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% Make the title bold
\title{\bf The Right Arm Bias in ITF Taekwon-Do \\ Patterns Chon-Ji to Juche}

% Author information
\author{Bjørn Michelsen, III. Dan \\
  \texttt{<bjorn@bmichelsen.no>} \\
  \\
  ITF Tromsdalen School of Taekwon-Do \\
  Tromsø, Norway
  }

% Print date
\date{\today}

% Produce the title
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% Sections
\section*{\centering Abstract}
\begin{em}

  When performing patterns in ITF Taekwon-Do, one of the factors mentioned in
  the condensed Encyclopedia is that there should be an equal number of
  techniques to both sides of the body. Here we analyze hand techniques in
  Chon-Ji through Juche to establish whether or not there is a bias towards
  either side. This is done by attaching metadata, in the form of tags, to each
  pattern movement. These tags are generated from the Encyclopedia's description
  of the movements, and supplemented by keywords that were identified by
  carefully examining each pattern. We then apply concepts from set theory to
  retrieve the information we are interested in, and find that there are seven
  more techniques on the right side than on the left.

\end{em}


\Section{Introduction}

  A \emph{pattern} in International Taekwon-Do Federation (ITF) is defined as
  a choreographed sequence of fundamental movements. These \emph{fundamental
  movements} are basic elements which represent an attack or defense against a
  specific target area, or a predetermined action of an attacker.

  Combined in a pattern, it allows the student to systematically deal with one
  or several imaginary opponents using every available attacking and blocking
  tool from different directions. In addition, the techniques should also be
  evenly distributed between the left and the right side\cite{cyclo:vol1}.

  It has, however, recently been observed that there is a bias towards the
  right leg. The study by Gibbs\cite{rlb} show that there is a total of 152
  kicks in patterns Chon-Ji to Tong-Il. 85 kicks are with the right leg, and
  67 kicks are with the left leg. This means that 56 \% of the kicks are with
  the right leg, and 44 \% are with the left leg.

  The work by Gibbs focused on kicks in all patterns, whereas this article
  examines patterns Chon-Ji to Juche. Looking at kicks in these patterns using
  Gibbs' paper, we find that there are 72 kicks in total. 42 kicks are with
  the right leg, and 30 kicks are with the left leg. Roughly 58 \% of the
  kicks are with the right leg, and about 42 \% with the left. Thus, the right
  leg bias still holds.

  In this article we analyze hand techniques in patterns Chon-Ji to Juche
  using tags, and then report our findings of a right arm bias.


\SubSection{Tags}

  In a hierarchical and exclusive classification system, each object belongs
  to one unambiguous category, which in turn belongs within another more
  general category.

  Take the hierarchy of folders in a computer file system, for example. How we
  choose to organize the folders reflects a decision concerning the relative
  importance of each characteristic\cite{golder:ct}.

  Folder names are in themselves informative, in that, like tags, they
  describe the information held within them\cite{jones:folders}. Furthermore,
  the way folder names relate to each other shows a structural relationship
  between directories\cite{mathes:folk}.

  \emph{Tags}, on the other hand, are non-hierarchical descriptive terms,
  keywords or labels that is attached to an object for later retrieval
  \cite{golder:ct}\cite{huang:tt}\cite{shirky:ontology}.

  They are \emph{non-hierarchical} and \emph{inclusive}, which is to say that
  an object can be associated with a great variety of tags
  simultaneously\cite{golder:ct}. The \emph{descriptive terms},
  \emph{keywords} or \emph{labels} are metadata connected to a given object
  that describes a concept or type of information\cite{heymann:ccch}.


\SubSection{Tagging}

  \emph{Tagging} is the act of organizing a collection of objects into related
  groups\cite{shirky:ontology}.


\SubSection{Set Theory}
  A \emph{set} is a collection of distinct objects. It is ``a plurality
  thought of as a unit''\cite{hausdorff:sets}. \emph{Set theory}, then, is the
  branch of mathematics that studies sets.

  An object which has been tagged contains a collection, or a set, of tags.
  Each tag is an element of the set. The order of elements within the set is
  irrelevant, but each element can only occur once.

  For example, $\{1,5,8\}$ is a set with three elements: 1, 5 and 8.
  $\{5,8,1\}$ is the same set, since the order of the elements doesn't matter.
  $\{1,1,1\}$, however, is not a valid set because the element 1 occurs
  repeatedly. Elements in a set can contain strings as well, so $\{blocks,
  punches, strikes, thrusts\}$ is also a valid set.

