Q: The White Sox are really good at the fundamentals of baseball. Which is why they won the World Series in 2005.

A: The White Sox are really good at the fundamentals of baseball; which is why they won the World Series in 2005.

Is this correct?

No. Your clause after the semicolon is a dependent clause, not an independent clause. It cannot stand alone.

So I need to write

The White Sox are a really good at the fundamentals of baseball, which is why they won the World Series in 2005.

Yes.

Yes, that statement is correct. The White Sox won the World Series in 2005 largely due to their strong grasp of baseball fundamentals, such as solid defense, effective pitching, and timely hitting. They executed fundamental plays, made the right decisions on the field, and played as a cohesive team, leading them to secure the championship.