []

AvLeft2 = []
AvTop2 =[]

for i in range(0,6):
Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==1)
& ( ShotsPD['shooter_name'] == PlayerNames[Name])]
if NumShots3[i] > 1:
else:

AvLeft3.append(np.mean(Location['left']))
AvTop3.append(np.mean(Location['top']))

Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==0)
& ( ShotsPD['shooter_name'] == PlayerNames[Name])]
if NumShots2[i] > 1:
else:

AvLeft2.append(np.mean(Location['left']))
AvTop2.append(np.mean(Location['top']))

print('---------------------------------------------------------------')
print(PlayerNames[Name])
print('---------------------')
print('---- 3 Pointers ----')
print('Percentages')
print('---------------------')
print('Expected Values')
print(ExpectedValue3)

print('---- 2 Pointers ----')
print('Percentages')
print('---------------------')
print('Expected Values')
print(ExpectedValue2)

for mm in range(0,len(ExpectedValue3)):
if ExpectedValue3[mm] == 0:
Extra = mm
del ExpectedValue3[Extra]

xx = np.isnan(AvLeft3)
for mm in range(0, len(AvLeft3)):
if  xx[mm] == True:
DeleteVar = mm

del AvLeft3[DeleteVar]
del AvTop3[DeleteVar]

ExpectedValue = ExpectedValue3 + ExpectedValue2
ExpectedValueRound = np.round_(ExpectedValue, decimals=2)

AvLefts = AvLeft3 + AvLeft2
AvTops = AvTop3 + AvTop2

for u in range(0,len(AvLefts)):
if math.isnan(AvLefts[u]):
AvLefts[u]=90
if math.isnan(AvTops[u]):
AvTops[u]= 0

x = np.round(AvLefts,decimals=0)
y = np.round(AvTops,decimals=0)
valz = [str(ExpectedValueRound[0]),str(ExpectedValueRound[1]),str(ExpectedValueRound[2]),
str(ExpectedValueRound[3]),str(ExpectedValueRound[4]),str(ExpectedValueRound[5]),
str(ExpectedValueRound[6]),str(ExpectedValueRound[7]),str(ExpectedValueRound[8]),
str(ExpectedValueRound[9]),str(ExpectedValueRound[10])]
df = pd.DataFrame({
'x': x,
'y': y,
'group': valz
})

p1=sns.regplot(data=df, x="x", y="y", fit_reg=False, marker="o", color="skyblue", scatter_kws={'s':400})
for line in range(0,df.shape[0]):
p1.text(df.x[line]+0.2, df.y[line], df.group[line], horizontalalignment='left',
size='medium', color='black', weight='semibold')

plt.title(PlayerNames[Name])
plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.grid(False)
plt.show()

``````
``````---------------------------------------------------------------
Alec Burks
---------------------
---- 3 Pointers ----
Percentages
[0, 0.3888888888888889, 0.4, 0.37142857142857144, 0.2558139534883721, 0.30434782608695654]
---------------------
Expected Values
[0, 1.1666666666666667, 1.2000000000000002, 1.1142857142857143, 0.7674418604651163, 0.9130434782608696]
---- 2 Pointers ----
Percentages
[0.4816753926701571, 0, 0.0, 0.47619047619047616, 0.375, 0.36]
---------------------
Expected Values
[0.9633507853403142, 0, 0.0, 0.9523809523809523, 0.75, 0.72]
``````

``````---------------------------------------------------------------
Derrick Favors
---------------------
---- 3 Pointers ----
Percentages
[0, 0.26666666666666666, 0.19230769230769232, 0.0, 0, 0.3333333333333333]
---------------------
Expected Values
[0, 0.8, 0.576923076923077, 0.0, 0, 1.0]
---- 2 Pointers ----
Percentages
[0.6680584551148225, 0.3333333333333333, 0.3333333333333333, 0.2413793103448276, 0.3793103448275862, 0.44871794871794873]
---------------------
Expected Values
[1.336116910229645, 0.6666666666666666, 0.6666666666666666, 0.4827586206896552, 0.7586206896551724, 0.8974358974358975]
``````

``````---------------------------------------------------------------
Donovan Mitchell
---------------------
---- 3 Pointers ----
Percentages
[0, 0.36764705882352944, 0.5555555555555556, 0.271523178807947, 0.3287671232876712, 0.3333333333333333]
---------------------
Expected Values
[0, 1.1029411764705883, 1.6666666666666667, 0.814569536423841, 0.9863013698630136, 1.0]
---- 2 Pointers ----
Percentages
[0.5358931552587646, 0.7, 0.42857142857142855, 0.45454545454545453, 0.32558139534883723, 0.4]
---------------------
Expected Values
[1.0717863105175292, 1.4, 0.8571428571428571, 0.9090909090909091, 0.6511627906976745, 0.8]
``````

``````---------------------------------------------------------------
Ekpe Udoh
---------------------
---- 3 Pointers ----
Percentages
[0, 0, 0, 0, 0, 0]
---------------------
Expected Values
[0, 0, 0, 0, 0, 0]
---- 2 Pointers ----
Percentages
[0.5357142857142857, 0, 0.0, 0, 0.0, 0]
---------------------
Expected Values
[1.0714285714285714, 0, 0.0, 0, 0.0, 0]
``````

``````---------------------------------------------------------------
Jae Crowder
---------------------
---- 3 Pointers ----
Percentages
[0, 0.5833333333333334, 0.22580645161290322, 0.2702702702702703, 0.2571428571428571, 0.3333333333333333]
---------------------
Expected Values
[0, 1.75, 0.6774193548387096, 0.8108108108108109, 0.7714285714285714, 1.0]
---- 2 Pointers ----
Percentages
[0.5617977528089888, 0.5, 0.2222222222222222, 0.3125, 0.2, 0.35294117647058826]
---------------------
Expected Values
[1.1235955056179776, 1.0, 0.4444444444444444, 0.625, 0.4, 0.7058823529411765]
``````

``````---------------------------------------------------------------
Joe Ingles
---------------------
---- 3 Pointers ----
Percentages
[0, 0.45871559633027525, 0.5, 0.43434343434343436, 0.3655913978494624, 0.4642857142857143]
---------------------
Expected Values
[0, 1.3761467889908259, 1.5, 1.3030303030303032, 1.096774193548387, 1.3928571428571428]
---- 2 Pointers ----
Percentages
[0.5621890547263682, 0.5, 0.25, 0.3333333333333333, 0.3, 0.45454545454545453]
---------------------
Expected Values
[1.1243781094527363, 1.0, 0.5, 0.6666666666666666, 0.6, 0.9090909090909091]
``````

``````---------------------------------------------------------------
Joe Johnson
---------------------
---- 3 Pointers ----
Percentages
[0, 0.3076923076923077, 0.21739130434782608, 0.14285714285714285, 0.35714285714285715, 0.4]
---------------------
Expected Values
[0, 0.9230769230769231, 0.6521739130434783, 0.42857142857142855, 1.0714285714285714, 1.2000000000000002]
---- 2 Pointers ----
Percentages
[0.56, 0.5454545454545454, 0.0, 0.4, 0.43478260869565216, 0.5833333333333334]
---------------------
Expected Values
[1.12, 1.0909090909090908, 0.0, 0.8, 0.8695652173913043, 1.1666666666666667]
``````