  We usually denote a set by a capital letter for reference purposes. For
  instance, $S=\{1,5,8\}$.

  $a \in S$ denotes that the object $a$ is a member of the set $S$. If $a$
  is not a member of S, we write $a \notin S$.

  The \emph{union} of two sets $S$ and $T$ is the set

  \[
    S \cup T = \{x:x \in S \: or \: x \in T\}
  \]

  % Venn diagram, showing the union of two sets
  \input{venn_union.asy}

  This consists of those objects which lie in the set $S$ or in the set $T$,
  or in both. So,

  \[
    \{1, 2, 3\} \cup \{3, 4, 5\} = \{1, 2, 3, 4, 5\}
  \]

  The \emph{intersection} of two sets $S$ and $T$ is the set

  \[
    S \cap T = \{x:x \in S \: and \: x \in T\}
  \]

  % Venn diagram, showing the intersect of two sets
  \input{venn_intersect.asy}

  This consists of those objects which lie in both the set $S$ and the set
  $B$. So,

  \[
    \{1, 2, 3\} \cap \{2, 3, 4\} = \{2, 3\}
  \]

  The \emph{complement} of a set $T$ relative to a set $S$ is the set

  \[
    S - T = \{x:x \in S \: and \: x \notin T\}
  \]

  % Venn diagram, showing the complement of two sets
  \input{venn_complement.asy}

  This consists of those objects which lie in the set $S$ but not in the set
  $T$. So,

  \[
    \{1, 2, 3\} - \{2, 3, 4\} = \{1\}
  \]

  The \emph{symmetric difference} of the sets $S$ and $T$ is the set

  \[
    S \Delta T = \{x:(x \in S \: and \: x \notin T) \: or \: (x \in T \: and
    \: x \notin S)\}
  \]

  % Venn diagram, showing the symmetric difference of two sets
  \input{venn_difference.asy}

  This consists of those objects which lie either in one of the sets, but not
  in both. So,

  \[
    \{1, 2, 3\} \Delta \{2, 3, 4\} = \{1, 4\}
  \]


\Section{Method}

  In this section we describe where the data originates. Next we elaborate on
  the approach taken to register and investigate the dataset. Finally, we look
  at how each movement has been classified with emphasis on special cases.


\SubSection{The Data}

  Our data comes from two different sources. The terminology associated with
  pattern movements is from Taekwon-Do ITF Sonkal Praha\footnote{\url{http://
  sonkal.taekwondo.cz}}, and the English description of each movement is from
  the condensed encyclopedia\cite{cyclo:con}.

  The dataset is organized by pattern names. It contains a list of all
  techniques in patterns Chon-Ji to Juche. For each movement, the following
  data has been registered:

  \begin{enumerate}
    \item Movement number
    \item English description
    \item Terminology
    \item Tags
  \end{enumerate}


\SubSection{Approach}

  The movement number, together with the English description of each movement,
  was registered manually from the condensed encyclopedia. After reviewing and
  making minor corrections to the terminology, it too was added to the
  dataset.
  
  Suitable tags were then attached to every movement by first extracting
  keywords from their English description, and then adding more detailed tags
  while performing the pattern.

  We then defined the data models with DataMapper, an Object Relational
  Mapper\footnote{\url{http://www.datamapper.org}} (ORM) written in the Ruby
  programming language. The models are Ruby classes with properties and
  associations. Properties define field names and data types in the database,
  whereas the associations define the relationships and cardinality between
  the models.

  Next we created a Ruby script that reads the dataset and automatically
  populates the database. It sets up associations between models, and adds the
  appropriate tags to every movement, as well as associations between movement
  and pattern.

  Tagging movements in such a formalized manner, and registering it in a
  database, enables us to retrieve the data we are interested in using
  concepts from set theory.


\SubSection{Classification}

  Classification was done by attaching metadata, in the form of tags, to each
  pattern movement.

