Wordle Results Distribution Prediction Model and Difficulty Classification Model Using Word Linguistic Properties

Wordle is a word guessing game offered daily by the New York Times. The aim of our study is to use selected word linguistic properties to predict the percentages of successfully guessing a word in one to six tries or failing and classify words by difficulty. A prediction model was established based on stepwise linear regression and normal distribution probability density function (PDF). The percentages of a word were predicted using stepwise linear regression. The Jarque Bera test using MATLAB function indicated that 97.5% of word attempt distributions followed a corresponding normal distribution. Thus, these seven percentages were used as independent variables to predict the mean and variance of the corresponding normal distribution. The PDF was then obtained to correct percentages. Additionally, a word classification model was also established based on K-Means and support vector machines (SVM) to classify words by difficulty. The elbow method was used to divide words into two categories. The classification model was trained based on SVM. The prediction results showed that the sum of predicted percentages for each word fell between 99 and 101, which was superior to performing a single stepwise linear regression. The average root mean square error per word was 3.22. The classification model results showed that, based on 5-fold cross validation, area under curve, accuracy, recall and precision were 0.83, 77.1%, 75.16% and 73.72%, respectively, indicating the reliability of our method.