Very interesting. I'm curious if some of the particular cases of this are an accidental "ReCAPTCHA effect" as those get filled out with no surrounding context plus whatever context the user brings to it (programmers/mathematician-trained brains mentally prioritizing pattern matching nth over 11th). Certainly anecdotally I feel I've made the lith and nth 'mistakes' in ReCAPTCHA attempts.
The author makes no mention of the word "eleventh". "January eleven" and "January eleventh" do occur. The contribution is minor, but everything counts.<p>In English, we also say "11th of January" not only "January 11th".<p>ngrams comparison:<p><a href="https://books.google.com/ngrams/graph?content=11th+of+January%2CJanuary+11&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2C11th%20of%20January%3B%2Cc0%3B.t1%3B%2CJanuary%2011%3B%2Cc0" rel="nofollow">https://books.google.com/ngrams/graph?content=11th+of+Januar...</a><p>This usage was more popular until around 1860, then it declined.<p>The "n-th of Month" syntactic variation deserves a spot in the analysis, yet I see no mention of it.