[DirectorTsaarx]

All right - there are two problems; one, I missed a couple things in the explanation here on the forum, because it's much easier to draw formulas by hand than it is to enter via a text format. So, while my hand-written stuff included the "multiply by 900 (or 1000)" in the appropriate places, my stuff here didn't include the multiplier. The final equation did include the multipliers, but you'll have to take my word for that.

The other problem is my handwritten notes were slightly off, because I dropped an "N" someplace. I've corrected the error; text is here, spreadsheet (Excel '97) attached again, and the conclusion is essentially reversed (i.e., upgrade does turn out better than build better facilities slower).

Text for upgrade process:

Now, if we instead build N Mineral Miner Facility II's (MMF2's), at one turn per facility (cost=2000 minerals, exactly the build rate), we get (N-1)*900 + (N-2)*900 +... +1*900 minerals produced, from the time building starts until the Last building turn; note that at this point, the Last facility has not started producing. I'll explain why in a moment. This simplifies to:

900*N*(N-1)/2

We then subtract the cost of the facilities (2000*N) to get the net gain so far. Now, if we upgrade those facilities (to MMF3's), it costs (1250*N) for the upgrade. Everyone still with me?

Obviously, we still produce minerals during the upgrade cycle; this amounts to:

(1250*N/2000)*900
[cost divided by build rate, times number of facilities, times 900]

Technically, that number should be rounded up to the nearest integer to get actual number of turns, but we'll ignore that for a moment. In addition, this figure includes that first turn of production for the Last facility; that's why I didn't include it in the previous formula.

Now that the upgrade is finished, we can produce at MMF3 rates. In order to compare the "upgrade" strategy to the "build once" strategy, we include enough turns of production to equal the amount of time it takes to finish building the MMF3s from scratch. This amounts to:

{[(2*N)+1] - N - (1250/2000)*N}*N*1000

Obviously, (2*N)+1 is the number of turns required to build the MMF3's; N is the number
of turns required to build the MMF2's; and (1250/2000)*N is the number of turns required
to upgrade MMF2's to MMF3's. Again, that Last number should be rounded up; however, in the interest of simplifying the algebra, I've avoiding the rounding. Which really gives a slight overestimate in the amount of minerals produced in the "upgrade" strategy, since we're now calculating mineral production as 900/turn for part of a turn, and 1000/turn for the rest of that turn. After combining the above formulas and doing some algebra, we
come up with the following calculation for the upgrade strategy:

1450*N*N - 2762.5*N

Unfortunately, once I found the "dropped" N, it changed things drastically; it actually comes out better to build the lower tech facilities & then upgrade. (assuming you can't build the better facility in a single turn; by the time I've researched MMF3's, I usually have at least a PSY2, so I can build MMF3's in a single turn & the whole set of equations is useless).