Its 0.6% tech cost, on top of your existing sprawl, its linear.
As an example, if you're already at +100% tech cost, then the +2 Sprawl is only a 0.3% increase to your research time.
You cant think about it multiplicatively, you have to think about it additively, because its additive, which actually means thinking about it in terms of the base tech costs.
https://www.desmos.com/calculator/mbrk0ck2aq
This graph shows the time to tech completion for varying amounts of base research compared to varying values of additional research systems under consideration.
Visit the link to look at and understand the graph, or you wont understand anything I'm saying from here on.
The relevant takeaway from the graph is the intersection points between functions y2 to y6 with y1.
You can see that for no matter what value of N, the intersection points remain the same, this is because as I said, the penalty from Sprawl is linear.
You can treat the Y-value of the intersection points as the turns to tech completion breakpoint for whether acquiring a system of a particular value would be a net increase or net decrease to your tech completion rate.
To use y2 as an example, the y-intersect of y1 and y2 is 60, for all values of n. This means that if you're considering a system with a single point of physics research, and it will take you more than 60 turns to fully(from 0% to 100%) complete your current physics tech, that system will be a net increase to your
physics tech completion speed.
No matter how high your sprawl already is.
Since Sprawl affects all your research speeds however, the values might be considered in thirds, and can be processed as follows:
1 Research in system: If your average time to tech completion is more than
180, get it, otherwise dont.
2 Research in system: >90
3 Research in system: >60
4 Research in syetem: >45
5 Research in system: >36
6 Research in system: >30
7 Research in system: >25.5
8 Research in system: >23.5
9 Research in system: >20
To reiterate the purpose of the above mini chart; If the average time it takes you to fully complete techs, across the 3 branches of research, is higher than one of the above values, then a research system of corresponding output will be a net increase in your teching speed. The inverse is also true.
To repost the chart using the x-intercepts in case people find the mental math easier that way:
1 Research in system: If your average research output is less than 0.55% of your average tech cost, get it
2 Research in system: <1.11%
3 Research in system: <1.66%
4 Research in system: <2.22%
5 Research in system: <2.77%
6 Research in system: <3.33%
7 Research in system: <3.88%
8 Research in system: <4.44%
9 Research in system: <5%
Remember of course that increases to research station output can modify the above values by up to a factor of 1.6.
A key takeaway from the above, in my experience, is that since teching faster of course leads to higher tech costs, systems with at least 3 research stay valuable on average.
The above values do not factor in the Sprawl penalty to Unity output, and they also do not factor in station upkeeps, or other resources found in the system. They are
only a function of research speed increase/decrease for a given research value of system.