Even if you define the total metal income, the question is
still inadequately defined since the size of the individual mex matters to energy overdrive.
So I will proceed under the assumptions that:
* All metal extractors owned by the team have the same base income.
* All metal extractors are gridded to the singus
* All of the energy from the three singus, and no other energy, is available for overdrive
* 15 magpies rearm at a time; of the
minimum-total-time solutions for rearming 60 magpies at 16 individual pads, only using 15 at a time maximises the metal overdrive income (proving this is left as an exercise for the reader).
Let X be the number of metal eXtractors owned by a team and let M be the base metal income from each of those extractors. Let E (=3*225=675) be the energy income per second available for overdrive or Magpie rearming. Let A (=60) be the number of mAgpies. Let P (=15) be the number of individual Pads available.
An individual Magpie rearms for 12 seconds and requires 10 energy/s, so the Time required for all of the Magpies to rearm is
T=12*A/P=48
and the energy Cost per second during that time is
C=10*P=50
As per
http://zero-k.info/mediawiki/Overdrive the overdrive metal generated per second with no rearming occurring is:
OD1=0.25 * X * M * sqrt(E/X)
while the overdrive metal generated per second while the Magpies are rearming is:
OD2=0.25 * X * M * sqrt( (E-C) / X )
Taking the difference between these and multiplying by the time spent rearming yields the desired quantity.
---
Let's take a few examples with about the same amount of metal extractors:
About half the mex on Storm Siege (X=50, M=1.79):The mex themselves produce 89.5 mex metal/s, so 4296 metal in 48 seconds. (Unaffected by the magpies of course, but useful for perspective.)
With no rearming, overdrive produces 82.2 metal/s, so 3946 metal in 48 seconds.
While the Magpies are rearming, overdrive produces 72.5 metal/s, so 3480 metal in 48 seconds.
So rearming the Magpies cost about 466 metal; about 5.5% of the 8242 metal the metal extractors and overdrive were producing in that time.
About half the mex on Comet Catcher (X=39, M=2.28):In this case the base mex produce 4268 metal, and overdrive produces 4439 metal. Rearming the Magpies takes 524 out of the overdrive; slightly over 6%.
Bonus question: what if there is only one singu on Comet Catcher, so E=225?Now the base overdrive yields 2563 metal, of which 1083 (!) is lost by rearming the magpies; over 15% of the original income.
Moral of the story: As you put energy into overdrive, each unit of energy benefits you less and less. As you take energy OUT of overdrive, each unit of energy costs you more and more.
