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.