Tags: [Data Analytics], [Statistics]
Technical Skills: [Python], [Jupyter Notebook], [Pandas], [Numpy], [Matplotlib]
Theoretical Frameworks: [Poisson Distribution]
Note
An exercise done with the assistance provided from the Workearly team when I was doing my bootcamp back in 2023. They are specialised educational professionals that offer extraordinary upskilling bootcamps and more.
I started my journey of upskilling last February with them, and thanks to the learning structure they offer, they had helped me become adept in 6 different tools and use them in a professional environment in only 10 months, including how to utilise Python in Data Science as seen below.
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The dataset was distributed by the user GregorySmith(gregorut): https://www.kaggle.com/datasets/gregorut/videogamesales
A simplistic execution of EDA (Exploratory Data Analysis), to answer 7 questions, and perform a poisson distribution to model the data.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import math# Calling the CSV
df = pd.read_csv(r'B:\Python Environments\Video Game Data Analysis\Raw Data\vgsales.csv')
#r'' because I just want to copy/paste the path without changing all the \ to / or to \\Dropping N/A and nulls.
df.dropna(inplace=True)df.head()| Rank | Name | Platform | Year | Genre | Publisher | NA_Sales | EU_Sales | JP_Sales | Other_Sales | Global_Sales | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | Wii Sports | Wii | 2006.0 | Sports | Nintendo | 41.49 | 29.02 | 3.77 | 8.46 | 82.74 |
| 1 | 2 | Super Mario Bros. | NES | 1985.0 | Platform | Nintendo | 29.08 | 3.58 | 6.81 | 0.77 | 40.24 |
| 2 | 3 | Mario Kart Wii | Wii | 2008.0 | Racing | Nintendo | 15.85 | 12.88 | 3.79 | 3.31 | 35.82 |
| 3 | 4 | Wii Sports Resort | Wii | 2009.0 | Sports | Nintendo | 15.75 | 11.01 | 3.28 | 2.96 | 33.00 |
| 4 | 5 | Pokemon Red/Pokemon Blue | GB | 1996.0 | Role-Playing | Nintendo | 11.27 | 8.89 | 10.22 | 1.00 | 31.37 |
# Group by name and sum of global sales
top_selling = df.groupby('Name')['Global_Sales'].sum()
# Sort by global sales
top_selling = top_selling.sort_values(ascending=False)
# Displaying the top 15 games
print(top_selling.head(15))Name
Wii Sports 82.74
Grand Theft Auto V 55.92
Super Mario Bros. 45.31
Tetris 35.84
Mario Kart Wii 35.82
Wii Sports Resort 33.00
Pokemon Red/Pokemon Blue 31.37
Call of Duty: Modern Warfare 3 30.83
New Super Mario Bros. 30.01
Call of Duty: Black Ops II 29.72
Call of Duty: Black Ops 29.40
Wii Play 29.02
New Super Mario Bros. Wii 28.62
Duck Hunt 28.31
Call of Duty: Ghosts 27.38
Name: Global_Sales, dtype: float64
Most selling games is Wii Sports with 82.74m global sales, followed by Grand Theft Auto V with 55.92m global sales, followed by the old classic Super Mario Bros. with 45.31m global sales.
# Group by platform and sum of global sales
top_platform = df.groupby('Platform')['Global_Sales'].sum()
# Sort by platform sales
top_platform = top_platform.sort_values(ascending=False)
# Displaying the top 10 platforms
print(top_platform.head(10))Platform
PS2 1233.46
X360 969.60
PS3 949.35
Wii 909.81
DS 818.91
PS 727.39
GBA 305.62
PSP 291.71
PS4 278.10
PC 254.70
Name: Global_Sales, dtype: float64
Based on global sales, the most popular platform of all time is Playstation 2 with 1233.46m games being sold.
