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Rank is a representation of character reputation in the X-universe. Killing ships increases Combat Rank, reflecting the character's reputation of combat skill. Conducting trades increases Trade Rank, reflecting the character's reputation as an expert trader.
Missions often come with certain rank requirements, simulating a willingness by NPCs to trust the character with their vital interests.
Combat ranks are also used by the game to set up opposition forces. A higher combat rank generally implies that you have some skill at fighting. As a consequence the game likes to increase the challenge of fights by spawning heavier and more numerous combatants for you to face.
Per the Offical Egosoft FAQ: If you leave the game idle for a long period of time then your fight and trade ranks will start to decay. Your fight rank will drop by about 2% for every game hour without player input (or for every 6 minutes, on 1000% SETA), and your trade rank by around 0.25%.
It has been tested that the lowest your Combat and Trade ranks will fall is Fighter and Master Dealer, respectively.
 Combat ranks
 Trade Ranks