From Wordle to Insights: Using Tailored Clustering and CART to Forecast Difficulty Levels

Wordle, a popular daily puzzle in the New York Times, has garnered significant attention with its unique challenge. Players must decipher a five-letter word in six attempts or less, receiving feedback after each guess. Rooted in information theory and pragmatics, Wordle offers a valuable platform for exploration. Our research proposes an innovative approach consisting of two components. The first utilizes K-means clustering with tailored parameters: the forward difficulty evaluation index (Dforward) and the reverse difficulty evaluation index (Dreverse). Dforward is calculated by weighting factors like Nrepeat (normalized count of repeated letters), word frequency (F), and the number of vowels (Nvowel) in the word. Dreverse is obtained by normalizing the predicted number of successful guesses. The second component applies a CART decision tree model with difficulty level labels, predicting future solution complexities. By analyzing linguistic features in five-letter words, our study constructs a model that accurately determines word difficulty using statistical knowledge and machine learning techniques. Additionally, this model facilitates related linguistic analyses.