Wordle Statistics Update

Here are my latest Wordle statistics as of August 6th 2025:

It turns out that I've lost 25 games out of the total of 908 games that I've played. This corresponds to a win rate of 97.25% which Wordle has rounded down to the 97% shown above. My average is \( \textbf{3.94} \) guesses which is a slight increase from the \( \textbf{3.92} \) guesses recorded on the 7th October 2024. Is this a sign of mental decline or is Wordle getting slightly more difficult?

What has changed significantly however, is my win rate. On the previous date it was 98.25%. I had lost only 11 games out of the 629 games that I'd played. Since then I've lost another 14 games which has seriously impacted my win rate. I put the following question to Gemini:

Are there any statistics to support the fact that Wordle, the online word game, is getting more difficult over the past year or more. I'm interested because my win rate in the game has dropped from 98.25% to 97.25% over the past year. Am I getting worse or is Wordle getting harder. I'd be curious to know.

This is an excellent question that gets to the heart of a common Wordle player's frustration. The short answer is: yes, there's evidence to suggest that the game is, in fact, getting harder. Your experience is not just a personal feeling; it's a trend that has been observed and analyzed.

While The New York Times, which acquired Wordle, has stated that they haven't intentionally made the game more difficult, and even removed some more obscure words, the inherent structure of the game's pre-determined word list is the likely culprit.

Here's a breakdown of the statistical and logical reasons why Wordle is getting harder:

1. The Finite and Ordered Word List

The game's original creator, Josh Wardle, established a list of about 2,300 possible solution words. These were likely curated with common words appearing earlier in the list and more obscure or challenging words appearing later. As the game progresses through this list, the words naturally become less common, contain more unusual letter combinations, or have tricky repeating letters.

2. "Confusability" of Words

A major factor in a Wordle puzzle's difficulty is its "confusability"—that is, how many other valid five-letter words share a similar letter pattern. As the game's word list gets further in, there are more words that fit this profile. For example, a word ending in "-OUND" could be "FOUND," "MOUND," "ROUND," "POUND," etc. As you get hints, you might narrow it down to the correct letters but be left with several possibilities for your last few guesses, making a loss more likely. Words with repeated letters, like "MOMMY" or "CORER," also fall into this category and have a higher failure rate.

3. Data from WordleBot and Player Averages

The New York Times' own tool, WordleBot, analyzes player data for each puzzle, including the average number of guesses and the solve rate. This data has shown that certain words are consistently more difficult for players. For instance, an analysis of the "10 most difficult Wordles of 2024" showed words like "HUNCH," "FIBER," and "PIPER" had high average guess counts and low solve rates. These difficult words, with their repeated letters and multiple possible solutions, are appearing more frequently as the game's long-term list is exhausted. One report even noted that a recent month was "officially Wordle's toughest month ever," with an average score of 4.22, significantly higher than the game's overall average of around 3.97.

What This Means for You

Your win rate dropping from 98.25% to 97.25% is a very small, statistically normal change over a year, but it aligns with the overall trend of the game getting slightly more difficult. It's highly unlikely that you are "getting worse" at the game; rather, the game's inherent difficulty is increasing. The words are becoming less common and are more likely to have the characteristics that make a puzzle a "streak-breaker." 

My Wordle Statistics

Figure 1 shows a screenshot of my Wordle statistics as of the 6th October 2024, a day on which I turned 75.5 years old.

Figure 1

Even though I've played 629 games, I lost 11 of them because I didn't guess the correct word in six tries or under. In order to accurately assess my average score, these losses need to be taken into account. To do that, I think the best approach is to add the number 7 to the guess distribution and include the 11 losses there. This then gives the following (number, frequency) distribution:$$(\textbf{1},0), (\textbf{2},38),(\textbf{3},196),(\textbf{4},234),(\textbf{5},113),(\textbf{6},37),(\textbf{7},11)$$The arithmetic mean can then be calculated using the formula:$$ \begin{align} \text{mean} &= \frac{\text{total of number} \times \text{frequency}}{\text{frequency total}}\\ &= \frac{2464}{629}\\ &\approx 3.92 \end{align} $$So there we have it. My average is slightly under 4 tries in successfully guessing the correct word. Google's Gemini confirms that the introduction of the 7 is the best way to calculate the average. How do I compare with the rest of the world? Well, there is an interesting site that lists statistics regarding Wordle results worldwide. Figure 2 shows a world map. 

Figure 2: data as of 22nd August 2023

Canberra, Australia, is the global city with the best Wordle average: 3.58 guesses. Sweden is the world’s best country at Wordle, with an average of 3.72. The source used to obtain this data was tweets on Twitter or X as it's now called. Clearly this introduces a huge bias because only people who are keen Wordle players will bother tweeting about their Wordle expertise and there will be a decided bias toward posting impressive success rather than bare wins (six guesses) or losses (failing to identify the word within six guesses). There's also the possibility of straight out cheating.

There's also hard mode and default mode. On every turn in the former you must use all the letters guessed on the previous turn. I haven't set Wordle to hard mode but I always play that way, although occassionally I'll slip up and forget to use a letter that I've already guessed. There's an online site that will generate your average once you input your data. Based on data input to this site, the statistics shown in Figure 3 seem more believable:

Figure 3: source

Once again however, only very dedicated players will be using this site but at least it shows that my average is higher than the national average for Australia. There is a site that lists the results for each day's Wordle and this site is based on actual attempts made that day to the Wordle site. See Figure 4.

