Visual and Data Analysis - FIFA 19 Players

• Created by Andrés Segura Tinoco
• Created on May 1, 2019

3. Principal Component Analysis

Loading main libraries and data

# Load the Pandas libraries
import pandas as pd
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
import numpy as np

# Load visualization libraries
import matplotlib.pyplot as plt
import seaborn as sns
from mpl_toolkits.mplot3d import Axes3D

# Read FIFA 19 players data only using the current skill values
dataURL = "../data/fifa19_overall_data.csv"
data = pd.read_csv(dataURL)

Selecting categorical and numeric variables

Only the numeric variables of the dataset will be used to perform the PCA. Then, the variables that you do not want to include in the analysis are discarded, and finally, the data is filtered with the median of the overall of the players.

# UTIL FUNCTION - Get Dataframe Columns List By Type
def getColumnsByType(data, colType, equals, show):
    colList = []
    for col in data.columns:
        if (equals and str(data[col].dtype) == colType) or (not equals and str(data[col].dtype) != colType):
            colList.append(col)
            if show:
                print(str(data.columns.get_loc(col)) + " - " + col + " - " + str(data[col].dtype))
    return colList;

# Show object (string or date) type columns
objColList = getColumnsByType(data, "object", True, True)

2 - Name - object
4 - Photo - object
5 - Nationality - object
6 - Flag - object
9 - Club - object
10 - Club Logo - object
14 - Preferred Foot - object
18 - Work Rate - object
19 - Body Type - object
20 - Real Face - object
21 - Position - object
23 - Joined - object
24 - Loaned_From - object
25 - Contract Valid Until - object

# Show numeric (float or integer) type columns
numColList = getColumnsByType(data, "object", False, True)

0 - Order - int64
1 - ID - int64
3 - Age - int64
7 - Overall - int64
8 - Potential - int64
11 - Value € - float64
12 - Wage € - float64
13 - Special - int64
15 - International Reputation - float64
16 - Weak Foot - float64
17 - Skill Moves - float64
22 - Jersey Number - float64
26 - HeightMts - float64
27 - WeightLbs - float64
28 - LS - int64
29 - ST - int64
30 - RS - int64
31 - LW - int64
32 - LF - int64
33 - CF - int64
34 - RF - int64
35 - RW - int64
36 - LAM - int64
37 - CAM - int64
38 - RAM - int64
39 - LM - int64
40 - LCM - int64
41 - CM - int64
42 - RCM - int64
43 - RM - int64
44 - LWB - int64
45 - LDM - int64
46 - CDM - int64
47 - RDM - int64
48 - RWB - int64
49 - LB - int64
50 - LCB - int64
51 - CB - int64
52 - RCB - int64
53 - RB - int64
54 - Crossing - float64
55 - Finishing - float64
56 - HeadingAccuracy - float64
57 - ShortPassing - float64
58 - Volleys - float64
59 - Dribbling - float64
60 - Curve - float64
61 - FKAccuracy - float64
62 - LongPassing - float64
63 - BallControl - float64
64 - Acceleration - float64
65 - SprintSpeed - float64
66 - Agility - float64
67 - Reactions - float64
68 - Balance - float64
69 - ShotPower - float64
70 - Jumping - float64
71 - Stamina - float64
72 - Strength - float64
73 - LongShots - float64
74 - Aggression - float64
75 - Interceptions - float64
76 - Positioning - float64
77 - Vision - float64
78 - Penalties - float64
79 - Composure - float64
80 - Marking - float64
81 - StandingTackle - float64
82 - SlidingTackle - float64
83 - GKDiving - float64
84 - GKHandling - float64
85 - GKKicking - float64
86 - GKPositioning - float64
87 - GKReflexes - float64
88 - Release Clause € - float64

# Split data into header and skills dataframes
header = pd.DataFrame()
skills = pd.DataFrame()

for col in data.columns:
    if col in objColList:
        header[col] = data[col]
    else:
        skills[col] = data[col]