``````---------------------------------------------------------------
Jonas Jerebko
---------------------
---- 3 Pointers ----
Percentages
[0, 0.4883720930232558, 0.4772727272727273, 0.3548387096774194, 0.3333333333333333, 0.2857142857142857]
---------------------
Expected Values
[0, 1.4651162790697674, 1.4318181818181819, 1.064516129032258, 1.0, 0.8571428571428571]
---- 2 Pointers ----
Percentages
[0.5424836601307189, 0.14285714285714285, 0.36363636363636365, 0.2, 0.75, 0.4]
---------------------
Expected Values
[1.0849673202614378, 0.2857142857142857, 0.7272727272727273, 0.4, 1.5, 0.8]
``````

``````---------------------------------------------------------------
Raul Neto
---------------------
---- 3 Pointers ----
Percentages
[0, 0.5, 0.46153846153846156, 0.375, 0.38461538461538464, 0.2]
---------------------
Expected Values
[0, 1.5, 1.3846153846153846, 1.125, 1.153846153846154, 0.6000000000000001]
---- 2 Pointers ----
Percentages
[0.5232558139534884, 0.25, 0, 0.2857142857142857, 0.14285714285714285, 1.0]
---------------------
Expected Values
[1.0465116279069768, 0.5, 0, 0.5714285714285714, 0.2857142857142857, 2.0]
``````

``````---------------------------------------------------------------
Ricky Rubio
---------------------
---- 3 Pointers ----
Percentages
[0, 0.2558139534883721, 0.40625, 0.39080459770114945, 0.42857142857142855, 0.23255813953488372]
---------------------
Expected Values
[0, 0.7674418604651163, 1.21875, 1.1724137931034484, 1.2857142857142856, 0.6976744186046512]
---- 2 Pointers ----
Percentages
[0.47346938775510206, 0.45454545454545453, 0.5, 0.40425531914893614, 0.41935483870967744, 0.4772727272727273]
---------------------
Expected Values
[0.9469387755102041, 0.9090909090909091, 1.0, 0.8085106382978723, 0.8387096774193549, 0.9545454545454546]
``````

``````---------------------------------------------------------------
Rodney Hood
---------------------
---- 3 Pointers ----
Percentages
[0, 0.4074074074074074, 0.26666666666666666, 0.44086021505376344, 0.26666666666666666, 0.423728813559322]
---------------------
Expected Values
[0, 1.222222222222222, 0.8, 1.3225806451612903, 0.8, 1.271186440677966]
---- 2 Pointers ----
Percentages
[0.5220588235294118, 0.375, 0.5, 0.4897959183673469, 0.2653061224489796, 0.4583333333333333]
---------------------
Expected Values
[1.0441176470588236, 0.75, 1.0, 0.9795918367346939, 0.5306122448979592, 0.9166666666666666]
``````

``````---------------------------------------------------------------
Royce O
---------------------
---- 3 Pointers ----
Percentages
[0, 0.34285714285714286, 0.3684210526315789, 0.4166666666666667, 0.15789473684210525, 0.4]
---------------------
Expected Values
[0, 1.0285714285714285, 1.1052631578947367, 1.25, 0.47368421052631576, 1.2000000000000002]
---- 2 Pointers ----
Percentages
[0.4689655172413793, 0, 0.0, 0.5833333333333334, 0.5, 0.6666666666666666]
---------------------
Expected Values
[0.9379310344827586, 0, 0.0, 1.1666666666666667, 1.0, 1.3333333333333333]
``````

``````---------------------------------------------------------------
Rudy Gobert
---------------------
---- 3 Pointers ----
Percentages
[0, 0, 0, 0, 0, 0]
---------------------
Expected Values
[0, 0, 0, 0, 0, 0]
---- 2 Pointers ----
Percentages
[0.636150234741784, 0, 0, 0.25, 0, 0.3333333333333333]
---------------------
Expected Values
[1.272300469483568, 0, 0, 0.5, 0, 0.6666666666666666]
``````

``````---------------------------------------------------------------
Thabo Sefolosha
---------------------
---- 3 Pointers ----
Percentages
[0, 0.45, 0.42857142857142855, 0.35714285714285715, 0.23076923076923078, 0.3333333333333333]
---------------------
Expected Values
[0, 1.35, 1.2857142857142856, 1.0714285714285714, 0.6923076923076923, 1.0]
---- 2 Pointers ----
Percentages
[0.6120689655172413, 0.25, 0.625, 0.3684210526315789, 0.16666666666666666, 0.3333333333333333]
---------------------
Expected Values
[1.2241379310344827, 0.5, 1.25, 0.7368421052631579, 0.3333333333333333, 0.6666666666666666]
``````

Statistical Significance

At low sampling rates, a given shot could have a high expected value purely by chance. For example, 25% of the time, a 50% shooter will make two shots in a row. If those two shots are the only sample we have, we might conclude that the shooter is a 100% shooter. For this reason, it is important to determine if results are statistically significant, or if they most likely occured by chance. Hypothesis testing is a good way to measure statistical significance. It involves formulating a null hypothesis that you would like to disprove, calculating the probability of a given result occurring if you were to assume that the null hypothesis is true, and rejecting the null hypothesis if that probability is sufficiently low.

Hypothesis Testing:

Player p-test:

• Take as the null hypothesis that the shooting percentage for a given shot is less than or equal to the average percentage for that player for threes or twos.

Team p-test:

• Take as the null hypothesis that the shooting percentage for a given shot is less than or equal to the average percentage for the whole team for threes or twos.

Location p-test:

• Take as the null hypothesis that the shooting percentage for a given shot is less than or equal to the average percentage for the whole team from that location.
``````shots_array = np.array([["shooter", "three", "cluster", 'num_shots', "num_makes", "pct", "expectedval",
"Player_p", "Team_p", "Location_p"]])

for shooter in threePD["shooter_name"].unique():
for cluster in ShooterShots["LocationCluster"].unique():
num_shots =  len(ClusterShots)
pct = num_makes/num_shots
expectedval = pct*3
# player p-value
# total 3 pt avg for this player
mu = num_shots*avg_pct  # mean number of makes for this cluster assuming average shooting
sigma = sc.sqrt(mu*(1-avg_pct))  # standard deviation?
player_p = 1-norm.cdf(num_makes, loc=mu, scale=sigma)
# team p-value
avg_pct = len(threePD[threePD["made/missed"]==1])/len(threePD)  # total 3 pt avg for the team
mu = num_shots*avg_pct
sigma = sc.sqrt(mu*(1-avg_pct))
team_p = 1-norm.cdf(num_makes, loc=mu, scale=sigma)
# location p-value
teamClusterPD = threePD[threePD["LocationCluster"] == cluster]
# team 3 pt avg from this cluster
mu = num_shots*avg_pct
sigma = sc.sqrt(mu*(1-avg_pct))
location_p = 1-norm.cdf(num_makes, loc=mu, scale=sigma)

shots_array = np.append(shots_array, [[shooter, 1, cluster, num_shots,
num_makes, pct, expectedval, player_p,
team_p, location_p]], axis=0)

for shooter in twoPD["shooter_name"].unique():
for cluster in ShooterShots["LocationCluster"].unique():
num_shots =  len(ClusterShots)
pct = num_makes/num_shots
expectedval = pct*2