  The first movement in Chon-Ji, for instance, is to ``[m]ove the left foot to
  B, forming a left walking stance toward B while executing a low block to B
  with the left forearm\cite{cyclo:vol1}.'' Removing the redundant parts of
  the description leaves us with:

  \[
    \{left \: walking \: stance, \: low \: block, \: left \: forearm\}
  \]

  Supplementing the above with more detailed tags gives us:

  \begin{align*}
    \{walking \: stance, \: left \: stance, \: low \: technique, \\
    left \: technique, \: block, \: forearm, \\
    outer \: forearm, normal \: motion\}
  \end{align*}

  Information about the stance type is presented first, followed by stance
  side (left, right or none where applicable --- for example a sitting
  stance), technique height (low, middle, high), technique side (left arm or
  right arm, it can also be both), direction of the technique (when needed),
  primary technique type (attack, block, kick), technique group (block, punch,
  strike, thrust), tool group (forearm, knife hand, finger etc.), tool (inner
  forearm, outer forearm, double finger etc.), and finally motion type (normal
  motion, slow motion, consecutive motion and so on).

  In most cases, applying tags to movements has been straightforward.
  However, there are movements that need special mention. These movements fall
  into two categories.

  The first category consists of movements where both arms are part of the
  technique by either forming the technique, or by being two separate
  techniques in a single movement.

  In cases where both arms are used in one technique, the movement has been
  tagged with $\{left\_technique, \: right\_technique\}$ to reflect that both
  arms are needed for the technique, or that the movement contains two
  separate hand techniques.

  An example of a movement where both arms are required to form the technique
  can be found in the 13\textsuperscript{th} movement of Joong-Gun Tul, which
  is \emph{Gunnun so kyocha joomuk chukyo makgi}.

  When it comes to a movement with two separate hand techniques, the
  27\textsuperscript{th} movement of Joong-Gun Tul, being \emph{Nachuo so
  sonbadak noollo makgi}, serves as a good illustration.

  The implications of tagging movements with $\{left\_technique, \:
  right\_technique\}$ are that the total amount of hand techniques on either
  side are higher than what actually is the case. This flaw does not affect
  the bias we are investigating, though.

  The second category comprises ambiguous movements, and thus contains
  clarification on why certain tags were added.

  Below is a list of all the special cases from both categories.

