Edit:
Findings so far.....
[rateOfFire] is inversely proportional to [attNum]. The reciprocal of [attNum] is multiplied by another mystery number to get [rateOfFire].
Example cases from tevent.txt taken from same battle:
[attNum]ˉ¹ * (x) = [rateOfFire]USS Thalestris fires beam on DSS 007A-00210 at range: 1800.00
DSS 007A-00210: HP: 152/152 Shield: Strength: 237/243 Lev: 0 Replenish: 24
USS Thalestris: HP: 494/494 Shield: Strength: 1010/1010 Lev: 0 Replenish: 101
MaxRange: 1800.00 attLev: 200 attNum: 6 attMul: 1 attStr: 30
Shield Penetration: 0 rateOfFire: 43690 numFired: 6
Target Defense Level: 74
Hit probability: 108.0%
USS Colossus fires beam on DSS 007A-00210 at range: 2754.06
DSS 007A-00210: HP: 152/152 Shield: Strength: 243/243 Lev: 0 Replenish: 24
USS Colossus: HP: 970/970 Shield: Strength: 1620/1620 Lev: 0 Replenish: 162
MaxRange: 1800.00 attLev: 200 attNum: 14 attMul: 1 attStr: 60
Shield Penetration: 0 rateOfFire: 18724 numFired: 14
Target Defense Level: 74
Hit probability: 98.0%
or written as: (1/[attNum]) * (x) = [rateOfFire]
In these 2 example cases (x) = 26143 so...
14ˉ¹ * 262143 = 18724.5
or written as: (1/14) * 262143 = 18724.5
and
6ˉ¹ * 262143 = 43690.5
The result is truncated to a whole number, not rounded.
[rateOfFire] does not change during battle, so the mystery number doesn't either.
I don't know where 262143 came from but separate ships of multiple types in the same battle shared the number, I'll do some more experiments tomorrow.
These things do not enter into the equation of the mystery variable:
Any stats of the defending ship, including any distances.
Beam Strength
Attack Rating
Hit Probability
Attack Multiplier
[numFired]
Command used in the battle screen
Attacking ship type (e.g. Command, Strike, Destroyer)
Any defensive stats of the attacking ship (hull/shield/agility)
~~ Ok that random number seems to be a constant? Just tried the test again, One Fed Command ship vs one dominion colony ship. The same number was used by both even though I changed the tech level of both races.