# Statistical Modelling of Level Difficulty in Puzzle Games

arXiv: https://arxiv.org/abs/2107.03305 · HTML: https://mlsanity.com/paper/2107.03305/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 5 Jul 2021.

## Builds on (most cited first, 3 of 3)

- [Finding Game Levels with the Right Difficulty in a Few Trials through Intelligent Trial-and-Error](https://mlsanity.com/paper/2005.07677/) (2020)
- [Strategies for Using Proximal Policy Optimization in Mobile Puzzle Games](https://mlsanity.com/paper/2007.01542/) (2020)
- [Extended Poisson-Tweedie: properties and regression models for count data](https://mlsanity.com/paper/1608.06888/) (2016)

## Built on by (most cited first, 3 of 3)

- [Reinforcement Learning for High-Level Strategic Control in Tower Defense Games](https://mlsanity.com/paper/2406.07980/) (2024)
- [Personalized Game Difficulty Prediction Using Factorization Machines](https://mlsanity.com/paper/2209.13495/) (2022)
- [Difficulty Modelling in Mobile Puzzle Games: An Empirical Study on Different Methods to Combine Player Analytics and Simulated Data](https://mlsanity.com/paper/2401.17436/) (2024)

## Abstract (arXiv)

Successful and accurate modelling of level difficulty is a fundamental component of the operationalisation of player experience as difficulty is one of the most important and commonly used signals for content design and adaptation. In games that feature intermediate milestones, such as completable areas or levels, difficulty is often defined by the probability of completion or completion rate; however, this operationalisation is limited in that it does not describe the behaviour of the player within the area. In this research work, we formalise a model of level difficulty for puzzle games that goes beyond the classical probability of success. We accomplish this by describing the distribution of actions performed within a game level using a parametric statistical model thus creating a richer descriptor of difficulty. The model is fitted and evaluated on a dataset collected from the game Lily's Garden by Tactile Games, and the results of the evaluation show that the it is able to describe and explain difficulty in a vast majority of the levels.