#total 3 pt avg for this player
mu = num_shots*avg_pct  # mean number of makes for this cluster
sigma = sc.sqrt(mu*(1-avg_pct))  # standard deviation?
player_p = 1-norm.cdf(num_makes, loc=mu, scale=sigma)
# team p-value
avg_pct = len(twoPD[twoPD["made/missed"]==1])/len(twoPD)  # total 3 pt avg for the team
mu = num_shots*avg_pct
sigma = sc.sqrt(mu*(1-avg_pct))
team_p = 1-norm.cdf(num_makes, loc=mu, scale=sigma)
# location p-value
teamClusterPD = twoPD[twoPD["LocationCluster"] == cluster]
# team 3 pt avg from this cluster
mu = num_shots*avg_pct
sigma = sc.sqrt(mu*(1-avg_pct))
location_p = 1-norm.cdf(num_makes, loc=mu, scale=sigma)

shots_array = np.append(shots_array, [[shooter, 0, cluster, num_shots,
num_makes, pct, expectedval, player_p,
team_p, location_p]], axis=0)
``````
``````/Users/averysmith/anaconda/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:1732: RuntimeWarning: invalid value encountered in double_scalars
x = np.asarray((x - loc)/scale, dtype=dtyp)
``````
``````NewLocationPD = pd.DataFrame(data=shots_array[1:],
columns=shots_array[0])
``````
``````NewLocationPD["three"] = NewLocationPD["three"].map(int)
NewLocationPD["cluster"] = NewLocationPD["cluster"].map(int)
NewLocationPD["num_shots"] = NewLocationPD["num_shots"].map(int)
NewLocationPD["num_makes"] = NewLocationPD["num_makes"].map(int)
NewLocationPD["pct"] = NewLocationPD["pct"].map(float)
NewLocationPD["expectedval"] = NewLocationPD["expectedval"].map(float)
NewLocationPD["Player_p"] = NewLocationPD["Player_p"].map(float)
NewLocationPD["Team_p"] = NewLocationPD["Team_p"].map(float)
NewLocationPD["Location_p"] = NewLocationPD["Location_p"].map(float)
print(NewLocationPD.dtypes, '\n')
``````
``````shooter         object
three            int64
cluster          int64
num_shots        int64
num_makes        int64
pct            float64
expectedval    float64
Player_p       float64
Team_p         float64
Location_p     float64
dtype: object
``````
``````# print the 40 best expected value shots()
``````
shooter three cluster num_shots num_makes pct expectedval Player_p Team_p Location_p
68 Rudy Gobert 0 4 1 1 1.000000 2.000000 0.219013 1.654043e-01 0.084870
120 Raul Neto 0 5 2 2 1.000000 2.000000 0.070967 8.451872e-02 0.055618
127 Royce O 0 1 1 1 1.000000 2.000000 0.148750 1.654043e-01 0.124909
56 Jae Crowder 1 1 24 14 0.583333 1.750000 0.002547 1.302116e-02 0.032321
15 Donovan Mitchell 1 2 45 25 0.555556 1.666667 0.001011 3.902713e-03 0.017140
2 Joe Ingles 1 2 82 41 0.500000 1.500000 0.144763 5.447301e-03 0.033559
43 Raul Neto 1 1 6 3 0.500000 1.500000 0.308538 2.455023e-01 0.306089
133 Jonas Jerebko 0 4 4 3 0.750000 1.500000 0.166598 1.724358e-01 0.044999
53 Jonas Jerebko 1 1 43 21 0.488372 1.465116 0.170106 4.596406e-02 0.114789
51 Jonas Jerebko 1 2 44 21 0.477273 1.431818 0.207412 6.035049e-02 0.150673
76 Donovan Mitchell 0 1 10 7 0.700000 1.400000 0.099649 1.195645e-01 0.042443
4 Joe Ingles 1 5 56 26 0.464286 1.392857 0.368013 6.071480e-02 0.041625
41 Raul Neto 1 2 13 6 0.461538 1.384615 0.325306 2.340261e-01 0.327786
1 Joe Ingles 1 1 109 50 0.458716 1.376147 0.361958 2.067597e-02 0.100186
31 Thabo Sefolosha 1 1 20 9 0.450000 1.350000 0.267932 2.139309e-01 0.319572
60 Derrick Favors 0 0 479 320 0.668058 1.336117 0.000679 7.471357e-12 0.000002
126 Royce O 0 5 3 2 0.666667 1.333333 0.258235 2.983175e-01 0.215423
10 Rodney Hood 1 3 93 41 0.440860 1.322581 0.120899 6.343204e-02 0.042846
3 Joe Ingles 1 3 99 43 0.434343 1.303030 0.560276 7.488420e-02 0.050744
30 Thabo Sefolosha 1 2 28 12 0.428571 1.285714 0.308814 2.411689e-01 0.382603
27 Ricky Rubio 1 4 35 15 0.428571 1.285714 0.174564 2.160885e-01 0.081620
66 Rudy Gobert 0 0 426 271 0.636150 1.272300 0.308772 2.249937e-07 0.001403
13 Rodney Hood 1 5 59 25 0.423729 1.271186 0.254158 1.729582e-01 0.130013
48 Royce O 1 3 12 5 0.416667 1.250000 0.270146 3.541097e-01 0.329155
104 Thabo Sefolosha 0 2 8 5 0.625000 1.250000 0.329155 2.648511e-01 0.056156
100 Thabo Sefolosha 0 0 116 71 0.612069 1.224138 0.080125 1.723821e-02 0.150045
12 Rodney Hood 1 1 27 11 0.407407 1.222222 0.392461 3.222499e-01 0.463034
24 Ricky Rubio 1 2 64 26 0.406250 1.218750 0.186086 2.447323e-01 0.465276
6 Joe Johnson 1 5 5 2 0.400000 1.200000 0.253123 4.348063e-01 0.414141
38 Alec Burks 1 2 15 6 0.400000 1.200000 0.277314 3.880836e-01 0.502873
45 Royce O 1 5 10 4 0.400000 1.200000 0.327360 4.082131e-01 0.379516
26 Ricky Rubio 1 3 87 34 0.390805 1.172414 0.229947 3.062398e-01 0.246089
85 Joe Johnson 0 5 12 7 0.583333 1.166667 0.298303 3.152880e-01 0.160097
125 Royce O 0 3 12 7 0.583333 1.166667 0.235837 3.152880e-01 0.099837
37 Alec Burks 1 1 18 7 0.388889 1.166667 0.292241 4.154618e-01 0.533750
42 Raul Neto 1 4 13 5 0.384615 1.153846 0.545075 4.406020e-01 0.305157
40 Raul Neto 1 3 8 3 0.375000 1.125000 0.557383 4.757867e-01 0.454265
106 Joe Ingles 0 0 201 113 0.562189 1.124378 0.053589 8.558441e-02 0.524781
135 Jae Crowder 0 0 89 50 0.561798 1.123596 0.019917 1.832057e-01 0.519463
83 Joe Johnson 0 0 75 42 0.560000 1.120000 0.179038 2.124386e-01 0.530371
``````# identify the mean location for each of the six clusters identified through kMeans
# (ignoring two and three point differences)
left_coordinates = np.array([])
top_coordinates = np.array([])
clusters = np.arange(0, 6)
for cluster in clusters:
left_coord = cluster_df["left"].mean()
top_coord = cluster_df["top"].mean()
left_coordinates = np.append(left_coordinates, left_coord)
top_coordinates = np.append(top_coordinates, top_coord)
``````
``````# plot the mean location of each cluster on the court for reference purposes
import seaborn as sns

df = pd.DataFrame({
'x': left_coordinates,
'y': top_coordinates,
'group': clusters
})

p1=sns.regplot(data=df, x="x", y="y", fit_reg=False, marker="o", color="skyblue", scatter_kws={'s':400})
for line in range(0,df.shape[0]):
p1.text(df.x[line]+0.2, df.y[line], df.group[line], horizontalalignment='left',
size='medium', color='black', weight='semibold')

plt.title('Clusters')
plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.grid(False)
plt.show()
``````

We choose a threshold for significance of p < .05 in order to reject the null hypothesis.

For each p-test we used, we filter the results for only the statistically significant shots.

The way to interpret these p-values is: if that location was not better than average (for the player or team as a whole), then the p-value represents the probability that the player would still, by coincidence, shoot as well from that location as they did.

Player p-test

