Shanatus1, Atlantic Ocean, 1695519160445023121

It's not completely clear what impacts your combat power. Below are the different ways you can increase your power. While I don't have a breakdown of how much each thing impacts the total score, each one seems to be equally important. I often see people with high quality ships who I have a much higher power ranking than since I have high levels in other places. So it other words, it's not just your ship.

1. Ship stats

a. The stats of the built ship (includes the battle specific skills) - NOTE: while certain stats will increase the battle "power" of the ship, it may not be as useful. If you have a ship geared towards melee, and your ram power is maxed out with very low melee, it may show up as a more powerful ship, but it won't do you as much good in combat. 

b. The equipment (parts) you have on the ship.

c. Your Understanding of the ship (this is like your ship's level and needs to be increased by using the ship).

2. Captain stats (Ship Expertise)

a. Level (combat) (also impacted by transcendence which allows you to increase your level)

b. Equipment equipped

c. Promotions and Training

Increasing all of these values will increase your combat score.

Note: it is important that you spend time on your combat skills. You really want to work to get the captains with the same skills unlocked on the same ship. Each captain with the same skill on the same ship significantly adds to the power of the skill. Getting a specific skill to level 10 should be a major goal to be successful. The total value of this is not always reflected in the total combat power, but will have a massive impact on your success in battle. For example, getting your area attack skill up to level 10 to massively increase the area of effect and multiplier is worth equipping captains with less combat power, if just to get their skill. Auto equiping captains does not take this into consideration. I always recommend trying to assign captains manually.