Figure 4: source

These results most accurately depict the correct state of affairs I think. I've posted previously about Wordle: Wordle Statistics on 7th of February 2022 and More Wordle Statistics on 8th of February 2022.

More Wordle Statistics

My last post titled Wordle Statistics was long enough so I didn't want to add more newly found information to that and hence I'm making a fresh post. 3Blue1Brown has just created a YouTube video that involves a statistical analysis of Wordle.

There's a lot to digest in this video but my main takeaway after first viewing it was that CRANE was a good starting word! I clearly need to watch it again and again to fully absorb what he's saying. However, for today's Wordle I started with CRANE and the results were almost disastrous as can be seen in Figure 1.

Figure 1

Looking at Figure 1, it can be seen that I had a spectacular start with three letters in the correct positions. There were only two remaining letters to guess. However, I nearly failed because there were just so many possible words that could be made from *RA*E. 

Referring to kaggle, a database of English word frequencies, we can see that TRADE was a good second choice because it has by far the highest frequency. Had I known about word frequencies, my third choice would have been FRAME and I would have solved the puzzle in a mere three attempts.

CRANE: 4,888,961 FIFTH

                                        TRADE: 110,086,585 FIRST

                                        ERASE: 3,086,642 SIXTH

                                        GRACE: 17,642,126 THIRD

BRAKE: 9,321,885 FOURTH

                                        FRAME: 46,079,991 SECOND 

Using Google search with quotes e.g. "trade" yields the following statistics:

CRANE: 166,000,000 SIXTH

                                         TRADE: 1,930,000,000 SECOND

                                         ERASE:  242,000,000 FIFTH

                                         GRACE:  918,000,000 THIRD

 BRAKE:  503,000,000 FOURTH

                                         FRAME:   2,350,000,00 FIRST

Interestingly, using the Google search, FRAME and TRADE swap places with the former being markedly more frequent (in searches at least). CRANE and ERASE also swap positions in fifth and sixth places.

I downloaded the CSV file of word frequencies from kaggle (it's only 5MB) and filtered out words that were not five letters in length. Here are the initial five letter words with the highest frequencies:

about 1,226,734,006

other 978,481,319

which 810,514,085

their         782,849,411

there 701,170,205

first         578,161,543

would 572,644,147

these 541,003,982

click         536,746,424

price         501,651,226

state         453,104,133

email 443,949,646

world 431,934,249

music 414,028,837

after         372,948,094

video 365,410,017

where 360,468,339

books 347,710,184

links         339,926,541

years 337,841,309

As can be seen, ABOUT comes out clearly on top with a frequency of over 1.2 billion! This might not be a bad starting word. Anyway, more food for thought went tackling Wordle.

Wordle Statistics

In my Pedagogical Posturing blog, I recently posted about Wordle but in post I want to focus on the statistics of the letter frequencies. Of primary interest of course is how frequently the various letters of the alphabet occur within the Wordle "universe". In A Mathematician's Guide to Wordle, it's explained that:

Wordle has both a ‘source’ word list and a ‘target’ word list. You can guess anything from the source word list (which is the 5 letter words from CSW19) ... The target word list is a small hand-curated subset of less than 2500 of these words.

CSW stands for Collins Scrabble Words that consists of 279,496 words. The article just quoted from goes on to say that:

It is well known that when you order letters by frequency of appearance in English words, you get ETAOIN SHRDLU. However ... if you take all 5 letter words in CSW19, you get SEAORY LTNUDY.

Figure 1 shows the full sequence of letters and their relative frequencies. The commentary on this chart includes:

• In fact, they're essentially tied, S appearing only three more times than E in the 64,860 letters in the word list. That's a 0.0046 percentage point difference.
  
  
• After those two, the distribution doesn't fall off that much. A is 9.2%, O is 6.8%, R is 6.4%.
  
  
• The top 10 most frequent letters in the list make up 67% of the occurrences. That's all five vowels, plus the Wheel of Fortune consonants, R S T L N.
  
  
• For those of you wondering about that "other" vowel, Y is 12th at 3.2%.
  
  
• The least common 5 letters, Q X J Z V, combine for a mere 2.8% of the occurrences, about the same as the letter H, the 16th ranked letter.
  
  
• The most common letter, S, is overwhelmingly more likely to be in fifth position (59%). Otherwise, it's more likely that it appears first (23%) than in any of the middle positions combined.
  
  
• Vowels occur most commonly in the second position. That is unless you're E, which is more common in the fourth spot (35%) than second (24%). Again, "-ed" words are a plausible explanation.
  
  
• For you Y fans: The pseudo-vowel shows up in the last spot 63% of the time when it appears.
  
  
• Of the most common letters, L has the most level distribution, appearing most in the third position (25%) and least in the last position (14%).
  
  
• Words in which letters appear twice make up a little more than 35.8% of the accepted word list.
  

Figure 1: source

Looking at Figure 1, it would seem that the AROSE would be a good starting point. Figure 2 shows the positions within a word of the most common letters.

Figure 2: source

Figure 2 shows that S occurs most frequently in the final position and so the previous choice of AROSE is perhaps not as good a choice as it first seemed. There are no permutations of this word that have S in the final position. Finally Figure 3 shows the frequency of letters occurring twice in a word compared with their overall frequency.

Figure 3: source

Given that both E are S more likely to occur twice in a word, it would seem that EASES might be good choice of starting word. Some other suggested starting words are:

• TARES
• SORES
• CARES
• CORES
• REAIS
• BLAHS
• SOLAR

There are a lot of factors to consider but this post is at least a start and will definitely improve my Wordle prowess.