out of left field means having nothing to do with the matter being discussed
Since he was napping during the meeting, his idea came out of left field.

One of its likely origins is that a runner attempting to score from third base will have his back to left field, thus a throw to the plate “out of left field” can arrive seemingly out of nowhere as a surprise to the runner.

out in left field means a little crazy
I think your idea is way out in left field.

One suggested origin is that it was crazy to buy left field seats during the time of Babe Ruth because he hit toward the right field.

For more details, check here.

hit or miss means to either achieve success or completely fail.
Attempts to solve the problem are likely to be hit or miss.

hit or miss means to happen or not happen.
The rain showers across the area have been hit or miss.

This phrase is a reference to a batter either hitting or missing a pitched baseball.

heavy hitter means a powerful or influential person
They hired him as their heavy hitter to get them through the crisis.

This phrase is a reference to a batter that has many home runs or extra base hits.

to go to bat for someone means to support or be a substitute for them
He went to bat for her when she asked for a raise.

This phrase is a reference to one batter subsitituting for another.

curveball means a totally unexpected surprise
When you are thrown a curveball like cancer, it can be overwhelming.

This phrase is a reference to the curveball being a baseball pitch designed to fool the batter by curving unexpectedly.

cover all the bases means to be prepared for every contingency
The thorough investigation covered all the bases.

This phrase is a reference to a baseball player covering a base by standing close to it, ensuring a runner can not reach it safely.

caught off base means caught unprepared
The sudden storm during the hike caught him off base.

way off base means completely incorrect
The weather forecast was way off base.

This phrase is a reference to the situation of a baseball runner being away from a base and taking a risk of being put out.

big leagues means at the highest level

You’re in the big leagues now.

This phrase is a reference to major league baseball where the career goal of the athlete is to move from the minors to the majors.

batting a thousand means to achieve success at each attempt

He’s batting a thousand so far in the new job.

This phrase comes from the practice of reckoning the batting average of a hitter in thousandths. It would mean that the hitter reached first base every time he was up to bat.

ballpark means general vicinity
Let’s get in the ballpark, then worry about the fine details.

a ballpark figure means an educated guess
Could you at least give me a ballpark figure for the project?

in the right ballpark means within an acceptable range
His answer wasn’t even in the right ballpark.

to hit one out of the ballpark means to produce a spectacular achievement
They really hit one out of the ballpark with this event!