For playoff season, let's learn some baseball slang!

What does "heavy hitter" mean? For example "She is a heavy hitter for the company division in Chicago."

What does "left field" mean? For example "She finally had a solution to the problem, and it came out of left field."

What is a a "rain check?" For example "I'll take a rain check on that." 

To do a task or meet someone at a later time.

What does "play ball" mean? For example "Let's play ball and stop stalling on the new project."

What does "cover all the bases" mean? For example "We need to cover all the bases for this new assignment."