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You can increase ship star influence GP two ways: increasing crew power, or increasing stars on your ship. Crew GP contribution is straight up how much your crew can contribute if they were maxed out units

Increasing stars on a ship ONLY increases the star influence GP amount, but increasing a crew members power would increase both crew GP and star influence GP

Star Influence GP is really just ((crew_contrib_power * ship_star_multiplier) - crew_contrib_power) * 1.5 where crew_contrib_power is the sum of all the crew powers. For multi member ships crew_contrib_power is sum_of_crew_power * crew_count_multiplier. This is a way to scale the total down based on the total number of crew members so you don't get 60k power on three crew ships, you get 60k * 0.35