Tooltips for ship equipment display different stats under different conditions. They display one value when I'm in sector space, a different value in a system, and another on the ground. Scaling equipment shows yet a fourth value when it's just been equipped.
For example: When I'm in sector space, the tooltip for the scaling Emitter-Linked Phaser Beam Array that came with my Crossfield Science Spearhead says it deals 523.2 damage per volley. If I enter the Starbase 39/Sierra system and check again, it shoots up to 597.1 damage per volley. These numbers seem to be affected by ship equipment (they go down if I unequip tactical consoles) but not by power settings (shifting power to or away from weapons doesn't change anything).
If I then beam down to the station, the Emitter-Linked Phaser Beam Array drops all the way down to 330.6 damage per volley, and this value does not appear to be affected by ship equipment (removing tactical consoles doesn't change it). If I remove the array from my ship and examine it in my inventory, it still says 330.6, but if I then re-equip it, it goes all the way down to 150. If I beam up it goes back up to 597.1 regardless of whether it was 330.6 or 150 before.
A common Phaser Beam Array Mark XII displays the same numbers--523.2 in sector space, 597.1 in the system, 330.6 on the ground, affected by other equipment everywhere except ground. It doesn't drop down to 150 when freshly equipped, though.
In a phenomenon that may or may not be related, the tooltip for the basic Discovery-style Phaser Beam Arrays that came with my Discovery character's tutorial starship (which have nothing suggesting that they're scaling in any way) show much higher stats than the scaling array: 429.2 damage per volley on the ground, 702.2 in the system, and 621.8 in sector space. This doesn't seem like it could possibly be right, but I'm not sure how I could confirm or deny.
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I think I didn't communicate properly what's going on with the scaling equipment, which is two different issues. The equipment that's marked as scaling (e.g. the Emitter-Linked Phaser Beam Array) normally shows stats equivalent to Mark 12 equipment. I don't think that's an issue, it seems reasonable.
The first issue is that, when I equip a piece of scaling equipment (as in I move it from the inventory to an equipment slot, not when I have it in an equipment slot already upon beaming down), its stats suddenly dip way down to be in the neighborhood of Mark 1 equipment, like it thinks I'm at level 1. It fixes itself when I return to space, so it doesn't really make a difference to gameplay, but again it's annoying.
The second issue is that I also still have the phasers that came with the tutorial starship back when I created my Discovery character, which according to the description are just regular non-scaling phasers and as starting equipment would presumably be weak, but their stats display as if they were scaling and in fact are scaled higher than my "infinity" scaling equipment or any non-scaling phaser beam arrays I own. So either their stats are displaying totally wrong (stat display issue), or they're "stealth" scaling weapons that aren't marked as scaling for some reason (incorrect/misleading item description issue).