andyskinner:
Here is a copy/paste of the relevant section of the email I sent to Daniel Kast concerning the current formula, the RPD+R formula, and the revised formula that we implemented. Hopefully this should explain why the RPD+R isnt really workable in the current design IMO.
Note that we've been using this modified spreadsheet now and it feels a LOT better. There are true decisions between upping RoF vs upping Pen/Dmg or just increasing the number of weapons on the ship...decisions that were not present with the original formula.
Here you go:
That said, as I'm sure your aware from the Forum that the base formula for the weapon cost is somewhat buggered. For a while, we just sort of ignored it and played for 'spirit of the rules', but after a few games, its become apparent that we needed to 'fix' the problem. We have some players that are more or less hardcore into design and some that are more casual and just throw whatever looks cool onto the ships and go from there. For the hardcore players, we have deliberately avoided trying to use 'optimized' weapons where possible, but it really cuts down on the options when you are avoiding using RoF (because it is, by FAR, the most efficient way to go in every way). The sticking points come when the casual players show up with ships that are 'accidentally' quite a bit better than the others simply because they plugged in a lot more higher RoF ships. The difference is very pronounced and even the casual players could see that certain ships were really MUCH more effective overall than others for roughly the same cost.
Ok, that gives the background. 
I sat down with one of my more mathematically inclined (and excel skilled) friends and looked to 'solve' the problem. We think we have done so, but some of it requires the designer's original intent as well. So, here is what we've found and what we've surmised.
Ok, we understand that everything else equal, RoF is better to increase than PEN or DAM because it is more useful vs Fighters. We are implementing that with the theory that for ship to ship, there is little actual difference between a 3/1/1 weapon and a 1/1/3 weapon or a 1/3/1 weapon. There will be different 'flavors' from the three options, but total 'firepower'...ie, 'dice on target' will remain the same.
From that, lets assume we want to put 3 'dice on target'. Our options are a 3/1/1, a 1/1/3 (or 1/3/1), or 3 x 1/1/1 weapons. Under the current formula, the 3/1/1 provides a HUGE margin over the 1/1/3....the 1/1/3 is 50% more expensive (6 compared to 4) AND the 3/1/1 is 3x more effective vs Fighters. So you are paying less, but for quite a bit more capability (that is a 'double dip' in our opinion...you are not only paying less for the same capability, you are paying less for more). The 3x 1/1/1 option costs 50% more, but has the same AA capabilities. Its also slightly more survivable (there are more Battery hits on the latter ship, but not 3x more).
Also, under the basic formula, when dealing with a '1' RoF, you are never doing any good by increasing PEN or DMG. You are always better off simply putting more weapons on the ship. For example, a 1/2/2 puts out 4x as many dice on target as a 1/1/1, but cost exactly 4x as much SU and CR. So, having 4x 1/1/1 on your ship gives you the exact same ship-to-ship capability, but 4x the AA capability and is more survivable to boot....again, this is a major difference is capability between ships.
The same holds true as you go up the scale. Increasing RoF is economical...increasing the other stats results in diminishing returns vice just adding extra weapons.
Hopefully that was at least somewhat clear. I just wanted to demostrate just how far the deviation was between intended (RoF is more costly for more capability) and reality (RoF is less costly for more capability).
There have been a number of solutions proposed (including by me), but most dont really fix the problem. A few mitigate the problem, but it took a lot of futzing around with algebra to actually make a formula that we felt best imposes your original design intent without unhinging the rest of the game's mechanics (a very real danger when monkeying around with the foundations of the weapon costs).
We tried (R*P*D)+R first. It looks workable on the surface, but it causes other problems. For one thing, it means that the base weapons are too cheap overall, leading to way too much firepower compared to protection for ships. You cant do much to increase your defense, but this formula lets you pack on more weapons overall....considerably more in some cases. Also, it doesnt fix the 'break points' at 2/1/1 and 3/1/1. The cost for those options was still exactly 2x and 3x respectively of having equivalent 1/1/1s, but were more vulnerable.
The base formula we came up with is (R*P*D)+(3(R)+P+D)/5.
I know you have a mathematical bend to you, so I wont go through all the specifics, but what it does in the end is weight 'R' higher than P and D while not applying that multiplier completely across the larger weapons. The theory here is that a 3/3/3 weapon is still a total waste to fire at a fighter, so you should not be paying the same premium on the RoF going from 1/3/3 to 3/3/3 as going from 1/1/1 to 3/1/1. The simultaneous goal is to make sure that you are getting a substantial discount when employing a larger weapon than going with the equivalent number of 'dice on target' in smaller weapons. Again, this is to make sure that a 2/2/2 is more cost effective than 8x 1/1/1s because it is far worse vs Fighters and is far more vulnerable to be taken out completely (although this is dependent on the size of the ship, its always going to be present). So there has to be a reason to select a 2/2/2 over the 8x 1/1/1 and in our formula, that reason is about a 38% discount. That seems to be a good trade off. Similar trade-offs will occur evenly throughout the 27 combos of R/P/D.
OK, that gives a great base to start from, but there is one final problem with it. Even though the current game's formula is flawed, it appears that the rest of the weapon multipliers and indeed, many of the calculations are predicated on weapons having that somewhat high inherent base cost. Using our forumla, weapons are still a little too cheap compared to what you have now (although RoF is properly weighted). So, to restore the situation, we've imposed a flat 20% increase in weapon costs. So, the final formula reads:
1.2*(R*P*D +(3(R)+P+D)/5)
This puts weapons back on par with current costs, but in the correct weightings. Its now more costly to put a 3/1/1 than a 1/1/3, but cheaper than going with 3x 1/1/1 (marginally). Again, the same will apply nearly evenly across the board, with the discount increasing as the weapons get bigger (and thus simultaneously more vulnerable to being taken out and and worse against Fighters).
