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\hypersetup{
  pdftitle={Metrics for Exploration Games},
  pdfauthor={Ross Mawhorter; Peter Mawhorter},
  pdfkeywords={exploration; metrics; games},
  hidelinks,
  pdfcreator={LaTeX via pandoc}}
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\copyrightyear{2026}
\copyrightclause{Copyright for this paper by its authors.
  Use permitted under Creative Commons License Attribution 4.0
  International (CC BY 4.0).}

\conference{EXAG 2026:
  Workshop on Experimental Artificial Intelligence in Games
  at the 2026
  Artificial Intelligence in Interactive Digital Entertainment Conference,
  November 9-13, 2026,
  Federal University of Minas Gerais
  Belo Horizonte, MG, Brazil}

\author[1]{Ross Mawhorter}[%
orcid=0000-0000-0000-0000,
email=TODO,
url=TODO,
]
\cormark[1]
\fnmark[1]
\address[1]{TODO}

\author[2]{Peter Mawhorter}[%
orcid=0000-0000-0000-0000,
email=pmawhort@wellesley.edu,
url=https://cs.wellesley.edu/~pmwh,
]
\cormark[1]
\fnmark[1]
\address[2]{Wellesley College, 106 Central Street, Wellesley, MA, USA}

%% Footnotes
\cortext[1]{Corresponding author.}
\fntext[1]{These authors contributed equally.}
\usepackage[]{natbib}
\bibliographystyle{elsarticle-num-names}

\title{Metrics for Exploration Games}
\date{2026-8-14}

\begin{document}
\begin{abstract}
Procedural generation and analysis techniques like quality-diversity
search, genetic algorithms, and expressive range analysis use metrics to
define how they operate, and their results are limited by what the
metrics used can capture. Existing metrics for measuring the quality and
complexity of exploration-based games are very rudimentary. We propose
new representations for exploration-based game spaces that are necessary
to support richer metrics for evaluating their gameplay properties, and
give examples of metrics that can be derived from these representations.
We show that these new metrics are potentially useful by using them to
explain observable variation between the design of several
exploration-based games.
\end{abstract}
% CEUART style
\begin{keywords}
  exploration\sep metrics\sep games
\end{keywords}
\maketitle



\section{Introduction}\label{introduction}

\section{Examples}\label{examples}

\subsection{Example Metric: Cyclic
Fraction}\label{example-metric-cyclic-fraction}

One simple metric measurable from the decision graph alone is ``cyclic
fraction'' -- The fraction of all decisions which are part of some cycle
(as opposed to being part of a branching structure or dead end that does
not contain any cycles).

\section{Fragments}\label{fragments}

``\,``\,'' Unfortunately, there is no established set of metrics for
dungeon levels like there is for platformer levels {[}14{]}. Therefore,
we follow the example set by Smith et al.~{[}30{]} and adapted the
metrics put forth by Lavender {[}15{]}, which were in turn inspired by
Smith and Whitehead {[}29{]} ``\,``\,''

{[}14{]} is: Britton Horn, Steve Dahlskog, Noor Shaker, Gillian Smith,
and Julian Togelius. 2014. A comparative evaluation of procedural level
generators in the mario ai framework. In Foundations of Digital Games
2014, Ft. Lauderdale, Florida, USA (2014). Society for the Advancement
of the Science of Digital Games, 1--8. See refs.bib or 15, 29, and 30.

Individual metrics by nature capture only part of the variation that is
desirable and/or of interest, so groups of metrics are used together to
try to get a fuller picture of what's being studied/generated. For
complex artefacts like games, metrics can be especially difficult to
deal with, because reducing a complex interactive artefact to a series
of numbers can be done in so many different ways, and because each of
those ways offers insight into only a thin slice of the game being
measured.

  \bibliography{refs.bib}

\end{document}
