There's a substantial difference in meaning between the two: 'again' just says something recurred or occurred again. 'yet again' says something recurred or occurred again, AND you are not quite happy or enthused that it happened again, or you are questioning why it happened again. Example: "They went on holidays again" = I am only saying they went on holidays another time. I am not saying any more than that. "They went on holidays yet again" = I am saying they went on holidays another time, BUT, I am also questioning why they did it again. Perhaps I am personally frustrated they have the money to do it and I don't. Or perhaps I think they shouldn't have gone again so soon.

I think maybe deference is how many times it repeat

“Yet again” is usually used when something has been repeated more than one time. The “yet” is used as emphasis, and can be used in both a negative and positive way. Example: “He failed the test twice last year, and yet again this year.” “She was named Most Valuable Player three times in the 1990’s, and yet again in 2003 and 2004.”

What's the difference?