Word Analysis

Wordle Start Word Analysis

Purpose

What is the most common letter frequencies of 5-letter words in each letter position. These make good candidates for opening or second words with highest probability of getting green or yellow letters

TL;DR: Try these words to start:

SANES, SALES, SORES, CARES, BARES, TARES, SATES, SERES, PARES, MARES

Note: As far as wordle strategy goes, you might not want to pick words from this list that have duplicate letters!

Method

First load a dictionary of English words and subset them to only 5-letter words. Here I’m using the Grady Ward Augmented English dictionary.

# load a dictionary
data(GradyAugmented)

# filter to only 5 letter words and convert to uppercase
wordles <- toupper(GradyAugmented[str_length(GradyAugmented)==5])

flextable(data.frame(Words = sample(wordles,10))) %>% 
  set_caption(caption = "Example Wordles") %>% 
  set_table_properties(layout = "autofit", width = 0.2)

Example Wordles

Words
SLUGS
AFOUL
SPANK
SONSY
ZANZA
SPIKY
HEXER
FLINN
YAUDS
CRUET

For each of the five letter positions, we can calculate how often each letter appears in that position. For example, how often does the letter ‘S’ appear as the first letter of a 5-letter word, how often does ‘T’ appear as the second letter etc.

The plot below shows the top 10 letters in each word position showing that S is the most common start (and last!) letter in 5-letter words.

# function to tabulate letter frequency from a vector of letters
letter_freq <- function(x){
  tbl <- table(x)
  res <- cbind(tbl,round(prop.table(tbl)*100,2))
  colnames(res) <- c('Count','Percentage')
  res <- res %>% 
    as.data.frame() %>% 
    rownames_to_column("Letter") %>% 
    arrange(desc(Percentage))
}

# wrapper function for letter table by letter position
letter_table <- function(n){letter_freq(str_sub(wordles,n,n))}

# collect the letter freq tables for all 5 letter positions
wordle_freq <- map_dfr(seq(1:5), letter_table, .id = "position" )

wordle_freq %>% 
  group_by(position) %>% 
  top_n(10, Percentage) %>% 
  ungroup() %>% 
  mutate(position = as.factor(position),
         Letter = reorder_within(Letter,Percentage, position)) %>% 
  
  ggplot(aes(Letter, Percentage, fill = position)) +
  geom_col(show.legend = FALSE) +
  facet_wrap(~position, scales = 'free_y') +
  coord_flip() +
  scale_x_reordered() +
  theme_bw() +
  labs(y = "Percent Letter Frequency",
       title = "Letter Frequency of 5-letter words by Letter Positions 1-5",
       subtitle = "Dictionary: Grady Wards Augmented Dictionary")

Applying the letter frequencies by position to each 5-letter wordle in our dictionary, we can then calculate a combined score by averaging each letter frequency in the word.

# function to score word by calculating mean percentage of letter position based on freq table
score_word <- function(word){
  chars <- data.frame(Letter = unlist(strsplit(word, split = "")), stringsAsFactors = FALSE) %>% 
    mutate(position = as.character(row_number())) %>% 
    inner_join(wordle_freq, by = c("position", "Letter"))
  
 # score <- mean(chars$Percentage)
  df <- data.frame(Word = word, Score = mean(chars$Percentage))
  return(df)
}

# get word scores
word_scores <- map_dfr(wordles, score_word)
saveRDS(word_scores, "word_scores.rds")

flextable(df.wordscores) %>% 
  set_caption(caption = "Top 10 Words by average letter position frequency score") %>% 
  set_table_properties(layout = "autofit", width = 0.5)

Top 10 Words by average letter position frequency score

Word	Score
SANES	16.618
SALES	16.492
SORES	16.310
CARES	16.260
BARES	16.090
TARES	16.032
SATES	15.978
SERES	15.960
PARES	15.948
MARES	15.912