Then I would say that you did a rather poor job testing things out. As long as the planet's research or income bonus is less than +890%, you will see a net benefit from using 1% of the planetary production to feed a project rather than directing all of the production into research or income. Accounting for rounding error in the allocation setting, it's only really safe to do this for a bonus to the desired output which is less than 567%. The net benefit you obtain is marginal, but using the project does produce a higher total output

Assuming you get only one output type out of the planet, a world's total output is given by

O(m) = (1 - m) * P * (1 + B + 0.1 * ceil(m * (1 + M) * P / 10))

where O(m) is the planet's output, m is the fraction of production given over to manufacturing, P is the planet's base production, B is the planet's bonus to the output type corresponding to the project used, M is the planet's bonus to manufacturing, and ceil(X) is the function which returns the smallest nonnegative integer N such that N >= X.

I agree that the benefits of the projects are too small, but to claim that they provide no benefit whatsoever under any circumstances is simply wrong.

I think you have a poor way of explaining yourself.  OK, let me use some real numbers, because I doubt anyone wants to follow your equation:

51.7 base research (if 100%), +400% research bonuses

52.0 base manufacturing (if 100%), +195% manf bonuses

If I put 100% into research I get 257 research

If I enable research project, and put 1% (and I had to spend a minute, trying to find a fraction of that percent as well), I get 260.3 max.  

So, to get a "gain" I have to put 99% manufacturing in (I save 1% manufacturing for a rediculously long build), and get 1% extra research out, and spend time fighting the sliders.  I think that would still qualify as "not worth it in any way".  

dansiegel30, you will note that I did not dispute that research and economic projects are not generally worthwhile, and in fact said that I agreed with that sentiment. You will note that what I took exception to is the demonstrably false claim that the use of economic and research projects is strictly inferior to directing planetary production into the desired output types.

The statement "I tried it on a planet where I had ALL Manufacturing (and yes Marigold, an approval building, as well as some farms), and I tried to see which was better, to put population points into Research or Economy, or use my awesome manufacturing capability with the Research Project or Economic Stimulus.  In all attempts, using population points won!  In every possible way." constitutes a claim that, under what are essentially the most favorable conditions for the use of projects, the use of economic and research projects is strictly inferior under any performance metric to directing all planetary production into the desired output type. In other words, you made the claim that there are no conditions under which you will see a net benefit to using a research or economic project as opposed to simply directing production into the desired output. Worse, this is the only support you provided in the original post for your claim that economic and research projects are not worthwhile. This is a demonstrably false statement, and it is the only support you provided for your case.

No, they don't. It isn't communicated that well within the game, but the bonus granted by the project is equal to

0.1 * ceil(m * s * (1 + M) * P / 10)

where m is the fraction of planetary production put towards manufacturing, s is the fraction of manufacturing allocated to social production, M is the planet's manufacturing bonus, P is the planet's production, and ceil(X) is the function which returns the smallest nonnegative integer N such that N >= X. You can see this in game by looking at the tool tip for the output type corresponding to the project; 0% manufacturing means that the project doesn't show up, while social manufacturing in the interval (0, 10] gives a bonus of 10%, social manufacturing in the interval (10, 20] gives a bonus of 20%, and so on.

The net bonus of an economic or research project is less than this, of course, being

P - m * (1 + B + P)

where m is the fraction of the planet's production given over to manufacturing instead of the desired output type, B is the planet's bonus to the output type corresponding to the project, and P is the bonus you expect to see from the project.

Which means?

very true Marigold.  I just fail to see the point of the mechanic, as it offers no value, except for the trivial 1% pointed out above.  

It would be a more useful mechanic to have Research Project simply put 100% manpower, except current economic, into research.  Cancelling this option puts it back the way it was before.  Same for economic stimulus, moving current manufacturing manpower all to economic.  I think we have all been in the situation where we were about to run out of money, or need to tech rush for a dozen turns or so, and need to max out a planet.  Fully agreed that long term, you never want to stop manufacturing, but desperate times can call for desperate measures.

The sliders are an arse pain, and I am sure the original intent was to reduce micromanagement, which it offers no value, except for the trivial 1% (which I'm sure was not design intent in the first place).

Back at some point in beta, Research Project and Economic Project gave a flat +1 rather than 10%. If my understanding at the time was correct, the project bits were to aid non-specialized planets (ex. factories+labs or factories+markets), or possibly giving factory specialized worlds something to do when not building things. However, in effect they ended up making non-specialized planets more powerful than specialized ones based on pure research/credits produced, never mind the benefits from factories aiding how quickly one could build more improvements. As a result, they were changed to being a percentage value, like Birthing Subsidiaries, but were made functionally useless due to this, yet for whatever reason these two projects were left in this state.

Due to this, I second dansiegel30's suggestion and additionally propose that Economic Stimulus and Research Project are unlocked from the start if it were implemented.

Based on my soak observations, the AI uses birthing subsidies almost exclusively. Note that I said almost.

Sometimes the AI does not yet have the tech that you want. Plus if you play with tech trading disabled...

And certainly OP  On a game I accidentally disabled it, I was surrounded by the bad guys, and all 3 DOWed me by turn 75.  Fook that!