# Delete original dataset from memory
del data

# Show first 5 rows of header dataframe
header.head()

	Name	Photo	Nationality	Flag	Club	Club Logo	Preferred Foot	Work Rate	Body Type	Real Face	Position	Joined	Loaned_From	Contract Valid Until
0	L. Messi	https://cdn.sofifa.org/players/4/19/158023.png	Argentina	https://cdn.sofifa.org/flags/52.png	FC Barcelona	https://cdn.sofifa.org/teams/2/light/241.png	Left	Medium/ Medium	Messi	Yes	RF	1-Jul-04	NaN	2021
1	Cristiano Ronaldo	https://cdn.sofifa.org/players/4/19/20801.png	Portugal	https://cdn.sofifa.org/flags/38.png	Juventus	https://cdn.sofifa.org/teams/2/light/45.png	Right	High/ Low	C. Ronaldo	Yes	ST	10-Jul-18	NaN	2022
2	Neymar Jr	https://cdn.sofifa.org/players/4/19/190871.png	Brazil	https://cdn.sofifa.org/flags/54.png	Paris Saint-Germain	https://cdn.sofifa.org/teams/2/light/73.png	Right	High/ Medium	Neymar	Yes	LW	3-Aug-17	NaN	2022
3	De Gea	https://cdn.sofifa.org/players/4/19/193080.png	Spain	https://cdn.sofifa.org/flags/45.png	Manchester United	https://cdn.sofifa.org/teams/2/light/11.png	Right	Medium/ Medium	Lean	Yes	GK	1-Jul-11	NaN	2020
4	K. De Bruyne	https://cdn.sofifa.org/players/4/19/192985.png	Belgium	https://cdn.sofifa.org/flags/7.png	Manchester City	https://cdn.sofifa.org/teams/2/light/10.png	Right	High/ High	Normal	Yes	RCM	30-Aug-15	NaN	2023

# Show first 5 rows of skills dataframe
skills.head()

	Order	ID	Age	Overall	Potential	Value €	Wage €	Special	International Reputation	Weak Foot	...	Composure	Marking	StandingTackle	SlidingTackle	GKDiving	GKHandling	GKKicking	GKPositioning	GKReflexes	Release Clause €
0	0	158023	31	94	94	110500000.0	565000.0	2202	5.0	4.0	...	96.0	33.0	28.0	26.0	6.0	11.0	15.0	14.0	8.0	226500000.0
1	1	20801	33	94	94	77000000.0	405000.0	2228	5.0	4.0	...	95.0	28.0	31.0	23.0	7.0	11.0	15.0	14.0	11.0	127100000.0
2	2	190871	26	92	93	118500000.0	290000.0	2143	5.0	5.0	...	94.0	27.0	24.0	33.0	9.0	9.0	15.0	15.0	11.0	228100000.0
3	3	193080	27	91	93	72000000.0	260000.0	1471	4.0	3.0	...	68.0	15.0	21.0	13.0	90.0	85.0	87.0	88.0	94.0	138600000.0
4	4	192985	27	91	92	102000000.0	355000.0	2281	4.0	5.0	...	88.0	68.0	58.0	51.0	15.0	13.0	5.0	10.0	13.0	196400000.0

5 rows × 75 columns

Data Quality Process with Standardization

• Filter player with an overall below a threshold (85)
• Remove columns that are not relevant for the analysis
• Replace NaN values with average of columns
• Standardize the Data

# Filter/Delete player with an overall below 85
var_filter = "Overall"
threshold = 85
skills = skills.loc[skills[var_filter] >= threshold]
len(skills)

110

# Remove columns that are not relevant for the analysis
nonColumns = ["Order", "ID", "Overall", "Potential", "Value €", "Wage €", "Release Clause €"]
skills = skills.drop(nonColumns, axis = 1)
numColList = [e for e in numColList if e not in nonColumns]