\begin{itemize}
  \item
    \emph{Do-San Tul}
    \begin{itemize}
      \item
        {\bf Movement 13}, \emph{Gunnun so bakat palmok nopunde hechyo makgi},
        is tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 17}, \emph{Gunnun so bakat palmok nopunde hechyo makgi},
        is tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
    \end{itemize}
  \item
    \emph{Yul-Gok Tul}
    \begin{itemize}
      \item
        {\bf Movement 24}, \emph{Gunnun so ap palkup bandae taerigi}, is
        tagged with $\{front\_strike\}$ due to the English description of
        striking with the right front elbow.
      \item
        {\bf Movement 27}, \emph{Gunnun so ap palkup bandae taerigi}, is
        tagged with $\{front\_strike\}$ due to the English description of
        striking with the left front elbow.
    \end{itemize}
  \item
    \emph{Joong-Gun Tul}
    \begin{itemize}
      \item
        {\bf Movement 8}, \emph{Gunnun so wipalkup taerigi}, is tagged
        $\{upper\_strike, \: upper\_elbow\}$ since the English description
        says that the movement is ``a right upper elbow strike.''
      \item
        {\bf Movement 10}, \emph{Gunnun so wipalkup taerigi}, is tagged
        $\{upper\_strike, \: upper\_elbow\}$ since the English description
        says that the movement is ``a left upper elbow strike.''
      \item
        {\bf Movement 11}, \emph{Gunnun so sang sewo jirugi}, is tagged as a
        left and right technique, with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of punches on
        both sides.
      \item
        {\bf Movement 12}, \emph{Gunnun so sang dwijibo jirugi}, is tagged as
        a left and right technique, with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of punches on
        both sides.
      \item
        {\bf Movement 13}, \emph{Gunnun so kyocha joomuk chukyo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 27}, \emph{Nachuo so sonbadak noollo makgi}, is tagged as
        a $\{middle\_technique, \: low\_technique\}$ because the left hand is
        in the middle section and the right hand, forming the pressing block,
        is in the low section of the body. The movement has, additionally, been
        tagged as a $\{right\_technique, \: left\_technique\}$ to reflect that
        two separate blocks are executed.
      \item
        {\bf Movement 29}, \emph{Nachuo so sonbadak noollo makgi}, is tagged as
        a $\{middle\_technique, \: low\_technique\}$ because the right hand is
        in the middle section and the left hand, forming the pressing block, is
        in the low section of the body. The movement has, additionally, been
        tagged as a $\{right\_technique, \: left\_technique\}$ to reflect that
        two separate blocks are executed.
    \end{itemize}
  \item
    \emph{Toi-Gae Tul}
    \begin{itemize}
      \item
        {\bf Movement 7}, \emph{Gunnun so kyocha joomuk noollo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 8}, \emph{Gunnun so sang sewo jirugi}, is tagged as a
        left and right technique, with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of punches on
        both sides.
      \item
        {\bf Movement 20}, \emph{Gunnun so}, has only the stance registered
        although the English description says to ``[e]xtend both hands upward
        as if to grab the opponent's head.''
      \item
        {\bf Movement 29}, \emph{Gunnun so kyocha joomuk noollo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
    \end{itemize}
  \item
    \emph{Hwa-Rang Tul}
    \begin{itemize}
      \item
        {\bf Movement 24}, \emph{Gunnun so kyocha joomuk noollo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
    \end{itemize}
  \item
    \emph{Choong-Moo Tul}
    \begin{itemize}
      \item
        {\bf Movement 11}, \emph{Gunnun sogi}, has only the stance registered
        as part of the terminology though the English description says to
        ``[e]xtend both hands upward as if to grab the opponent's head.''
      \item
        {\bf Movement 27}, \emph{Niunja so kyocha sonkal kaunde momcho makgi},
        is tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
    \end{itemize}
  \item
    \emph{Kwang-Gae Tul}
    \begin{itemize}
      \item
        {\bf Movement 21}, \emph{Nachuo so sonbadak noollo makgi}, is tagged as
        a $\{middle\_technique, \: low\_technique\}$ because the right hand is
        in the middle section and the left hand, forming the pressing block, is
        in the low section of the body. The movement has, additionally, been
        tagged as a $\{right\_technique, \: left\_technique\}$ to reflect that
        two separate blocks are executed.
      \item
        {\bf Movement 22}, \emph{Nachuo so sonbadak noollo makgi}, is tagged as
        a $\{middle\_technique, \: low\_technique\}$ because the right hand is
        in the middle section and the left hand, forming the pressing block, is
        in the low section of the body. The movement has, additionally, been
        tagged as a $\{right\_technique, \: left\_technique\}$ to reflect that
        two separate blocks are executed.
      \item
        {\bf Movement 31}, \emph{Gunnun so sang sewo jirugi}, is tagged as a
        left and right technique, with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of punches on
        both sides.
      \item
        {\bf Movement 32}, \emph{Gunnun so sang dwijibo jirugi}, is tagged as
        a left and right technique, with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of punches on
        both sides.
      \item
        {\bf Movement 36}, \emph{Gunnun so sang dwijibo jirugi}, is tagged as
        a left and right technique, with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of punches on
        both sides.
    \end{itemize}
  \item
    \emph{Po-Eun Tul}
    \begin{itemize}
      \item
        {\bf Movement 6}, \emph{Annun so ap joomuk noollo makgi}, consists of
        two blocks. The first is a ``pressing block with the left fore fist,''
        and the second one is a ``side front block with the right inner
        forearm.'' When searching, this movement will only register as one
        block.
      \item
        {\bf Movement 7}, \emph{Annun so ap joomuk noollo makgi}, consists of
        two blocks. The first is a ``pressing block with the right fore
        fist,'' and the second one is a ``side front block with the left inner
        forearm.'' When searching, this movement will only register as one
        block.
      \item
        {\bf Movement 8}, \emph{Annun so an palmok kaunde hechyo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 24}, \emph{Annun so ap joomuk noollo makgi}, consists of
        two blocks. The first is a ``pressing block with the right fore
        fist,'' and the second one is a ``side front block with the left inner
        forearm.'' When searching, this movement will only register as one
        block.
      \item
        {\bf Movement 25}, \emph{Annun so ap joomuk noollo makgi}, consists of
        two blocks. The first is a ``pressing block with the left fore fist,''
        and the second one is a ``side front block with the right inner
        forearm.'' When searching, this movement will only register as one
        block.
      \item
        {\bf Movement 26}, \emph{Annun so an palmok kaunde hechyo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
    \end{itemize}

    Movements 6, 7, 24 and 25 for pattern Po-Eun also have the following tags
    attached:

  \begin{align*}
    \{sitting\_stance, \: low\_technique, \: high\_technique, \\
    left\_technique, \: right\_technique, \: block, \\
    pressing\_block, fore\_fist, \: forearm, \\
    inner\_forearm, \: side\_front\_block, \\
    continuous\_motion\}
  \end{align*}

