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Edit: Updated T4I, SF fleet types +3 evasion due to speed doctrine
Updated T6s, CRF fleet types +3 evasion due to traded speed doctrine
DD fleet types have neutron weapons, due to traded neutron tech
Updated T7s, DD fleet modernization, +10 shields to flanks and +15 to centers. +2 to maximum potential

0rph3u5:
Custom Fleet type Building:
Each faction comes with its own type of ships which different weapons and stats. A fleet is all of these ship stats added together.
You can create your own new fleet type! You just have to submit the list of ship types, I'll add the stats together for you. Just make sure you stay within the limitations, these being:

Each ship has a command cost, a center fleet has a maximum of 30 command, while a flank is half of that, 15. In addition to the command cost, there is a limit to how many ships of the same type you can put in a single fleet.
A flank needs to have some similarity to its center part.
Special note for the UGC; You can't mix Mercenary vessels with those of the UGCR. (You can of course have your fleet be a mix of mercenary and regular fleet types)

(Also, don't forget to give it a cool name).

Run this new fleet configuration by your faction's minister, who can then initiate a Fleet Proposal project to make it official. After this, Admirals can then refit their fleets to make use of this new fleet type. You can submit a center and its flank at the same time.

For your own fleet assembling needs, here are the ship types of each faction:
SF Ships
DD Ships
CRF Ships
UGCR Ships
Fleets


Each faction comes with a 3 preset fleet types and the initial fleets may be composed of these available ones from the start. Each faction can have a maximum of 4 fleet types (center+flank), existing fleets can be edited or replaced if desired.

Fleet statistics:
Shields: Effectively serve as hitpoints that regenerate each new tactical combat turn.
Strength: Your fleet's hitpoints, unlike shields, these do not regenerate on their own. In order to repair this damage a fleet must be resupplied at a shipyard. Fleets below 50% strength suffer a 25% penalty to the damage they deal.
Evasion: A flat percentage to avoid a shot.
Experience: Fleet experience will go up one a level after a tactical combat*, and adds to the Potential. New fleets start at Regular (+0) and go up to Veteran (+1) and Elite (+2)
Garrison fleets do not gain Experience.
(*Actual combat, so no trying to raise your fleet experience by going into tactical combat with someone and not shooting at each other)
Morale: Like Experience, Morale adds to the Potential of a fleet. Morale is generally influenced by faction and Admiral achievements.
Morale ranges from Broken (-2), Shaken (-1), Ok (+0), Good (+1), Excellent (+2) and Zealous (+3)
Potential: There are several factors that can contribute to a fleet's effectiveness, such as good morale, crew experience, a solid commander in charge and so forth. But there is only so much a motivated crew can do to overcome technical limitations. This is reflected in a fleet's potential.
This stat affects a fleet's damage and evasion.

 -Neutron: These weapons ignore 10% of the enemy shields.
 -EMP: When a EMP weapon hits an enemy fleet, it applies a 10% accuracy debuff that lasts for a single tactical combat turn. (Make sure to fire it before the enemy gets a chance to fire this turn!) This effect can stack.
 -ECM: This reduces the enemy potential by 1, it remains active for as long as the fleet that has it remains alive on the field. ECM does not stack.
 -Fire Control: adds a +3 hit bonus on point defense and secondary batteries to all allied fleets currently on the same grid as the fleet that has the carrier. Fire Control does not stack.

Lorric:


A starbase is subject to a few special rules.
It occupies its own grid and does not move. Ships adjacent to the starbase can fire their 0 and 1 range weapons at it. Fleets cannot move on or through the starbase grid.

A starbase will fire its weapons at the closest, highest strength, target in range each phase of the tactical battle. (So it can fire at something five times during a single tactical combat turn)
Starbase stats are the same for each faction (though it will benefit from things like neutron weapons if the faction has this technology)
Like Garrison fleets, starbases repair themselves at a rate of 25% per strategic phase, free of charge and cannot be manually repaired.


(Starbase picture courtesy of the interwebs)

0rph3u5:
Another question, so right now this only goes in how to compose our fleet centres but what of the fleet's flanks?

Third and lastly, (and I feel stupid for not seein this way before now), does fleet composition impact speed in tactical combat? (to find a balance between positioning and the raw order efficency that comes with keeping your flanks attached to the centre)

Enioch:
There are two fleet types: Centre and Flank in the spreadsheet.

If you keep your flanks attached, you can move the entire fleet with one tactical action (Centre moves attached flanks as well). If you break them up, you get bonuses in combat (i.e. flanking, better positioning for firing), but you need more than one action to separate / move the flanks.

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