Hmm, what I did was a approximative calculation (on the example of research):

Total Research = Rt = Production*Research-modificator

with

Production = P = P0 + n1*PB

and

Research-modificator = R = R0 + n2*PB

n1 and n2 are the number of boni (PB and RB respectively) of the type which raise production (food improvements) and research (research improvements)

now you have a limited number of boni you can take per planet n, such that n = n1 + n2.

At this point I have also made the approximation of no adjacency boni.

Now I can determine the maximum of Rt(n1), which turns out to be:

n1_optimal = n/2 + R0/2RB - P0/2PB

ok, so for R0/RB = P0/PB the optimal balance is 50% production improvements and 50% research improvements.

If we now assume for example, that we don't need approval improvements and that one bonus corresponds to one maximum tier improvement, we get:

P0 = 8 = 3 (colony capital production) + 5 (colony capital food)

PB = 5 (Lossless Farm)

R0 = 100%

RB = 60% (Discovery sphere)

and therefore:

n1_optimal = 1/2 * ( n + 1.67 - 1.6 ) = n/2 + 0.035

Thus approximately half of all improvements should be food improvements.

**So what would a starbase do?**

A starbase will add 50% to R0, since it does not cost you an improvement tile, so with 4 research starbases you get:

R0 = 300% = 100% (base value planet) + 4x50% (4 starbases with best starbase module)

RB = 60% ...

R0/RB = 5

and

n1_optimal = n/2 + 1.67

The balance is shifted in favor of food improvements!

**We can do the same for capitals:**

We add the difference of the gains of the capital and a normal improvement to the Base value:

R0 = 140% = 100% (base value planet) + 100% (Tech capital) - 60% (1 discovery sphere)

RB = 60%

R0/RB = 2.33

n1_optimal = n/2 + 0.33

Again, the balance is shifted towards food improvements

The same applies for manufacturing capitals, power plants, etc.

**Further Considerations:**

Vice versa, somthing that increases your food like the +1 food tech (or an asteroid mine) will increase the P0 value and therefore shift the balance in favor of research buildings.

Approval will decrease the Bonus effect of food improvements, since you need 1 approval building per farm for example and therefore PB is cut in half. Thus starbase approval modules can increase the number of food improvements by a lot, since for a while you don't need to build approval improvements.

Starbases in general are a big deal and all you can do on them allows you to have more food improvements. This also has the side effect that you don't need to specialize your worlds so much anymore! A world with high food, 4 starbases with manufacturing modules and a power plant is a decent manufacturing world and manufacturing worlds will contribute a lot more to research. And both will contribute a lot more to economics if you build the appropriate starbase modules.

So, this is where I get my 50-70% figure from. For normal improvements without adjacencies it is clos to 50% and starbases, player and galactic achievements, passive boni from tech etc. contribute a lot more to shift it towards having more food improvements. Plus all worlds are more versatile.

So, the take home message is: get starbases for all worlds! You can get up to 6 for a single world and the manufacturing cost for maxing a starbase is lower then the cost of getting highest tier planetary improvements for the same amount of boni (hubs and uniques not withstanding). It is even more efficient if a starbase covers 2+ planets.

edit: I should probably also clarify why I assum I can neglect approval; my approval without improvemnts usually is:

3 (colony capital) + 2 (content 2 faction trait) + 8 (passive from approval tech tree) + 20-30 (starbases)

multiplied by

100% (base value) + 20% (government tech tree) + 25% (virtual world)

=

47.85 - 62.35

if I am malevolent with intimidation center:

64.35 - 83.85

The gap can usually be compensated by 1 or two additional approval buildings, so I tend to neglect it.

edit2: I would also like to point out, that there are range extension modules for starbases. You can have 9 starbases affecting a planet with the first range extension and 14 with the second one. These require a special shape of th first 5 however (you can only have 5 without range extension in that shape).

I also found a formation that allows 4 starbases without and 10 with the first range extension, but only 11 total with the second range extension.