Bottom note box.
Know Your Phrase -  An Alphabetical List of Common Phrases, Sayings and Idioms With Their Meanings and Origins > R-Letter Expressions
The origins of this idiom.
The meaning of this phrase.
Phrases and Idioms - The Meanings and Origins For Many Common Idioms and Phrases
Immediately or done in a hurry; without delay.
* Look, Bill, before you buy this house I have to tell you about a huge problem right off the bat... this house is infested with termites. Besides that, everything is great!
Note: A phrase's origins are sometimes not very clear. Thus, in the cases of the origins being unclear, what you will see listed are popular or plausible theories for how or where a phrase came to be. However, remember these are just theories and should not be taken as fact.

The quotes listed that contain the idiom come from old books, newspapers, plays, and so on. The purpose of the quote is to give you an idea on how old some of these expressions are. Most of the time, I will try to find the oldest recording available, but sometimes I will quote something that came slightly later because I like the way it is worded more.
Title picture for the expression Right Off The Bat.
The origins for this phrase are likely to be rooted in the sport of baseball.

In baseball, this phrase references the ball coming off the bat after a successful
strike, which is then immediately followed by the batter making a quick decision to
run towards first base. The immediate response taken by batters after a successful
swing would be my guess on how this saying got its figurative meaning of doing
things quickly, or without delay.

From what I've found, the age of this phrase goes back to at least the 1870-80s. I say this because I can't find it in any newspapers before that time. Anyways, during the 1880s, this expression is used in newspapers both in the context of baseball and in the figurative sense of 'doing things fast' that we know today. An example of the former is found in the Albion New Era newspaper, 1883, where it says:

"A person unused to it would net catch one 'fly' out of fifty, and as for stopping and holding a hot liner
right off the bat, he might as well attempt to gather in a solid shot fired point blank from a Parrot gun."

That quote is talking about baseball. This next one, however, is an example of the saying being used in a figurative way. The term is used five years later in the Biddeford Journal, 1888:

"Let me hear that kid use slang again, and I'll give it to him right off the bat. I'll wipe up the floor with him."
A bat and a baseball!