"I rarely see athletes here."
Translation:Ritkán látok itt sportolókat.
With everything else being equal, i.e., leaving all other words in place, these are the possible positions for "itt":
- Itt ritkán látok sportolókat
- Ritkán látok itt sportolókat
- Ritkán látok sportolókat itt
The first two are the most common, the most neutral, they are mostly the same. The third one follows closely.
Now, the "ritkán látok", that is an adverb and a verb. The adverb is modifying the verb. "I rarely see". If you split it up and insert something in-between, then the adverb will try to modify that other word. This is just like in English. "Rarely see" vs "rarely here".
Back to your version: "Ritkán itt sportolókat látok". My first reaction is that it is wrong. But it is not hopelessly wrong. "Rarely" is kind of a negative word, it refers to an exception. If we replace it with a more neutral adverb, "sometimes", the sentence becomes more neutral. "Sometimes" is "néha" in Hungarian:
"Néha itt sportolókat látok." - Sometimes here I see athletes.
And this sentence is perfectly fine.
The issue with "ritkán" ("rarely") is that it wants a verb to follow it. Both in English and Hungarian. "Néha" ("sometimes") is not so picky.
There is, of course, the "You are rarely here" or "I am rarely hungry" type of sentence that contradicts what I just said. But I think it is special. "Rarely" sits in the middle of a "to be + adverb(?)" structure. Or "I drive very rarely". I think these are a different category. The verb is before the word "rarely", and there is very little after it.
Back to your sentence. I could throw in a few extra words to make it more normal:
"Ritkán előfordul az (is), hogy itt sportolókat látok."
"Rarely it (also) occurs/happens that here I see athletes".
So, "ritkán" ("rarely") now refers to a verb again: "előfordul" - "(it) happens/occurs".