Video Games and the

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Video Games and the
Communities They Foster


A statistical study of the video gamersphere: its
games, gamers, and societal gaming communities.


Colin Bayer

Aaron Miller

Zak Dehlawi

Patrick Carroll

The
University of Washington

June 2008

INTRODUCTION

Wit
h the advent of Microsoft’s Xbox Live online gaming platform,
now more than ever gaming has become a social event. Therefore
,
one can logically hypothesize that communities of gamers
exist inside
today’s video gamer
sphere.

These communities

must
share
char
acteristic traits:
games

played

in common
,

game genres, etc.

Furthermore, we can extract general descriptive statistics regarding
the games in our dataset: those wh
ich are the most challenging,

the
easiest,

and most and least popular.


Data clustering

is t
he practice of segmenting a dataset into a
finite amount of subsets. These subsets are called
clusters

and the
data which belong to each cluster share a common trait: often the
value of a mathematical measure of proximity to the cluster’s other
members.


C
lustering gamers requires a metric of distance.
Microsoft
requires each Xbox Live
-
enabled game
to provide some number of
achievements
, in
-
game goals that award
Gamerscore

points to users
who complete them. A

user's Gamerscore is equ
al to the sum of the
Ga
merscore
points pro
vided by
each achievement that they have

completed, or "unlocked".

The ratio that each game has contributed to
a user’s

Gamerscore is a simplistic, yet

useful distance metric.

METHODS


Clustering gamers necessitat
es
that
the

dataset con
tain the
achievements and their
Gamerscore values each gamer has

unlocked
during his/her gaming career.

Addition
ally, to reduce computation, the
dataset
should

include
each gamer’s Gamerscore.

The dataset was
obtained in two pieces:
first
a list of gamer u
sernames
,

then the
ir
achievements and associated G
amerscores.
The usernames were
pulled by crawling
MyGamerCard.net
’s
leader
-
board and live
-
tracker
(which shows who is currently online in the Xbox Live system) as well
as a few other sites such as
360voice.
com
. T
he achievements and
associated G
amerscores per gamer were scraped from
the

Xbox Live
web
site
(
xbox.live.com
)
by using regular expression matching for the
attained usernames.

The
results of the crawling and scraping were

inserted into a MySQL database

which affords ea
sy data selection for
analysis.


To cluster gamers using rational

Ga
merscore per game, each
gamer was

treated as a point in the gamesphere’s n
-
dimensional
space, where n is the number of

disti
nct games in the dataset. The i
th

coordinate of

the gamer
’s

n
-
tuple is the ratio of how much the
corresponding game has contributed to the gamer’s Gamerscore.


We implemented three common clustering methods/algorithms:
hierarchical, k
-
means, and
model
-
ba
sed.
Hierarchical clustering

follows
this
algorit
hm
:

1.

Cluster

the two gamers who, when represented by gamer
-
points
are the closest together
, have the smallest Euclidian distance
between them.

2.

Repeat the initial step; however one of the gamers may be
replaced by the centroid of an existing cluster.

3.

Stop wh
en a decided
-
upon maximum number of clusters is
attained.

K
-
Means clustering

assigns each n
-
dimensional gamer
-
point
to the
cluster whose
centroi
d
lies nearest. The centroid is computed by
averaging each of the n
-
dimensions separately. The K
-
Means
algorithm

follows five core steps:

1.

Assume finite number of clusters,
k
, exists.

2.

Randomly generate each cluster’s centroid.

3.

Assign each gamer
-
point to the centroid whose Euclidian
distance is at a minimum.

4.

Recompute the cluster’s centroids.

5.

Repeat Steps 3 and 4 unt
il no change in cluster assignment
occurs.

//TODO:

Describe model
-
based clustering and how it chooses a k
-
value for you to k
-
means cluster on.

For game descriptive statistics we examined summary statistics as well
as created histograms which visually
conve
y

summary statistics
.