  \item
    \emph{Ge-Baek Tul}
    \begin{itemize}
      \item
        {\bf Movement 1}, \emph{Niunja so kyocha sonkal kaunde momcho makgi},
        is tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 7}, \emph{Gunnun so nopunde doo bandalson makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 20}, \emph{Annun so gutja makgi}, is tagged as a left
        and a right technique with $\{left\_technique, \: right\_technique\}$.
        This increases the total number of blocks on both sides.
      \item
        {\bf Movement 23}, \emph{Twimyo yopcha jirugi}, the height of the kick
        is not registered.
      \item
        {\bf Movement 24}, \emph{Gunnun so sang sewo jirugi}, is tagged as a
        left and right technique, with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of punches on
        both sides.
      \item
        {\bf Movement 25}, \emph{Gunnun so nopunde doo bandalson makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 34}, \emph{Gunnun so sang sewo jirugi}, is tagged as a
        left and right technique, with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of punches on
        both sides.
      \item
        {\bf Movement 36}, \emph{Annun so gutja makgi}, is tagged as a left
        and a right technique with $\{left\_technique, \: right\_technique\}$.
        This increases the total number of blocks on both sides.
    \end{itemize}
  \item
    \emph{Eui-Am Tul}
    \begin{itemize}
      \item
        {\bf Movement 5}, \emph{Gunnun so kyocha joomuk naeryo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 18}, \emph{Gunnun so kyocha joomuk naeryo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 27}, \emph{Gunnun so sonkal kaunde hechyo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 29}, \emph{Dwitbal so sang sonbadak naeryo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 32}, \emph{Gunnun so sonkal kaunde hechyo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 34}, \emph{Dwitbal so sang sonbadak naeryo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
    \end{itemize}
  \item
    \emph{Choong-Jang Tul}
    \begin{itemize}
      \item
        {\bf Movement 18}, \emph{Gunnun so kyocha joomuk noollo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 19}, \emph{Moorup najunde apcha busigi}, is tagged with
        $\{front\_snap\_kick, \: knee\}$ because the English description says
        to perform ``a low front snap kick to C with the right knee.'' This
        has an effect on the total number of low front snap kicks.
      \item
        {\bf Movement 24}, \emph{Dwitbal so sang sonbadak noollo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 38}, \emph{Gunnun so bandae gutja makgi}, is tagged as a
        left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on
        both sides.
      \item
        {\bf Movement 40}, \emph{Gunnun so bandae gutja makgi}, is tagged as a
        left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on
        both sides.
      \item
        {\bf Movement 41}, \emph{Gunnun so sang sonkal soopyong taerigi}, is
        tagged with $\{knife\_hand, \: twin\_knife\_hand\}$.
    \end{itemize}
  \item
    \emph{Juche Tul}
    \begin{itemize}
      \item
        {\bf Movement 1}, \emph{Annun so an palmok narani makgi}, is tagged as
        left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 4}, \emph{Waebal so bakat palmok narani makgi}, is
        tagged as a left and a right technique with $\{left\_technique, :\
        right\_technique\}$. This increases the total number of blocks on both
        sides. The movement also has the tag $\{parallel\_block\}$ attached to
        it.
      \item
        {\bf Movement 13}, \emph{Annun so an palmok narani makgi}, is tagged
        as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
      \item
        {\bf Movement 16}, \emph{Waebal so bakat palmok narani makgi}, is
        tagged as a left and a right technique with $\{left\_technique, :\
        right\_technique\}$. This increases the total number of blocks on both
        sides. The movement also has the tag $\{parallel\_block\}$ attached to
        it.
      \item
        {\bf Movement 38}, \emph{Sasun so sang sonbadak chookyo makgi}, is
        tagged as a left and a right technique with $\{left\_technique, \:
        right\_technique\}$. This increases the total number of blocks on both
        sides.
    \end{itemize}
\end{itemize}


\Section{Results}

  Our findings show that of 519 techniques, 256 (49 \%) are with the left arm
  and 263 (51 \%) with the right arm (Table \ref{tab:table1}). Looking at the
  total amount of techniques, only 7 techniques (about 1 \%) separates an even
  distribution to both sides.