# Group by genre and sum of global sales
top_genre = df.groupby('Genre')['Global_Sales'].sum()
# Sort by genre sales
top_genre = top_genre.sort_values(ascending=False)
# Displaying the top 10 genres
print(top_genre.head(10))Genre
Action 1722.84
Sports 1309.24
Shooter 1026.20
Role-Playing 923.83
Platform 829.13
Misc 789.87
Racing 726.76
Fighting 444.05
Simulation 389.98
Puzzle 242.21
Name: Global_Sales, dtype: float64
region_sales = df[['NA_Sales','EU_Sales','JP_Sales','Other_Sales']].sum()
# Creating the bar graph
region_sales.plot(kind='bar')
plt.title('VGS By Region')
plt.xlabel('Region')
plt.ylabel('Sales (in Mil.)')
plt.show<function matplotlib.pyplot.show(close=None, block=None)>
# Creating the Scatterplot
plt.scatter(df['Year'],df['Global_Sales'])
plt.title('Year of Release vs. Global Sales')
plt.xlabel('YoR')
plt.ylabel('Global Sales (in Mil.)')
plt.show()
Clearly, there is no positive correlation between the year of release a game released against how it sold. If there was, we should be able to see for a specific year, density of points towards the higher scales of the Global Sales (the Y axis.)
Therefore, Hypothesis 1 is rejected.
# Creating the Scatterplot
plt.scatter(df['Publisher'],df['Global_Sales'])
plt.title('Publisher vs. Global Sales')
plt.xlabel('Publisher')
plt.ylabel('Global Sales (in Mil.)')
plt.show()
Whoops! It seems we need to do an extra step for this one. Let's try to group them by sales and then sort them.
# Grouping by the sum of sales
publisher_vs = df.groupby('Publisher')['Global_Sales'].sum()
# Sorting by highest selling publisher
publisher_vs = publisher_vs.sort_values(ascending=False)
# Creating the bar plot
publisher_vs.head(15).plot(kind='bar')
plt.title('Publisher vs. Global Sales')
plt.xlabel('Publisher')
plt.ylabel('Global Sales (in Mil.)')
plt.show()
In the graph above, we immediately observe that Nintendo and EA has had most sales of all times in video games sales.
We could go as far to state that since the dataset supports that Nintendo did not achieve those numbers by an irregularity/outlier (i.e one good selling game), but through consistent successful entries, there is definitely something to be learnt from that company.
mean = df['Global_Sales'].mean()
var = df['Global_Sales'].var()exp_mean = mean
exp_var = varprint('Mean sales', mean)
print('Variance of sales', var)
print('Expected mean', exp_mean)
print('Expected variance', exp_var)Mean sales 0.5409103185808114
Variance of sales 2.456568802945086
Expected mean 0.5409103185808114
Expected variance 2.456568802945086
To evaluate that a Poisson distribution can be applied for the model, we need a goodness-of-fit test. That is done by calculating the mean and variance, as we have done above on steps 8.1.1. and 8.1.2. and by comparing the observed values to the expected values.
If the mean and var have approx. similar values or are equal, then the distribution can be applied. Also for each category, if the mean and var. vs the expected mean and var. have a closer range, then it definitely fits.
In this case, there is a quite substantial difference between mean and var. without even comparing the expected mean and var. Regardless, we will still attempt to fit the Poisson Distribution to the data and see how well it fits.
def poisson_prob(k, lam):
return (lam**k)*math.exp(-lam)/math.gamma(k+1)
mean = np.mean(df['Global_Sales'])
# Generating a histogram of the sales
n, bins, patches = plt.hist(df['Global_Sales'], bins=50, density=True, alpha=0.5)
# Calculating the distribution
poisson_dist = [poisson_prob(b,mean) for b in bins]
# Plotting the distribution over the histogram
plt.plot(bins, poisson_dist, 'r-', linewidth = 1)
# Labelling the plot
plt.title('Poisson Distribution of Global Sales')
plt.xlabel('Global Sales (in Mil.)')
plt.ylabel('Probability')Text(0, 0.5, 'Probability')
In the histogram above, the red line acts as the depiction of the distribution. To be more exact, the red line represents the Poisson probability mass function (PMF).
The PMF is a function over a sample of a discrete value X which annotates the probability of value X that is equals to a certain value (f(x) = P[X=x]).
As we had already seen on the goodness-for-fit test, the distribution does not work well, as it is clear that the PMF overestimates the frequency of low sales and underestimates that of the high volume of sales. That concludes that Poisson is indeed not a good fit for this dataset.
Note
That does not necessarily mean that this data set does not follow any probability distribution, just that it does not follow specifically a Poisson distribution.