What are some points in a nation to determine their influential power?

I'm working on a story of sorts and I'd like to be as detailed with the power dynamic among the nations as I can. The different nations are based around older/ancient civilizations of the real world. Medieval Europe, Feudal Japan, Ancient Egypt, etc.

If one or more nations were to try forming alliances or waging wars against the others, what are some things those in political power would need to consider? Things such as resources, wealth, military forces, etc. What else?