touch base means to make sure everyone has the same information
He just wanted to touch base before he left for vacation.

This phrase is a reference to touching the bases as a runner heads toward home plate. It could be considered briefly “checking in” at each base.

step up to the plate means to assume a responsibility
It’s time for you to step up to the plate and help solve this problem.

This phrase is a reference to stepping up to home plate to bat.

screwball means eccentric or crazy
He had another screwball idea we thought would never work.

right off the bat means immediately or without delay
It was clear right off the bat that the debate team was not prepared.

This phrase is a reference to the immediate acceleration of a baseball just after being hit by a bat.

to play hardball means to be, or act, tough and aggressive
It got ugly when the political candidates started playing hardball.

This phrase is a reference to the difference between balls in baseball and softball.

knock it out of the park means to do something exactly as it should be done
She really knocked it out of the park with that speech.

This phrase is a reference to a home run which is the best a hitter can do.

hit a home run means a complete success
The TV producers hit a home run with this one.

This phrase is a reference to a home run being the best outcome for a hitter.

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.