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There is a general logic in the game based on ranks and reputation. These 2 factors could be used as parameters in the multiplier’s equation. As the price of the ship performing the action.
I’d allow for more points per transaction when reputation, rank or ship price is higher.
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I don't think that rank, reputation or (and specially) ship price should have an effect on the influence a faction gains by player actions.
I see no reason why the successful completion of action X should have a different effect based on who did it and in what ship.
If a station needs 10t of grain and they get 10t of grain, then why should it matter if those 10t got delivered in a Hauler, Cobra or T-9?
For combat the rank of the wanted NPC or enemy NPC could affect the influence gain of that action. Not sure if this is something that should be added, but at least it is plausible for me. Depending on how killing wanted or enemy NPCs is considered to affect the influence of a system.
Same for reputation. Since influence affects all factions and in someway reflects the reaction of the other factions to that action, why should the reputation of the CMDR with one faction affect the other factions?
Rank could affect the influence since a higher ranked CMDR is helping a faction and this support alone could help the faction - just like celebrities endorsing a product in marketing.
But I think it would be better to not let rank affect the BGS.