Letter Frequency and Wordle

2022-02-09 14:27

Many of us like to start the daily Wordle by guessing a word containing the most frequent letters, to maximize the chances of learning some of the letters in the day’s target word.

The traditional list of letters in frequency order as they appear in English words goes something like this:

  [ e t a o i n s h r d l c u m w f g y p b v k j x q z ]

The problem with this frequency ordering is that it was arrived at by counting up the letters in a run of English text. However, English text is loaded with words such as the, of, an, and a, which don’t matter to Wordle; this skews the distribution. So what we want is the frequency count in words that might actually show up in the game.

We can start by downloading a complete list of Scrabble-legal words (the list I found has n=178,694 words) and extracting from that all 5-letter words (n=8,938). I found the most frequent letters in this corpus and, taking doubled letters into account, came up with the following frequency ordering:

  [ s e a o r i l t n u d c p y m h g b k f w v z x j q ]

We can actually get more exact than that. In various dark corners of the web, people have extracted from Wordle’s source code the actual list of words used by the game. This list has n=2,316. (Josh Wardle selected only reasonably common 5-letter words.) Using the process above, I found the following frequency ordering in Wordle’s target data:

  [ e a r o l t s i n u c y d h p g m b f k w v x z q j ]

Now let’s find what 5-letter words in the Scrabble-legal list are made up of 5 unique letters from the initial 7 (earolts) in the above distribution. Here they are (n=61):

  alert  lares  orals  roast  sorel  taels  toeas
  aloes  laser  orate  roles  sorta  taler  tolar
  alter  later  orles  roset  stale  tales  tolas
  altos  lears  rales  rotas  stare  tares  toles
  arles  least  ratel  rotes  steal  taros  toras
  arose  lores  rates  rotls  stela  teals  tores
  artel  loser  ratos  setal  stoae  tears  torse
  aster  lotas  reals  slate  stole  telos
  earls  oater  resat  solar  store  tesla

Any of these words should be a productive first guess in your daily Wordle. Especially if it’s a common word.

Should you wish to spend a second turn pinning down more letters, you might try these pairs of words that use all of the letters in the top 10 (h/t to Gary Stock for finding them):

alien – tours altos – urine arose – until
nails – route noise – ultra snail – outer
train – louse