  \begin{table}
    \centering
    \begin{tabular}{l|r|r} \hline \hline
      & Left Arm & Right Arm \\ \hline

      Blocks    & 148   & 133 \\
      Punches   &  60   &  71 \\
      Strikes   &  34   &  38 \\
      Thrusts   &  14   &  21 \\

      \hline
      \textbf{Total}   & \textbf{256}   & \textbf{263} \\
      \hline

    \end{tabular}
    \caption{Number of techniques per arm by category.}
    \label{tab:table1}
  \end{table}


\SubSection{Techniques by Category}

  In terms of category distribution, there are more blocks on the left side
  than on the right side. There are, therefore, more attacks on the right
  side, than on the left side (Figure \ref{fig:techniques_all}, Table
  \ref{tab:table2}).

  \begin{table}
    \centering
    \begin{tabular}{l|r|r} \hline \hline
      & Left Arm & Right Arm \\ \hline

      Blocks    &  57.81 \%    &  50.57 \% \\
      Punches   &  23.44 \%    &  27.00 \% \\
      Strikes   &  13.28 \%    &  14.45 \% \\
      Thrusts   &   5.47 \%    &   7.98 \% \\

      \hline
      \textbf{Total}   & \textbf{100 \%}   & \textbf{100 \%} \\
      \hline

    \end{tabular}
    \caption{Percent distribution of techniques per arm by category.}
    \label{tab:table2}
  \end{table}

  % Distribution of techniques by category
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/techniques_all}
    \caption{Distribution of techniques by category.}
    \label{fig:techniques_all}
  \end{figure}


\SubSection{Techniques by Height}

  % all techniques by height
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/height_all}
    \caption{All techniques by height.}
    \label{fig:height_all}
  \end{figure}

  Techniques by height follow the same trend when looking at all techniques
  combined or techniques to either side. Most of the techniques are in the
  middle section, although there is a greater occurrence of strikes in the
  high section, and very few attacks in the low section (Figure
  \ref{fig:height_all}).


\SubSection{Techniques by Stances}

  % All techniques by Walking, Sitting and L stances
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/stances_all}
    \caption{All techniques by walking, sitting and L stances.}
    \label{fig:stances_all}
  \end{figure}

  Because most techniques are performed in walking, sitting and L stances, the
  graphs in this section have been split into two groups. One group shows the
  majority of techniques (84 \%), while the other visualizes techniques
  performed in the remaining stances (16 \%).

  When looking at all techniques by walking stances, sitting stances and L
  stances (Figure \ref{fig:stances_all}), they roughly follow the same pattern
  on both sides. There are, however, two minor exceptions. Firstly, there are
  more strikes in L stances compared to walking stances on the left side.
  Secondly, there are more punches than blocks to the right side.

  % All techniques by stances except walking, sitting and L stances
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/stances_not_wsl}
    \caption{All techniques by stances except walking, sitting and L stances.}
    \label{fig:stances_not_wsl}
  \end{figure}

  When we look at all techniques excluding the frequently used walking,
  sitting and L stances (Figure \ref{fig:stances_not_wsl}), we find that there
  is an even distribution of techniques except for the closed stance, the
  fixed stance and the vertical stance, which have more techniques to the
  right side (Figure \ref{fig:stances_left_not_wsl}) than to the left (Figure
  \ref{fig:stances_right_not_wsl}).

  % Left techniques by stances except walking, sitting and L
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/stances_left_not_wsl}
    \caption{Left techniques by stances except walking, sitting and L stances.}
    \label{fig:stances_left_not_wsl}
  \end{figure}

  % Right techniques by stances except walking, sitting and L
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/stances_right_not_wsl}
    \caption{Right techniques by stances except walking, sitting and L
    stances.}
    \label{fig:stances_right_not_wsl}
  \end{figure}

  There are some additional stances which needs special mentioning. The closed
  stance is the only stance used for blocking, punching, striking and
  thrusting. The parallel stance is only used for punching, whereas the
  vertical stance is only used for striking. Only blocks are performed in the
  diagonal stance and the bending ready stance A. Finally, there are no
  techniques on the left side performed in the vertical stance.

  The total number of techniques for both sides is 37 blocks and 34 attacks.
  Of all techniques on the left side, 59.5 \% are blocks, 40.46 \% are
  attacks. This means that there are 19.05 \% more blocks than attacks
  performed on that side. The right side follows the same pattern as the left,
  with more blocks than attacks. 57.51 \% of techniques are blocks and 42.6 \%
  are attacks, meaning that there are 14.91 \% more blocks than attacks on the
  right side.


