I feel like military is just one part of influence and frankly and increasingly less important one (at least compared to 100+ years ago) as the global economy becomes more intwined. Economic and cultural influence are also quite important. Frankly the power of the dollar as a world reserve currency is worth more than every piece of military hardware we have in terms of international influence. Japan comes to mind as an example. Up until recently the effectively haven't had a military at all and still don't have much yet they're still one of the more powerful nations in the world.
But Japan has a guarantee of protection from the US. Take that away, and they would be toast, due to the nearness of China and Russia. As long as they have a guarantee that they cannot be bullied, they have big time power, economically.
Global economic power cannot exist, to any great extent, unless the threat of force is sufficient to discourage the 'cheaters.' Look at any era in the history of civilization to see the evidence. The US didn't become a world military power because it wanted to dominate the world. It did it in self defense. Thriving economies must have somebody to guarantee the 'sanctity' of the marketplace, because there will always be someone who wants to own things that they can't create for themselves.
Replies
"Nothing is safe from stupid." - Zee