``````statistically_significant_mask = NewLocationPD["Player_p"] < .05
SignificantPD.sort_values(by=["expectedval"], ascending=False)
``````
shooter three cluster num_shots num_makes pct expectedval Player_p Team_p Location_p
56 Jae Crowder 1 1 24 14 0.583333 1.750000 0.002547 1.302116e-02 0.032321
15 Donovan Mitchell 1 2 45 25 0.555556 1.666667 0.001011 3.902713e-03 0.017140
60 Derrick Favors 0 0 479 320 0.668058 1.336117 0.000679 7.471357e-12 0.000002
135 Jae Crowder 0 0 89 50 0.561798 1.123596 0.019917 1.832057e-01 0.519463
71 Donovan Mitchell 0 0 599 321 0.535893 1.071786 0.028644 1.412531e-01 0.920028

This indicates that Jae Crowder shoots significantly better from the right corner than he does from any other three point location, and Donovan Mitchell shoots significantly better from the left corner than he does from any other three point location. This information could help coaches modify the offense so that Crowder and Mitchell spend more time on the right and left side respectively.

Unsurprisingly, we found that Derrick Favors, Jae Crowder, and Donovan Mitchell all shoot better from the post than they do from any other two-point position. That is unsurprising because the post is much closer to the basket than other locations, and is expected to have a better shooting percentage.

``````statistically_significant_mask = NewLocationPD["Team_p"] < .05
TeamSignificantPD.sort_values(by=["expectedval"], ascending=False)
``````
shooter three cluster num_shots num_makes pct expectedval Player_p Team_p Location_p
56 Jae Crowder 1 1 24 14 0.583333 1.750000 0.002547 1.302116e-02 0.032321
15 Donovan Mitchell 1 2 45 25 0.555556 1.666667 0.001011 3.902713e-03 0.017140
2 Joe Ingles 1 2 82 41 0.500000 1.500000 0.144763 5.447301e-03 0.033559
53 Jonas Jerebko 1 1 43 21 0.488372 1.465116 0.170106 4.596406e-02 0.114789
1 Joe Ingles 1 1 109 50 0.458716 1.376147 0.361958 2.067597e-02 0.100186
60 Derrick Favors 0 0 479 320 0.668058 1.336117 0.000679 7.471357e-12 0.000002
66 Rudy Gobert 0 0 426 271 0.636150 1.272300 0.308772 2.249937e-07 0.001403
100 Thabo Sefolosha 0 0 116 71 0.612069 1.224138 0.080125 1.723821e-02 0.150045

This indicates that the three point shots noted above for Jae Crowder and Donovan Mitchell are also significantly better than the team average for three point shots. Joe Ingles (an excellent three point shooter) also shoots significantly better from both corners than the team three point average (although he does not shoot significantly better from the corners than he does from the other three point spots because his overall three point shooting percentage is so high). Jonas Jerebko also shoots significantly better from the right corner than the team average for three pointers.

For two pointers, we now find that Derrick Favors, Rudy Gobert, and Thabo Sefolosha all shoot significantly better from the post than the team average for two pointers. The p-values for Derrick Favors and Rudy Gobert are extremely small, partially due to the large number of shots taken by both players from that location (>400). Rudy Gobert likely didn’t show up on the previous list because such a high percentage of his shots are taken from the post that two point percentage is effectively the same as his shooting percentage from the post.

``````statistically_significant_mask = NewLocationPD["Location_p"] < .05
LocationSignificantPD.sort_values(by=["expectedval"], ascending=False)
``````
shooter three cluster num_shots num_makes pct expectedval Player_p Team_p Location_p
56 Jae Crowder 1 1 24 14 0.583333 1.750000 0.002547 1.302116e-02 0.032321
15 Donovan Mitchell 1 2 45 25 0.555556 1.666667 0.001011 3.902713e-03 0.017140
2 Joe Ingles 1 2 82 41 0.500000 1.500000 0.144763 5.447301e-03 0.033559
133 Jonas Jerebko 0 4 4 3 0.750000 1.500000 0.166598 1.724358e-01 0.044999
76 Donovan Mitchell 0 1 10 7 0.700000 1.400000 0.099649 1.195645e-01 0.042443
4 Joe Ingles 1 5 56 26 0.464286 1.392857 0.368013 6.071480e-02 0.041625
60 Derrick Favors 0 0 479 320 0.668058 1.336117 0.000679 7.471357e-12 0.000002
10 Rodney Hood 1 3 93 41 0.440860 1.322581 0.120899 6.343204e-02 0.042846
66 Rudy Gobert 0 0 426 271 0.636150 1.272300 0.308772 2.249937e-07 0.001403

The last hypothesis tested was whether certain players shot much better than the team average for that specific location. Apart from identifying some of the same shots as above, this test would be expected to ffind some players who shoot exceptionally well from more difficult spots.

Jonas Jerebko shooting two pointers from the right wing, Donovan Mitchell shooting two pointers from the right corner, Joe Ingles shooting from the top of the three-point arc, and Rodney Hood shooting three pointers from the left wing would all appear to fit in this category, although each falls just at the limits of statistical significance (.4 < p < .5).

Conclusions This information can help coaches and decision-makers design offensive sets and plays, and can help players with shot-selection.
For example, for the first p-test, we would advise Donovan Mitchell to take more three point shots from the left corner, and Jae Crowder to take more from the right corner. Coaches could design their offense so both players spend more time on those sides. We would also advise Donovan Mitchell to drive all the way to the basket when taking a two-point shot.

For the second p-test, we would advise the coaches to develop their offense to maximize corner threes by Crowder, Mitchell, Ingles, and Jerebko, and post shots by Favors and Gobert.

Home and Away Differences

• We wanted to explore how the expected values for each player differ in home games vs away games. Once agian, we used simple masking to compare how players shoot home and away
``````## HOME

# 3 pointers
PlayerIDs = np.unique(ShotsPD['shooter'])
PlayerNames = np.unique(ShotsPD['shooter_name'])
NumOPlayers = len(PlayerNames)
for Name in range(0,NumOPlayers):
NumShots = []
ExpectedValue3 =[]
AvLeft3 = []
AvTop3 =[]
PtVal3 = 3
PtVal2 = 2
NumShots3 = []
NumShots2 = []
ExpectedValue2 =[]
ExpectedValueRound = []

AvLeft2 = []
AvTop2 =[]

for i in range(0,6):
Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==1)
& ( ShotsPD['shooter_name'] == PlayerNames[Name])& ( ShotsPD['home/away'] == 0) ]
if NumShots3[i] > 1:
else:

AvLeft3.append(np.mean(Location['left']))
AvTop3.append(np.mean(Location['top']))

Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==0)
& ( ShotsPD['shooter_name'] == PlayerNames[Name]) & ( ShotsPD['home/away'] == 0) ]
if NumShots2[i] > 1:
else:

