interesting, does the game tell you the number of research points a given tech uses? Also, is the +250 research points indicated anywhere in the UI?
I'm not sure the +250 research points is even displayed in-game. As Larsenex has noted, this appears to modified based possibly on whether you have research tile resources or research building(s) on your starting planet(s). However, no access to game code = everything is observational inferences, and then some speculation & conjecture.
DISCLAIMER: Long post with math! You have been warned!
As for how to figure out how many research points a tech uses: you can plow through the XML data files to figure out what techs cost what. Based solely on the information displayed in-game however, you can estimate the possible range of the remaining cost, which will be equal to:
[(Total Research Point Generation) * (N - 1) + 1, (Total Research Point Generation) * (N)].
Range = (Research Per Turn) - 1.
where N is equal to the number of turns it takes to finish researching that technology, if your current research point generation remains static throughout the course of researching that technology (which it likely won't, but I digress).
Say the technology "I-Can-Build-A-DeathStar" (has a hidden cost of 3300 research points and we have not spent any research points towards yet) takes 9 (a.k.a. our 'N') turns to research, with a current research point generation of 390.
Therefore, we can estimate that the total remaining (but conveniently equal to the total cost because we have not started to research it!) cost of "I-Can-Build-A-DeathStar" to be in the range of:
= [(9 - 1) * 390 + 1, 9 * 390]
= [(8 * 390) + 1, 9 * 390]
= [3121, 3510]
Range = (390 - 1) = 389
Therefore, we can conclude that "I-Can-Build-A-DeathStar" costs between 3121 and 3510 research points. But what if you want a more accurate estimation of this? You would simply have to reduce your research output (temporarily of course, until you actually start researching! ), with your sliders & whatnot (if you have a lot of planets with their custom sliders, I'd suggest making a save-file before trying this!).
For example, say if we reduced our research point generation to 86 research/turn (and causing the N number of turns needed to increase to 39, so N = 39), we can make a new, more accurate estimation at the total research cost of "I-Can-Build-A-DeathStar" to be in the range of:
= [(39- 1) * 86 + 1, 39 * 86]
= [(38 * 86) + 1, 39 * 86]
= [3269, 3354]
Range = (86 - 1) = 85.
You may have realized at this stage (as zuPloed pointed out in the previous post): "if we set our RPT to 1, we'd be able to perfectly calculate the research cost (N * RPT = Cost)! D'oh!". That is a perfectly correct assumption as well!
However, setting your RPT to exactly 1 with multiple planets may not always be easy and sometimes impossible (e.g. you built a Thulium Data Archive... which gives a flat, non-negatable bonus that ignores your production slider), so this method is a just a decent way to approximate the hidden, remaining, research cost, short of trying to find the corresponding XML entries in the game data files.
Interesting to note is that this is also very similar to the mechanism you may have used to approximate the slope of a curve in a pre-calculus class at school (e.g. before you learned to take derivatives).