Why not use Right Recursion to avoid Left Recursion?

I am reading about Representative Grammars from book, where I encountered the following grammar:

$$E \rightarrow E + T \ | \ T$$ $$T \rightarrow T * F \ | \ F$$ $$F \rightarrow (E) \ | \ id$$

The above grammar is left-recursive, which is bad. So in order to eliminate left recursion, they changed it to the following:

$$E \rightarrow TE'$$ $$E' \rightarrow +TE' \ | \ \epsilon$$ $$T \rightarrow FT'$$ $$T' \rightarrow *FT' \ | \ \epsilon$$ $$F \rightarrow (E) \ | \ id$$

But why bother so much? Why not simply use a right recursion instead, like the following:

$$E \rightarrow T + E \ | \ T$$ $$T \rightarrow F * T \ | \ F$$ $$F \rightarrow (E) \ | \ id$$

• So I am confused about whether the Right Recursive Grammar I thought of is same as the original grammar or not?
• If not, what's the difference?
• If they are same, why don't we write all grammars as Right Recursion?
• "left-recursive, which is bad" -- perhaps you should try to better understand what "bad" actually means here. E.g. one might say it is bad because it is not LL(1), but then the right recursive variant has the same issue, so it is also "bad".
– chi
Jun 3 '17 at 12:30