AvLeft2.append(np.mean(Location['left']))
AvTop2.append(np.mean(Location['top']))

print('---------------------------------------------------------------')
print(PlayerNames[Name])
print('---------------------')
print('---- 3 Pointers ----')
print('Percentages')
print('---------------------')
print('Expected Values')
print(ExpectedValue3)

print('---- 2 Pointers ----')
print('Percentages')
print('---------------------')
print('Expected Values')
print(ExpectedValue2)

for mm in range(0,len(ExpectedValue3)):
if ExpectedValue3[mm] == 0:
Extra = mm
del ExpectedValue3[Extra]

xx = np.isnan(AvLeft3)
for mm in range(0, len(AvLeft3)):
if  xx[mm] == True:
DeleteVar = mm

del AvLeft3[DeleteVar]
del AvTop3[DeleteVar]

ExpectedValue = ExpectedValue3 + ExpectedValue2
ExpectedValueRound = np.round_(ExpectedValue, decimals=2)

AvLefts = AvLeft3 + AvLeft2
AvTops = AvTop3 + AvTop2

for u in range(0,len(AvLefts)):
if math.isnan(AvLefts[u]):
AvLefts[u]=90
if math.isnan(AvTops[u]):
AvTops[u]= 0

x = np.round(AvLefts,decimals=0)
y = np.round(AvTops,decimals=0)
valz = [str(ExpectedValueRound[0]),str(ExpectedValueRound[1]),str(ExpectedValueRound[2]),
str(ExpectedValueRound[3]),str(ExpectedValueRound[4]),str(ExpectedValueRound[5]),
str(ExpectedValueRound[6]),str(ExpectedValueRound[7]),str(ExpectedValueRound[8]),
str(ExpectedValueRound[9]),str(ExpectedValueRound[10])]
df = pd.DataFrame({
'x': x,
'y': y,
'group': valz
})

p1=sns.regplot(data=df, x="x", y="y", fit_reg=False, marker="o", color="skyblue", scatter_kws={'s':400})
for line in range(0,df.shape[0]):
p1.text(df.x[line]+0.2, df.y[line], df.group[line], horizontalalignment='left',
size='medium', color='black', weight='semibold')
plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.grid(False)

plt.show()
``````
``````---------------------------------------------------------------
Alec Burks
---------------------
---- 3 Pointers ----
Percentages
[0, 0.2222222222222222, 0.2857142857142857, 0.2631578947368421, 0.17647058823529413, 0.3333333333333333]
---------------------
Expected Values
[0, 0.6666666666666666, 0.8571428571428571, 0.7894736842105263, 0.5294117647058824, 1.0]
---- 2 Pointers ----
Percentages
[0.40540540540540543, 0, 0, 0.2, 0.47368421052631576, 0.38461538461538464]
---------------------
Expected Values
[0.8108108108108109, 0, 0, 0.4, 0.9473684210526315, 0.7692307692307693]
``````

``````---------------------------------------------------------------
Derrick Favors
---------------------
---- 3 Pointers ----
Percentages
[0, 0.38461538461538464, 0.2, 0.0, 0, 0.5]
---------------------
Expected Values
[0, 1.153846153846154, 0.6000000000000001, 0.0, 0, 1.5]
---- 2 Pointers ----
Percentages
[0.6329113924050633, 0.2857142857142857, 0.14285714285714285, 0.2857142857142857, 0.46153846153846156, 0.42857142857142855]
---------------------
Expected Values
[1.2658227848101267, 0.5714285714285714, 0.2857142857142857, 0.5714285714285714, 0.9230769230769231, 0.8571428571428571]
``````

``````---------------------------------------------------------------
Donovan Mitchell
---------------------
---- 3 Pointers ----
Percentages
[0, 0.3793103448275862, 0.47368421052631576, 0.2835820895522388, 0.3717948717948718, 0.3584905660377358]
---------------------
Expected Values
[0, 1.1379310344827585, 1.4210526315789473, 0.8507462686567164, 1.1153846153846154, 1.0754716981132075]
---- 2 Pointers ----
Percentages
[0.5144694533762058, 0.5, 0.5, 0.3888888888888889, 0.36585365853658536, 0.4444444444444444]
---------------------
Expected Values
[1.0289389067524115, 1.0, 1.0, 0.7777777777777778, 0.7317073170731707, 0.8888888888888888]
``````

``````---------------------------------------------------------------
Ekpe Udoh
---------------------
---- 3 Pointers ----
Percentages
[0, 0, 0, 0, 0, 0]
---------------------
Expected Values
[0, 0, 0, 0, 0, 0]
---- 2 Pointers ----
Percentages
[0.515625, 0, 0, 0, 0, 0]
---------------------
Expected Values
[1.03125, 0, 0, 0, 0, 0]
``````

``````---------------------------------------------------------------
Jae Crowder
---------------------
---- 3 Pointers ----
Percentages
[0, 0.8, 0.42857142857142855, 0.3, 0.23076923076923078, 0.2222222222222222]
---------------------
Expected Values
[0, 2.4000000000000004, 1.2857142857142856, 0.8999999999999999, 0.6923076923076923, 0.6666666666666666]
---- 2 Pointers ----
Percentages
[0.6129032258064516, 0.5, 0.4, 0.3333333333333333, 0.16666666666666666, 0.25]
---------------------
Expected Values
[1.2258064516129032, 1.0, 0.8, 0.6666666666666666, 0.3333333333333333, 0.5]
``````

``````---------------------------------------------------------------
Joe Ingles
---------------------
---- 3 Pointers ----
Percentages
[0, 0.425531914893617, 0.5135135135135135, 0.5098039215686274, 0.3902439024390244, 0.5333333333333333]
---------------------
Expected Values
[0, 1.2765957446808511, 1.5405405405405403, 1.5294117647058822, 1.1707317073170733, 1.6]
---- 2 Pointers ----
Percentages
[0.5670103092783505, 0.6, 0, 0.38461538461538464, 0.3333333333333333, 0.5]
---------------------
Expected Values
[1.134020618556701, 1.2, 0, 0.7692307692307693, 0.6666666666666666, 1.0]
``````

``````---------------------------------------------------------------
Joe Johnson
---------------------
---- 3 Pointers ----
Percentages
[0, 0.2, 0.15789473684210525, 0.0, 0.4444444444444444, 0.0]
---------------------
Expected Values
[0, 0.6000000000000001, 0.47368421052631576, 0.0, 1.3333333333333333, 0.0]
---- 2 Pointers ----
Percentages
[0.48936170212765956, 0.5555555555555556, 0, 0.4, 0.375, 0.5]
---------------------
Expected Values
[0.9787234042553191, 1.1111111111111112, 0, 0.8, 0.75, 1.0]
``````

``````---------------------------------------------------------------
Jonas Jerebko
---------------------
---- 3 Pointers ----
Percentages
[0, 0.35294117647058826, 0.42857142857142855, 0.4, 0.25, 0.375]
---------------------
Expected Values
[0, 1.0588235294117647, 1.2857142857142856, 1.2000000000000002, 0.75, 1.125]
---- 2 Pointers ----
Percentages
[0.5487804878048781, 0.3333333333333333, 0.5, 0.0, 0, 0.25]
---------------------
Expected Values
[1.0975609756097562, 0.6666666666666666, 1.0, 0.0, 0, 0.5]
``````