# Columns size validation
len(skills.columns) == len(numColList)

True

# Replace NaN values with average of columns
skills = skills.fillna(skills.mean())

# Standardize the Data
x = skills.loc[:,numColList].values
x = StandardScaler().fit_transform(x)

# Show skills data in temporary dataframe
dfSkills = pd.DataFrame(data = x, columns = numColList)
dfSkills.head()

	Age	Special	International Reputation	Weak Foot	Skill Moves	Jersey Number	HeightMts	WeightLbs	LS	ST	...	Penalties	Composure	Marking	StandingTackle	SlidingTackle	GKDiving	GKHandling	GKKicking	GKPositioning	GKReflexes
0	0.776706	0.724004	2.310325	0.743626	0.831174	-0.173639	-1.639945	-0.770754	0.818270	0.818270	...	0.595888	2.111447	-1.062921	-1.027494	-0.951904	-0.517153	-0.308874	-0.119577	-0.178222	-0.423847
1	1.361895	0.822752	2.310325	0.743626	1.693714	-0.548156	0.723295	0.560044	0.938657	0.938657	...	1.145324	1.955673	-1.267257	-0.919025	-1.059078	-0.475901	-0.308874	-0.119577	-0.178222	-0.303270
2	-0.686267	0.499921	2.310325	2.084591	1.693714	-0.173639	-0.983490	-1.269804	0.657753	0.657753	...	0.925549	1.799899	-1.308124	-1.172118	-0.701830	-0.393397	-0.393602	-0.119577	-0.136510	-0.303270
3	-0.393673	-2.052339	0.882596	-0.597339	-1.756444	-1.297189	1.379750	-0.271705	-2.713095	-2.713095	...	-1.327137	-2.250227	-1.798531	-1.280587	-1.416327	2.948037	2.826078	3.146120	2.908430	3.032701
4	-0.393673	1.024046	0.882596	2.084591	0.831174	-0.548156	-0.327034	-1.048004	0.577495	0.577495	...	0.815662	0.865254	0.367434	0.057193	-0.058784	-0.145883	-0.224145	-0.573146	-0.345068	-0.222885

5 rows × 68 columns

Correlation matrix between Features

# Calculate skills correlations
corr = dfSkills.corr()

# Generate a mask for the upper triangle
mask = np.zeros_like(corr, dtype = np.bool)
mask[np.triu_indices_from(mask)] = True

# Set up the matplotlib figure
fig, ax1 = plt.subplots(figsize = (18, 18))

# Generate a custom diverging colormap
cmap = sns.diverging_palette(10, 240, n = 9)

# Draw the heatmap with the mask and correct aspect ratio
sns.heatmap(corr, mask = mask, cmap = cmap, vmin = -1, vmax = 1, center = 0,
            square = True, linewidths = .5, cbar_kws = {"shrink": .5})

ax1.set_xticklabels(ax1.get_xticklabels(), rotation = 45, horizontalalignment = 'right');

# Add title
ax1.set_title("Skills Correlation Triangle", fontsize = 20)
plt.show()

PCA Process

Definition: Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. Source: Wikipedia

# Principal Component Analysis
pca = PCA(n_components = 5)
pcaData = pca.fit_transform(x)

# Create and show principal components DataFrame
pcaDF = pd.DataFrame(data = pcaData, columns = ["PC1", "PC2", "PC3", "PC4", "PC5"])
pcaDF = pd.concat([pcaDF, header[["Name"]]], axis = 1)
pcaDF = pcaDF[pcaDF["PC1"].notnull()]
pcaDF

	PC1	PC2	PC3	PC4	PC5	Name
0	-4.593481	-5.478033	1.127111	1.252885	-2.286953	L. Messi
1	-4.080334	-3.406618	4.334073	-0.485612	-2.817897	Cristiano Ronaldo
2	-4.048185	-5.546171	0.505673	0.616553	-1.730906	Neymar Jr
3	17.658339	-2.364764	-0.405911	1.214861	-1.087192	De Gea
4	-4.982714	-1.635134	0.422099	1.768055	-0.096850	K. De Bruyne
...	...	...	...	...	...	...
105	-1.458081	-2.661787	2.633530	-0.396837	0.622312	K. Benzema
106	-2.714554	2.392151	-0.847898	0.752160	-1.100449	Filipe Luís
107	0.784593	4.941324	1.491644	1.390592	-0.776510	V. Kompany
108	1.749388	5.147898	0.692962	0.374109	-1.701941	Pepe
109	-1.101967	-1.384143	5.518075	1.973968	0.789597	Z. Ibrahimović

110 rows × 6 columns

# Show correlation between components
fig, ax = plt.subplots(figsize = (10, 10))
sns.heatmap(pcaDF.corr(), square=True, annot=True)
ax.set_title("Correlation between Components", fontsize = 16)
plt.show()

As you can see, there is no correlation between the principal components because they are orthogonal.

PCA Variance Ratio

# The explained variance tells us how much information (variance) can be attributed to each of the principal components
list(pca.explained_variance_ratio_)

[0.6559769839499195,
 0.14857826650344874,
 0.04305208015677819,
 0.03029528547335026,
 0.02500385682900391]

# Create horizontal bar chart data
bars = ("PC1", "PC2", "PC3", "PC4", "PC5")
y_pos = np.arange(len(bars))
values = pca.explained_variance_ratio_ * 100
cum = np.cumsum(values)

# Set up the matplotlib figure
fig, ax2 = plt.subplots(figsize = (12, 10))

plt.bar(y_pos, values, align = "center", alpha = 0.7)
plt.xticks(y_pos, bars)
plt.plot(y_pos, cum, color = "orange", linewidth = 2, marker="o")
plt.title("Variance Ratio By Component", fontsize = 20)