\SubSection{Techniques by Motion Type}

  % all techniques by motion type
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/motion_all}
    \caption{All techniques by all motion types.}
    \label{fig:motion_all}
  \end{figure}

  There are 14 different motion types registered in our data set. The larger
  part of the techniques (76 \%) are performed in normal motion (Figure
  \ref{fig:motion_all}), followed by continuous motion (6 \%) and fast motion
  (4 \%).

  % all techniques by motion type except normal motion
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/motion_all_not_n}
    \caption{All techniques by motion type except normal motion.}
    \label{fig:motion_all_not_n}
  \end{figure}

  Excluding normal motion, it is interesting to note the high presence of
  blocks in continuous motion, which alone amounts to 34 \% of blocks
  performed (Figure \ref{fig:motion_all_not_n}). Continuing with Figure
  \ref{fig:motion_all_not_n}, it shows that there is a high occurence of
  punches performed in fast motion compared to other motion types.

  % left techniques by motion type except normal motion
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/motion_left_not_n}
    \caption{Left techniques by motion type except normal motion.}
    \label{fig:motion_left_not_n}
  \end{figure}

  % right techniques by motion type except normal motion
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/motion_right_not_n}
    \caption{Right techniques by motion type except normal motion.}
    \label{fig:motion_right_not_n}
  \end{figure}

  When examining the number of different motion types to either side, we find
  that there are more motion types on the right side, than on the left. The
  right side has flying motion and consecutive motion, in addition to motion
  types found on the left side. Also, there are more flying, slow, sliding and
  consecutive motions on the right side. However, there are more fast,
  stamping, continuous and connecting motions on the left side. Comparing the
  number of motion types on both sides reveals that there are equal amounts of
  slow, jumping, dodging, double stepping and shifting motions, although with
  different groups of techniques (Figures \ref{fig:motion_left_not_n},
  \ref{fig:motion_right_not_n}).



\SubSection{Techniques by Patterns}

  With a few exceptions, all techniques by all patterns for both sides, follow
  the same trend. There are more blocks than punches, more punches than
  strikes, and more strikes than thrusts (Figure \ref{fig:patterns_all}).
  This trend is also true when grouping the patterns by black belt patterns
  and color belt patterns (Figures \ref{fig:patterns_black_all},
  \ref{fig:patterns_color_all}).

  % all techniques by patterns
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/patterns_all}
    \caption{All techniques by patterns.}
    \label{fig:patterns_all}
  \end{figure}

  % all techniques by black belt patterns
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/patterns_black_all}
    \caption{All techniques by black belt patterns.}
    \label{fig:patterns_black_all}
  \end{figure}

  % all techniques by color belt patterns
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/patterns_color_all}
    \caption{All techniques by color belt patterns.}
    \label{fig:patterns_color_all}
  \end{figure}

  The exceptions for all techniques on both sides are: Chon-Ji (having more
  punches than blocks ), Choong-Moo, Choong-Jang and Juche (with more strikes
  than punches) and Po-Eun (where there are more thrusts than strikes).

  % left techniques by patterns
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/patterns_left}
    \caption{Left techniques by patterns.}
    \label{fig:patterns_left}
  \end{figure}

  % right techniques by patterns
  \begin{figure}
    \includegraphics[scale=0.65]{data/gnuplot/eps/patterns_right}
    \caption{Right techniques by patterns.}
    \label{fig:patterns_right}
  \end{figure}

  There are, however, patterns which do not follow the exceptions described
  above (Figures \ref{fig:patterns_left}, \ref{fig:patterns_right}). There
  are, for instance, more punches than blocks in patterns Chon-Ji and Dan-Gun
  on the right side than there are on the left side. And, when we compare the
  number of punches to strikes, both Toi-Gae and Choong-Moo have an equal
  amount of punches and strikes on the left side. Lastly, there is Choong-Jang
  with more strikes than punches on the right side.


\Section{Conclusions}

  There are more hand techniques performed on the right side than on the left
  side. Thus, there is a bias towards the right side.


% Unnumbered section (note the '*')
\section*{Acknowledgments}

  I would like to thank Odd-Magne Hansen (III. Dan), Frøydis Morken and Eirik
  Schwenke for helping me with reviewing and proof-reading the article.


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