``````---------------------------------------------------------------
Raul Neto
---------------------
---- 3 Pointers ----
Percentages
[0, 0.3333333333333333, 0.42857142857142855, 0.375, 0.5, 0.0]
---------------------
Expected Values
[0, 1.0, 1.2857142857142856, 1.125, 1.5, 0.0]
---- 2 Pointers ----
Percentages
[0.5192307692307693, 0.0, 0, 0.6666666666666666, 0.25, 0]
---------------------
Expected Values
[1.0384615384615385, 0.0, 0, 1.3333333333333333, 0.5, 0]
``````

``````---------------------------------------------------------------
Ricky Rubio
---------------------
---- 3 Pointers ----
Percentages
[0, 0.23529411764705882, 0.45454545454545453, 0.4523809523809524, 0.5882352941176471, 0.25]
---------------------
Expected Values
[0, 0.7058823529411764, 1.3636363636363635, 1.3571428571428572, 1.7647058823529411, 0.75]
---- 2 Pointers ----
Percentages
[0.49295774647887325, 0.5, 0.25, 0.43209876543209874, 0.3125, 0.4782608695652174]
---------------------
Expected Values
[0.9859154929577465, 1.0, 0.5, 0.8641975308641975, 0.625, 0.9565217391304348]
``````

``````---------------------------------------------------------------
Rodney Hood
---------------------
---- 3 Pointers ----
Percentages
[0, 0.35714285714285715, 0.1875, 0.4642857142857143, 0.32, 0.5161290322580645]
---------------------
Expected Values
[0, 1.0714285714285714, 0.5625, 1.3928571428571428, 0.96, 1.5483870967741935]
---- 2 Pointers ----
Percentages
[0.5581395348837209, 0.5, 0.3333333333333333, 0.5454545454545454, 0.3076923076923077, 0.5714285714285714]
---------------------
Expected Values
[1.1162790697674418, 1.0, 0.6666666666666666, 1.0909090909090908, 0.6153846153846154, 1.1428571428571428]
``````

``````---------------------------------------------------------------
Royce O
---------------------
---- 3 Pointers ----
Percentages
[0, 0.45, 0.375, 0.16666666666666666, 0.13333333333333333, 0.42857142857142855]
---------------------
Expected Values
[0, 1.35, 1.125, 0.5, 0.4, 1.2857142857142856]
---- 2 Pointers ----
Percentages
[0.5131578947368421, 0, 0.0, 0.5714285714285714, 0.3333333333333333, 0]
---------------------
Expected Values
[1.0263157894736843, 0, 0.0, 1.1428571428571428, 0.6666666666666666, 0]
``````

``````---------------------------------------------------------------
Rudy Gobert
---------------------
---- 3 Pointers ----
Percentages
[0, 0, 0, 0, 0, 0]
---------------------
Expected Values
[0, 0, 0, 0, 0, 0]
---- 2 Pointers ----
Percentages
[0.5555555555555556, 0, 0, 0.0, 0, 0.5]
---------------------
Expected Values
[1.1111111111111112, 0, 0, 0.0, 0, 1.0]
``````

``````---------------------------------------------------------------
Thabo Sefolosha
---------------------
---- 3 Pointers ----
Percentages
[0, 0.45454545454545453, 0.5, 0.6, 0.0, 1.0]
---------------------
Expected Values
[0, 1.3636363636363635, 1.5, 1.7999999999999998, 0.0, 3.0]
---- 2 Pointers ----
Percentages
[0.6226415094339622, 0.5, 0.75, 0.38461538461538464, 0.0, 0.0]
---------------------
Expected Values
[1.2452830188679245, 1.0, 1.5, 0.7692307692307693, 0.0, 0.0]
``````

``````## Away

# 3 pointers
PlayerIDs = np.unique(ShotsPD['shooter'])
PlayerNames = np.unique(ShotsPD['shooter_name'])
NumOPlayers = len(PlayerNames)
for Name in range(0,NumOPlayers):
NumShots = []
ExpectedValue3 =[]
AvLeft3 = []
AvTop3 =[]
PtVal3 = 3
PtVal2 = 2
NumShots3 = []
NumShots2 = []
ExpectedValue2 =[]
ExpectedValueRound = []

AvLeft2 = []
AvTop2 =[]

for i in range(0,6):
Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==1)
& ( ShotsPD['shooter_name'] == PlayerNames[Name])& ( ShotsPD['home/away'] == 1) ]
if NumShots3[i] > 1:
else:

AvLeft3.append(np.mean(Location['left']))
AvTop3.append(np.mean(Location['top']))

Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==0)
& ( ShotsPD['shooter_name'] == PlayerNames[Name]) & ( ShotsPD['home/away'] == 1) ]
if NumShots2[i] > 1:
else:

AvLeft2.append(np.mean(Location['left']))
AvTop2.append(np.mean(Location['top']))

print('---------------------------------------------------------------')
print(PlayerNames[Name])
print('---------------------')
print('---- 3 Pointers ----')
print('Percentages')
print('---------------------')
print('Expected Values')
print(ExpectedValue3)

print('---- 2 Pointers ----')
print('Percentages')
print('---------------------')
print('Expected Values')
print(ExpectedValue2)

for mm in range(0,len(ExpectedValue3)):
if ExpectedValue3[mm] == 0:
Extra = mm
del ExpectedValue3[Extra]

xx = np.isnan(AvLeft3)
for mm in range(0, len(AvLeft3)):
if  xx[mm] == True:
DeleteVar = mm

del AvLeft3[DeleteVar]
del AvTop3[DeleteVar]

ExpectedValue = ExpectedValue3 + ExpectedValue2
ExpectedValueRound = np.round_(ExpectedValue, decimals=2)

AvLefts = AvLeft3 + AvLeft2
AvTops = AvTop3 + AvTop2

for u in range(0,len(AvLefts)):
if math.isnan(AvLefts[u]):
AvLefts[u]=90
if math.isnan(AvTops[u]):
AvTops[u]= 0

x = np.round(AvLefts,decimals=0)
y = np.round(AvTops,decimals=0)
valz = [str(ExpectedValueRound[0]),str(ExpectedValueRound[1]),str(ExpectedValueRound[2]),
str(ExpectedValueRound[3]),str(ExpectedValueRound[4]),str(ExpectedValueRound[5]),
str(ExpectedValueRound[6]),str(ExpectedValueRound[7]),str(ExpectedValueRound[8]),
str(ExpectedValueRound[9]),str(ExpectedValueRound[10])]
df = pd.DataFrame({
'x': x,
'y': y,
'group': valz
})

p1=sns.regplot(data=df, x="x", y="y", fit_reg=False, marker="o", color="skyblue", scatter_kws={'s':400})
for line in range(0,df.shape[0]):
p1.text(df.x[line]+0.2, df.y[line], df.group[line], horizontalalignment='left',
size='medium', color='black', weight='semibold')

plt.imshow(img, zorder=0, extent=[0, 100, 0, 100.0])
plt.grid(False)

plt.show()
``````
``````---------------------------------------------------------------
Alec Burks
---------------------
---- 3 Pointers ----
Percentages
[0, 0.5555555555555556, 0.5, 0.5, 0.3076923076923077, 0.2857142857142857]
---------------------
Expected Values
[0, 1.6666666666666667, 1.5, 1.5, 0.9230769230769231, 0.8571428571428571]
---- 2 Pointers ----
Percentages
[0.5875, 0, 0, 0.5625, 0.2857142857142857, 0.3333333333333333]
---------------------
Expected Values
[1.175, 0, 0, 1.125, 0.5714285714285714, 0.6666666666666666]
``````

