# Personalized Game Difficulty Prediction Using Factorization Machines

arXiv: https://arxiv.org/abs/2209.13495 · HTML: https://mlsanity.com/paper/2209.13495/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 6 Sep 2022.

## Builds on (most cited first, 11 of 11)

- [Finding Game Levels with the Right Difficulty in a Few Trials through Intelligent Trial-and-Error](https://mlsanity.com/paper/2005.07677/) (2020)
- [Predicting Game Difficulty and Churn Without Players](https://mlsanity.com/paper/2008.12937/) (2020)
- [Next-Term Student Performance Prediction: A Recommender Systems Approach](https://mlsanity.com/paper/1604.01840/) (2016)
- [Interaction-aware Factorization Machines for Recommender Systems](https://mlsanity.com/paper/1902.09757/) (2019)
- [Modeling Individual Differences in Game Behavior using HMM](https://mlsanity.com/paper/1804.00245/) (2018)
- [Assessing Human Error Against a Benchmark of Perfection](https://mlsanity.com/paper/1606.04956/) (2016)
- [Dynamic Difficulty Adjustment via Fast User Adaptation](https://mlsanity.com/paper/2006.15545/) (2020)
- [DL-DDA -- Deep Learning based Dynamic Difficulty Adjustment with UX and Gameplay constraints](https://mlsanity.com/paper/2106.03075/) (2021)
- [Rapid Prediction of Player Retention in Free-to-Play Mobile Games](https://mlsanity.com/paper/1607.03202/) (2016)
- [Fast Game Content Adaptation Through Bayesian-based Player Modelling](https://mlsanity.com/paper/2105.08484/) (2021)
- [Statistical Modelling of Level Difficulty in Puzzle Games](https://mlsanity.com/paper/2107.03305/) (2021)

## Built on by (most cited first, 2 of 2)

- [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)
- [Robo-Saber: Generating and Simulating Virtual Reality Players](https://mlsanity.com/paper/2602.18319/) (2026)

## Abstract (arXiv)

The accurate and personalized estimation of task difficulty provides many opportunities for optimizing user experience. However, user diversity makes such difficulty estimation hard, in that empirical measurements from some user sample do not necessarily generalize to others. In this paper, we contribute a new approach for personalized difficulty estimation of game levels, borrowing methods from content recommendation. Using factorization machines (FM) on a large dataset from a commercial puzzle game, we are able to predict difficulty as the number of attempts a player requires to pass future game levels, based on observed attempt counts from earlier levels and levels played by others. In addition to performance and scalability, FMs offer the benefit that the learned latent variable model can be used to study the characteristics of both players and game levels that contribute to difficulty. We compare the approach to a simple non-personalized baseline and a personalized prediction using Random Forests. Our results suggest that FMs are a promising tool enabling game designers to both optimize player experience and learn more about their players and the game.