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Predicting and Classifying Solution Words in the Popular Wordle Puzzle Game


Core Concepts
The authors developed an ARIMA-based prediction model for the number of reported Wordle results, a regression model based on XGBoost for predicting the distribution of reported results, and a classification model using K-Means clustering and decision trees to categorize solution words by difficulty.
Abstract
The authors first preprocessed the Wordle data by removing and replacing any abnormal data. They then established an ARIMA-based prediction model to forecast the number of reported results on March 1, 2023, with a prediction interval of [20,337, 21,673]. Next, the authors selected three word attributes - frequency of word usage (FREQ), information entropy of the word (WIE), and number of repeated letters (NRE) - and performed correlation analysis. They found that FREQ was positively correlated with the number of tries, while WIE and NRE were negatively correlated. The authors then built a regression model using XGBoost to predict the distribution of reported results for each number of tries. They achieved an overall accuracy of 82.1% in predicting the percentage distribution, and were able to accurately predict the distribution for the word "EERIE". Finally, the authors used K-Means clustering to classify the solution words into three difficulty categories - easy, medium, and difficult. They then built a decision tree model to explore the relationship between the three word attributes and the difficulty classification, achieving an accuracy of 77.6%. The authors also found that for 83.9% of the words in the dataset, more than 90% of players needed 3 or more guesses to solve the word, indicating the overall difficulty of the Wordle game.
Stats
The frequency of word usage (FREQ) for the word "EERIE" is 0.000002437871. The information entropy (WIE) of the word "EERIE" is 1.4797732853992995. The number of repeated letters (NRE) in the word "EERIE" is 3.
Quotes
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Key Insights Distilled From

by Haidong Xin,... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2403.19433.pdf
Puzzle game

Deeper Inquiries

How could the Wordle game be further optimized to provide a more balanced and engaging experience for players of all skill levels?

To optimize the Wordle game for a more balanced and engaging experience, several strategies can be implemented: Difficulty Levels: Introduce different difficulty levels to cater to players of varying skill levels. This could include easy, medium, and hard modes, allowing players to choose the level that suits their abilities. Hint System: Implement a hint system that provides subtle clues to players who may be struggling with a particular word. This can help prevent frustration and keep players engaged. Word Variety: Expand the word database to include a wider range of words, from common to more obscure ones. This can add diversity to the gameplay and challenge players with different vocabulary levels. Community Features: Incorporate social features that allow players to interact, share tips, and compete with friends. This can enhance the sense of community and engagement among players. Feedback Mechanism: Provide constructive feedback after each guess to guide players in their word selection process. This can help players learn and improve their skills over time.

What other word attributes or external factors could be considered to improve the accuracy of the predictive and classification models?

In addition to the word attributes already considered in the predictive and classification models, the following factors could be incorporated to enhance accuracy: Word Length: The length of the word could be a significant factor in predicting difficulty. Longer words may generally be more challenging to guess compared to shorter ones. Word Origin: Considering the etymology or origin of words could provide insights into their complexity and difficulty level. Words with complex origins may be classified as more difficult. Semantic Similarity: Analyzing the semantic relationships between words in the dataset could help in grouping words with similar meanings or structures, leading to more accurate classifications. Player Feedback: Incorporating player feedback and behavior data, such as the time taken to guess a word or the number of attempts made, can provide valuable insights into word difficulty and player engagement. Cultural Relevance: Taking into account the cultural relevance of words and their familiarity to players from different backgrounds can improve the relevance and accuracy of the predictive models.

How might the insights from this Wordle analysis be applied to the design and development of other types of word-based puzzle games?

The insights from the Wordle analysis can be applied to the design and development of other word-based puzzle games in the following ways: Personalized Gameplay: Implementing predictive models to adjust the difficulty level based on player performance can create a personalized gaming experience tailored to individual skills. Dynamic Challenges: Using classification models to categorize words into difficulty levels can help create a dynamic challenge progression in other word games, keeping players engaged and motivated. Enhanced Player Experience: Leveraging player data and word attributes to provide targeted hints, feedback, and challenges can enhance the overall player experience and increase player retention. Innovative Game Modes: Introducing new game modes based on predictive insights, such as time-limited challenges or collaborative word-solving modes, can add variety and excitement to word-based puzzle games. Continuous Improvement: Regularly analyzing player data and feedback to refine predictive and classification models can lead to continuous improvement in game design and player satisfaction in other word games.
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