"Are you saying that someone could have 3 run batted in?"
When you're talking about 1 RBI, it's run batted in, when you have 2 or more, RBI stands for runs batted in. They're two different abbreviations.
"So then what you are saying is, that it should be RsBI. "
Runs starts with the letter "R". It does not need to be abbreviated to "Rs". When it's singular, would you abbreviate it as "Rn"?