Game Wordle report interpretation and analysis

As a word guessing puzzle game, Wordle is popular among players because of its fun. The algorithm design and thinking logic behind its unique gameplay are the topics of this paper.

Based on the official game report results from January 7,2022 to December 31,2022, we established a differential autoregressive moving average model ( ARIMA ) to predict the number of players on March 1,2023, and concluded that any attribute of the word will affect the percentage of players in the hard mode of the game. In the process of preprocessing the report data, we found and corrected the data of three missing or redundant words and letters and two abnormal numbers of game players. After the first-order difference processing of the data, the P value obtained by the stability test is 0.001, indicating that the time series data is stable and meets the nature of constructing an autoregressive model. For the construction of ARIMA model, the determination of its fitting parameters is undoubtedly particularly critical, which will affect the subsequent prediction accuracy. Therefore, we draw the ACF diagram and PACF diagram, and compare the AIC and BIC values corresponding to ARIMA models of different orders. Based on the consideration of retaining as much data information as possible and avoiding too many lag items that will increase the prediction error, we select the model with a smaller average value of AIC and BIC, and determine the correlation coefficient is third order, thus ensuring a better fitting effect.For Problem Ⅰ.

In order to more significantly describe the uncertainty of the relevant percentage of the future date ( 1,2,3,4,5,6, X ) and the influence of uncertain factors on the prediction results of the model, we further study the random disturbance term of the ARIMA model and establish a conditional heteroscedastic autoregressive model ( ARCH ). This model can produce volatility aggregation in terms of time series data fluctuations and make the disturbance term have the characteristics of thick tail distribution. In the process of Ljung-Box Q test to determine whether the data interference items are white noise, the P value calculated by us is 0, indicating that the interference items are independent of each other and there is no obvious correlation, thus ensuring that the subsequent prediction is of reference value. After interpreting the results of the report, we introduce the word influence factors such as the common degree of words, the number of letters repeated in words, the number of vowel letters, and the number of consonant letters. And according to the existing date to query and judge, we introduce the date influence factors such as whether the weekend, whether the holiday, so as to be able to make a reasonable prediction of the relevant percentage of words in the nth guess, and further analyze the influence of uncertain factors on the model prediction results. Taking the prediction of the word EERIE as an example, we get the ( 1,2,3,4,5,6, X ) correlation percentage is 0.46 %, 5.86 %, 22.75 %, 32.93 %, 23.62 %, 11.53 %, 2.81 %, which is more in line with the reality.

When classifying words based on the difficulty level, we tried K-means clustering, hierarchical clustering and other algorithms, and found that the classified categories were not uniform, and some categories even had only one sample data. In order to make the clustering results more uniform, we adjusted the algorithm, calculated the weight of each influencing factor by entropy weight method, substituted it into the data to calculate the comprehensive score and sorted it. Finally, based on the comprehensive score, the difficulty level of the word was divided equally, thus completing the uniform division of the word difficulty level. Taking the word EERI as an example, we obtain the weight of each influence factor by the entropy weight method. The specific values of the parameters of EERIE are multiplied by the corresponding weights and accumulated, and then the comprehensive score is obtained. Finally, the grade is judged. Among the four types of difficulty levels ( difficult, difficult, easy, easy ), the grade of EERIE is difficult.

Keywords : ARIMA model,  ARCH model,  Entropy weight method