Is there a correlation between the size of an empire and the amount of power it holds in the world?

Yes.

Explanation:

The largest empires in the history of humankind have had a large mount of power over the world, for example the Mongol empire for a while reign over a large portion of Asia, and it had a lot of power over the world, the Roman empire had the same amount of power and influence over western and eastern Europe for over 10 centuries. The expansion of a empire is directly correlated to the power and influence it holds in the world.