---
title: 'Metrics for Exploration Games'
author:
- Ross Mawhorter
- Peter Mawhorter
institute:
- University of Alberta
- Wellesley College
date: '2026-8-14'
keywords: [exploration, metrics, games]
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.
bibliography: refs.bib
documentclass: ceurart
classoption: []
biblio-style: elsarticle-num-names
anonymous: true
link-citations: true
...

# Introduction

# Examples

## 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.
In order to help this metric correspond to how players interact with the
decision graph, we consider only cycles of three or more decisions, and for
simplicity, we ignore transition requirements. Any decision with a
self-transition (i.e., 'action') forms a one-node cycle, and any two nodes
that have a pair of reciprocal transitions between them form a two-node
cycle, so focusing only on cycles of three or more decisions roughly
corresponds to "regions where the player could go around in a circle and
return to a place they'd started at," without including all decisions that
have actions or all hallways where the player can move back and forth
between pairs of nodes.

This is a large-scale structural metric that captures a very abstract
property of the overall decision graph shape, but it does relate to the
player experience in the sense that the amount of back-tracking the
player must do can be reduced by the inclusion of cycles in the design
(even though including cycles does not *necessarily* reduce
back-tracking).

Interestingly, when examining full-game maps, most have around 80% cyclic
nodes, indicating that most of the map is "on the way" to somewhere that
can connect in a cycle back to where you came from, while a small but
significant portion represents branching structures and dead ends that
attach to the cycles but which would require backtracking to fully
explore. One might imagine a relatively wide distribution of this
fraction between different games due to designer preferences, but in
fact, across a wide range of Metroidvania games, we see an incredible
consistency: TODO

# 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.