# Game Difficulty Prediction Based on Facial Cues and Game Performance
## 2 Related Work  
### Difficulty Prediction  
Some studies utilized heuristic functions to measure the difficulty level faced by the player. These methods typically use success rates, life points, and completion times to calculate game scores and assess difficulty [15]. For example, [PERSON] et al. [10] presented a method for automatically evaluating the difficulty of puzzle games that combines and weights features from several aspects, including level size, number of balls, and minimum number of moves, to generate the difficulty function. The weights of each feature are determined by optimizing the function on a set of known difficulties. [PERSON] et al. [16] used the average solution time of an evolutionary algorithm and the number of failures to grade the Sokoban boards' difficulty. [PERSON] et al. [12] introduced factorization machines (Fms) to predict game difficulty based on the observed attempt times from early levels and levels others played. Fms have been widely used in recommendation systems [17; 18]. It is a factorization model that can be used as a predictor for tasks such as classification and regression. The experimental results in the study showed the superiority of Fms over random forest (RF). Although, to some extent, the mentioned methods could predict the game difficulty, none of them take the objective user data generated during interactions into account, which limits the accuracy of prediction.  
Several studies have begun to utilize user data to measure game difficulty. [PERSON] et al. [19] used the RF classifier to categorize identified user facial expressions to predict the challenge difficulty of each chunk and adjusted the difficulty of each chunk accordingly. Compared to heuristic methods, this approach is smoother and more efficient (requiring fewer iterations). However, using a single facial expression may not accurately reflect the user's genuine sentiments about difficulty, resulting in limited enhancement of the game experience. In addition to facial expressions, physiological signals are alternative methods chosen by many researchers to evaluate game difficulty since they can objectively respond to the changes in users' physiological conditions. [PERSON] et al. [13] measured game difficulty using electroencephalogram (EEG) signals. After collecting and processing EEG signals, the authors trained a linear regression model to predict the game difficulty. Although the correlations of Pearson and Spearman between the predicted and actual difficulties were high, RMSE was relatively low. [PERSON] et al. [14] collected functional near-infrared spectroscopy (fNIRS) data from users and used sequence classification methods [20] to predict game difficulty. Unlike EEG signals, fNIRS is non-invasive, portable, and unaffected by user movements. However, it did not perform well (accuracy: 61.1%) in classifying game difficulty. Furthermore, [PERSON] et al. [21] achieved higher accuracy in game difficulty prediction by combining physiological signals, game performance, and personal characteristics.  
Some studies predict the difficulty of other tasks. For example, [PERSON] et al. [22] used eye-tracking features to estimate users' perceived difficulty when reading educational comics. Specifically, the authors first used a head-mounted device to collect multiple eye-movement information, including fixations, blinks, heat maps, etc. Then, a support vector machine (SVM) classification model was trained with these features and achieved F1 scores of 0.721 and 0.742 in user-dependent and user-independent models, respectively. The effectiveness of eye-tracking features has also been validated in text difficulty prediction [23; 24].