# Add bar labels
for i, v in enumerate(cum):
    ax2.text(i - .15, v + 1, (str(round(v, 1))+"%"), color = "black", fontweight = "normal", fontsize = 11)

# Plot setup
plt.xlabel("Components", fontsize = 12)
plt.ylabel("Explained variance in percent", fontsize = 12)
plt.legend(("Cum", "Var"), loc = "best")
plt.show()

PCs Dependencies

# Create a matshow plot of the Principal Components dependencies
fig = plt.figure(figsize = (16, 2))
plt.matshow(pca.components_, cmap = "viridis", fignum = fig.number, aspect = "auto")
plt.yticks([0, 1, 2, 3, 4], ["PC1", "PC2", "PC3", "PC4", "PC5"], fontsize = 10)
plt.colorbar()
plt.xticks(range(len(skills.columns)), skills.columns, rotation = 65, ha = "left")
plt.show()

PCA Plane Visualization

2D Chart: The first 2 components

# Show the total explained variance ratio of model: Only 2 components
n_components = 2
sum(pca.explained_variance_ratio_[0:n_components]) * 100

80.45552504533683

# Eigen-vectors data
n_vectors = 2
lengths = pca.explained_variance_[0:n_vectors]
vectors = pca.components_[0:n_components, 0:n_vectors]
means = pca.mean_[0:n_vectors]

# Function to draw vectors on plane
def draw_vector(v0, v1, ax = None):
    ax = ax or plt.gca()
    arrowprops = dict(arrowstyle = "->", linewidth = 2, shrinkA = 0, shrinkB = 0, color = "#ff7f0e")
    ax.annotate("", v1, v0, arrowprops = arrowprops)

# Create scatter plot with players label
fig, ax3 = plt.subplots(figsize = (14, 14))

# Create 2D scatter plot
plot = sns.regplot(ax = ax3, data = pcaDF, x = "PC1", y = "PC2", fit_reg = False
                   , marker = "o", color = "#1f77b4", scatter_kws = {"s": 75})

# Add annotations one by one with a loop
for ix in range(0, pcaDF.shape[0]):
    plot.text(pcaDF.PC1[ix] + 0.2, pcaDF.PC2[ix] - 0.05, pcaDF.Name[ix]
              , horizontalalignment = "left", size = "medium", color = "black", weight = "normal")

# Drawing the eigen-vectors
for length, vector in zip(lengths, vectors):
    v = vector * 3 * np.sqrt(length)
    draw_vector(means, means + v)

# Plot setup
ax3.set_xlabel("PC 1", fontsize = 12)
ax3.set_ylabel("PC 2", fontsize = 12)
ax3.set_title("2D Best Players FIFA 19", fontsize = 20)
ax3.legend(["Best Players (overall >= " + str(threshold) + ")"])
ax3.grid()

3D Chart: The first 3 components

# Show the total explained variance ratio of model: Only 3 components
sum(pca.explained_variance_ratio_[0:3]) * 100

84.76073306101465

# Create 3D scatter plot
fig = plt.figure(figsize = (16, 16))
ax4 = fig.add_subplot(111, projection = "3d")

# Get (x, y, z) axis values
xx = pcaDF.loc[:,["PC1"]].values
yy = pcaDF.loc[:,["PC2"]].values
zz = pcaDF.loc[:,["PC3"]].values

# Plot values
ax4.scatter(xx, yy, zz, c = "#1f77b4", marker = "o", s = 75)

# Add annotations one by one with a loop
for ix in range(0, len(x)):
    ax4.text(float(xx[ix]), float(yy[ix]), float(zz[ix]), pcaDF.Name[ix]
             , horizontalalignment = "left", size = "medium", color = "black", weight = "normal")

# Plot setup
ax4.set_xlabel("PC 1", fontsize = 12)
ax4.set_ylabel("PC 2", fontsize = 12)
ax4.set_zlabel("PC 3", fontsize = 12)
ax4.set_title("3D Best Players FIFA 19", fontsize = 20)
ax4.legend(["Best Players (overall >= " + str(threshold) + ")"])
ax4.grid()

Insights

• It is possible to perform a PCA of the skills of the players and maintain 80.5% of the variance of the data with only 2 components. Which allows us to plot the players on the plane and analyze which players resemble each other.
• The similarity between players is better identified with 2 components (2D plot and 80.5% variance explained) than with 3 components (3D plot and 84.8% variance explained).
• There is no correlation between the principal components because they are orthogonal.

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