``````---------------------------------------------------------------
Derrick Favors
---------------------
---- 3 Pointers ----
Percentages
[0, 0.17647058823529413, 0.18181818181818182, 0, 0, 0]
---------------------
Expected Values
[0, 0.5294117647058824, 0.5454545454545454, 0, 0, 0]
---- 2 Pointers ----
Percentages
[0.7024793388429752, 0.375, 1.0, 0.2, 0.3125, 0.46511627906976744]
---------------------
Expected Values
[1.4049586776859504, 0.75, 2.0, 0.4, 0.625, 0.9302325581395349]
``````

``````---------------------------------------------------------------
Donovan Mitchell
---------------------
---- 3 Pointers ----
Percentages
[0, 0.358974358974359, 0.6153846153846154, 0.2619047619047619, 0.27941176470588236, 0.30612244897959184]
---------------------
Expected Values
[0, 1.0769230769230769, 1.8461538461538463, 0.7857142857142858, 0.8382352941176471, 0.9183673469387755]
---- 2 Pointers ----
Percentages
[0.5590277777777778, 0.75, 0.3333333333333333, 0.5121951219512195, 0.28888888888888886, 0.37209302325581395]
---------------------
Expected Values
[1.1180555555555556, 1.5, 0.6666666666666666, 1.024390243902439, 0.5777777777777777, 0.7441860465116279]
``````

``````---------------------------------------------------------------
Ekpe Udoh
---------------------
---- 3 Pointers ----
Percentages
[0, 0, 0, 0, 0, 0]
---------------------
Expected Values
[0, 0, 0, 0, 0, 0]
---- 2 Pointers ----
Percentages
[0.5625, 0, 0, 0, 0.0, 0]
---------------------
Expected Values
[1.125, 0, 0, 0, 0.0, 0]
``````

``````---------------------------------------------------------------
Jae Crowder
---------------------
---- 3 Pointers ----
Percentages
[0, 0.42857142857142855, 0.058823529411764705, 0.23529411764705882, 0.2727272727272727, 0.4444444444444444]
---------------------
Expected Values
[0, 1.2857142857142856, 0.1764705882352941, 0.7058823529411764, 0.8181818181818181, 1.3333333333333333]
---- 2 Pointers ----
Percentages
[0.5344827586206896, 0.5, 0.0, 0.2857142857142857, 0.2222222222222222, 0.4444444444444444]
---------------------
Expected Values
[1.0689655172413792, 1.0, 0.0, 0.5714285714285714, 0.4444444444444444, 0.8888888888888888]
``````

``````---------------------------------------------------------------
Joe Ingles
---------------------
---- 3 Pointers ----
Percentages
[0, 0.4838709677419355, 0.4888888888888889, 0.3541666666666667, 0.34615384615384615, 0.38461538461538464]
---------------------
Expected Values
[0, 1.4516129032258065, 1.4666666666666666, 1.0625, 1.0384615384615383, 1.153846153846154]
---- 2 Pointers ----
Percentages
[0.5576923076923077, 0.4, 0.0, 0.3, 0.2727272727272727, 0.42857142857142855]
---------------------
Expected Values
[1.1153846153846154, 0.8, 0.0, 0.6, 0.5454545454545454, 0.8571428571428571]
``````

``````---------------------------------------------------------------
Joe Johnson
---------------------
---- 3 Pointers ----
Percentages
[0, 0.45454545454545453, 0.5, 0.2222222222222222, 0.2, 0.6666666666666666]
---------------------
Expected Values
[0, 1.3636363636363635, 1.5, 0.6666666666666666, 0.6000000000000001, 2.0]
---- 2 Pointers ----
Percentages
[0.6785714285714286, 0.5, 0.0, 0.4, 0.5714285714285714, 0.6666666666666666]
---------------------
Expected Values
[1.3571428571428572, 1.0, 0.0, 0.8, 1.1428571428571428, 1.3333333333333333]
``````

``````---------------------------------------------------------------
Jonas Jerebko
---------------------
---- 3 Pointers ----
Percentages
[0, 0.5769230769230769, 0.5217391304347826, 0.3125, 0.4166666666666667, 0.16666666666666666]
---------------------
Expected Values
[0, 1.7307692307692306, 1.5652173913043477, 0.9375, 1.25, 0.5]
---- 2 Pointers ----
Percentages
[0.5352112676056338, 0.0, 0.0, 0.3333333333333333, 1.0, 0]
---------------------
Expected Values
[1.0704225352112675, 0.0, 0.0, 0.6666666666666666, 2.0, 0]
``````

``````---------------------------------------------------------------
Raul Neto
---------------------
---- 3 Pointers ----
Percentages
[0, 0.6666666666666666, 0.5, 0, 0.3333333333333333, 0.3333333333333333]
---------------------
Expected Values
[0, 2.0, 1.5, 0, 1.0, 1.0]
---- 2 Pointers ----
Percentages
[0.5294117647058824, 0.5, 0, 0.0, 0.0, 0]
---------------------
Expected Values
[1.0588235294117647, 1.0, 0, 0.0, 0.0, 0]
``````

``````---------------------------------------------------------------
Ricky Rubio
---------------------
---- 3 Pointers ----
Percentages
[0, 0.2692307692307692, 0.3548387096774194, 0.3333333333333333, 0.2777777777777778, 0.21739130434782608]
---------------------
Expected Values
[0, 0.8076923076923077, 1.064516129032258, 1.0, 0.8333333333333334, 0.6521739130434783]
---- 2 Pointers ----
Percentages
[0.44660194174757284, 0.42857142857142855, 0.75, 0.36666666666666664, 0.5333333333333333, 0.47619047619047616]
---------------------
Expected Values
[0.8932038834951457, 0.8571428571428571, 1.5, 0.7333333333333333, 1.0666666666666667, 0.9523809523809523]
``````

``````---------------------------------------------------------------
Rodney Hood
---------------------
---- 3 Pointers ----
Percentages
[0, 0.46153846153846156, 0.35714285714285715, 0.40540540540540543, 0.2, 0.32142857142857145]
---------------------
Expected Values
[0, 1.3846153846153846, 1.0714285714285714, 1.2162162162162162, 0.6000000000000001, 0.9642857142857144]
---- 2 Pointers ----
Percentages
[0.46, 0.25, 1.0, 0.4444444444444444, 0.21739130434782608, 0.37037037037037035]
---------------------
Expected Values
[0.92, 0.5, 2.0, 0.8888888888888888, 0.43478260869565216, 0.7407407407407407]
``````

``````---------------------------------------------------------------
Royce O
---------------------
---- 3 Pointers ----
Percentages
[0, 0.2, 0.36363636363636365, 0.6666666666666666, 0.25, 0.3333333333333333]
---------------------
Expected Values
[0, 0.6000000000000001, 1.0909090909090908, 2.0, 0.75, 1.0]
---- 2 Pointers ----
Percentages
[0.42028985507246375, 0, 0, 0.6, 0.6, 0.5]
---------------------
Expected Values
[0.8405797101449275, 0, 0, 1.2, 1.2, 1.0]
``````

``````---------------------------------------------------------------
Rudy Gobert
---------------------
---- 3 Pointers ----
Percentages
[0, 0, 0, 0, 0, 0]
---------------------
Expected Values
[0, 0, 0, 0, 0, 0]
---- 2 Pointers ----
Percentages
[0.706140350877193, 0, 0, 0.5, 0, 0.25]
---------------------
Expected Values
[1.412280701754386, 0, 0, 1.0, 0, 0.5]
``````

