I used google translate for this question so I might have misunderstood it in some way. But, the concept is that the author badge counts the average of words for all your logs. So if you have an average of 10 and write a log with 200 words your average will go up. If you have an average of 100 and write a log with just "TFTC" you average will probably go down. It's total numer of words in all logs divided by number of logs so it also depends on how many caches you've logged.
So, if you have been writing long logs on caches between 26/08/2021 and 22/11/2021 and your average still gets lower (and you need a higher number to gain next badge) it's likely you have been using tactics that Project-GC filters out. There is a system in place to avoid some of the common ways to boost your numbers with gibberish, like writing words with spaces (L i k e T h i s) or using "Lorem Ipsum" to fill your logs could cause a decrease instead of an increase in your average because it's not counted.