``````---------------------------------------------------------------
Thabo Sefolosha
---------------------
---- 3 Pointers ----
Percentages
[0, 0.4444444444444444, 0.35714285714285715, 0.2222222222222222, 0.2727272727272727, 0.0]
---------------------
Expected Values
[0, 1.3333333333333333, 1.0714285714285714, 0.6666666666666666, 0.8181818181818181, 0.0]
---- 2 Pointers ----
Percentages
[0.6031746031746031, 0.0, 0.5, 0.3333333333333333, 0.25, 0.6666666666666666]
---------------------
Expected Values
[1.2063492063492063, 0.0, 1.0, 0.6666666666666666, 0.5, 1.3333333333333333]
``````

** Conclusions**

From this, we can see that some players shoot different shots at much different expected valeus based on whether they are home or away. This could come from that players maybe have more nerves at away games and shoot worse altogher, or maybe they are more comfortable with certain courts and stadiums. In the comparison below, we can see that Ricky Rubio is a much better 3-point shooter at home. But interestingly enough, he shoots that baseline jumper 3x better away than at home. It is intersting to think players can shoot better or worse just depending on whether it is a home or an away game

Score Prediction

Finally, we were able to look at predicting a game based on the knowledge of the shot attempts to guess the team score and individual scores. We actually did quite well by looking at the boxscore listed below. This was the first game of the season. We over predicted Donavan Mitchel’s score, probbly as this was his first game in the NBA, and he may have shot worse due to nerves and getting used to the flow. Alec Burks was playing better at the time, so he actually did better than we predicted. We were able to decently predict a score based upon the expected values we found. However, our methods don’t take into account free throws, so our final scores will be a little off depending on free throws.

We were able to be within 7 points for each player. The model predicted Joe Johnson’s score perfectly while we were 7 off of Alec Burks actual total. We were 8 short of the team total.

``````GameOfInterest = 1
GameX = ShotsPD[ShotsPD['game'] == GameOfInterest]
``````
``````# Predicting a game
# 3 pointers
PlayerIDs = np.unique(GameX['shooter'])
PlayerNames = np.unique(GameX['shooter_name'])
NumOPlayers = len(PlayerNames)
TotalPts = []
PlayerToalPts = []
PlayerToalPtsActual = []
TotalPtsActual = []
TotalTotalPts = []
for Name in range(0,NumOPlayers):
NumShots = []
ExpectedValue3 =[]
PtVal3 = 3
PtVal2 = 2
NumShots3 = []
NumShots2 = []
ExpectedValue2 =[]
ExpectedValueRound = []

NumShotsRecreate3 = []
NumShotsRecreate2 = []
LocationRecreate2 = []
LocationRecreate3 = []
ExpectedPoints3Recreate = []
ExpectedPoints2Recreate= []
PlayerToalPts = []

NumShotsRecreate3Actual = []
NumShotsRecreate2Actual = []
LocationRecreate2Actual = []
LocationRecreate3Actual = []
ExpectedPoints3RecreateActual = []
ExpectedPoints2RecreateActual= []
PlayerToalPts = []

for i in range(0,6):
Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==1)
& ( ShotsPD['shooter_name'] == PlayerNames[Name])]
if NumShots3[i] > 1:
else:

AvLeft3.append(np.mean(Location['left']))
AvTop3.append(np.mean(Location['top']))

Location = ShotsPD[(ShotsPD['LocationCluster']==i) & (ShotsPD['ThreePt']==0)
& ( ShotsPD['shooter_name'] == PlayerNames[Name])]
if NumShots2[i] > 1:
else:

AvLeft2.append(np.mean(Location['left']))
AvTop2.append(np.mean(Location['top']))

for i in range(0,6):
LocationRecreate3 = GameX[(GameX['LocationCluster']==i)& (GameX['ThreePt']==1)
& ( GameX['shooter_name'] == PlayerNames[Name])]
ExpectedPoints3Recreate.append(NumShotsRecreate3[i]*ExpectedValue3[i])

for i in range(0,6):
LocationRecreate2 = GameX[(GameX['LocationCluster']==i)& (GameX['ThreePt']==0)
& ( GameX['shooter_name'] == PlayerNames[Name])]
ExpectedPoints2Recreate.append(NumShotsRecreate2[i]*ExpectedValue2[i])

Player3pts = np.sum(ExpectedPoints3Recreate)
Player2pts = np.sum(ExpectedPoints2Recreate)

PlayerToalPts = Player3pts + Player2pts

TotalPts.append(int(PlayerToalPts))

## Actual Results of the Game

for i in range(0,6):
LocationRecreate3Actual = GameX[(GameX['LocationCluster']==i)& (GameX['ThreePt']==1)
& ( GameX['shooter_name'] == PlayerNames[Name])
ExpectedPoints3RecreateActual.append(NumShotsRecreate3Actual[i]*3)

for i in range(0,6):
LocationRecreate2Actual = GameX[(GameX['LocationCluster']==i)& (GameX['ThreePt']==0)
& ( GameX['shooter_name'] == PlayerNames[Name])
ExpectedPoints2RecreateActual.append(NumShotsRecreate2Actual[i]*2)

Player3ptsActual = np.sum(ExpectedPoints3RecreateActual)
Player2ptsActual = np.sum(ExpectedPoints2RecreateActual)

PlayerToalPtsActual = Player3ptsActual + Player2ptsActual

TotalPtsActual.append(int(PlayerToalPtsActual))

print('---------------------------------------------------------------')
print(PlayerNames[Name])
print('Predicted: ' + str(int(PlayerToalPts)))
print('Actual: ' + str(PlayerToalPtsActual))

TotalTotalPts = np.sum(TotalPts)
TotalTotalPtsActual = np.sum(TotalPtsActual)
print('---------------------------------------------------------------')
print('---------------------------------------------------------------')
print('Final Jazz Score:')
print('Predicted: ' + str(TotalTotalPts))
print('Actual: ' + str(TotalTotalPtsActual))

``````
``````---------------------------------------------------------------
Alec Burks
Predicted: 9
Actual: 16
---------------------------------------------------------------
Derrick Favors
Predicted: 14
Actual: 14
---------------------------------------------------------------
Donovan Mitchell
Predicted: 12
Actual: 6
---------------------------------------------------------------
Ekpe Udoh
Predicted: 0
Actual: 0
---------------------------------------------------------------
Joe Ingles
Predicted: 7
Actual: 11
---------------------------------------------------------------
Joe Johnson
Predicted: 10
Actual: 10
---------------------------------------------------------------
Ricky Rubio
Predicted: 8
Actual: 7
---------------------------------------------------------------
Rodney Hood
Predicted: 4
Actual: 6
---------------------------------------------------------------
Rudy Gobert
Predicted: 11
Actual: 14
---------------------------------------------------------------
Thabo Sefolosha
Predicted: 7
Actual: 6
---------------------------------------------------------------
---------------------------------------------------------------
Final Jazz Score:
Predicted: 82
Actual: 90
``````

Conclusion:

We successfully were able to:

• Acquire the data needed from ESPN
• Clean the data to extract the needed values for analysis
• Cluster the shots into natural groupings
• Look at expected values for both the team and individuals
• Run significance testing on the data
• Compare home and away games
• Predict a Jazz game outcome using a create model

Ideas for future study:

• Effects on fatigue and overshooting in locations

• Correlation between shot selection and winning

• Compare losing streak with winning streak

• Predict fouls and foul shots

• Evolution of Donovan Mitchell over the season