Playing Idle now for several weeks (reached Fort Harbor recently).
When I try to calculate different options for best effort, I struggle with the techs:

So my last army-camp tech-upgrades tell me:

Increase armies given from army camps by 20%

but my army outcome went from 14.2 k/sec to 15.1 k/sec and right now from 30.0 to 31.9

same with increase ore production of mines:

Before a 20% upgrade Gaspo produced 23/s and after 25/s.

I expected my last army upgrade jumping from 30 to 36, and the mine upgrade from 23 to 28 (27.6)

What is wrong here?

Your previous upgrades stack with your current upgrades, based on your case.

reality is often disappointing

Can you please stop adding off-topic stuff here. Thanks.

Can you please stop adding off-topic stuff here. Thanks.

Edited 8/16/2021 12:06:26

Upgrades stack before they are multiplied with the base income

So if you have +15% from tech 1, +15% from tech 2, +20% from tech 3, +50% from your advancements and +25% from an artifact (just some random numbers), you would get a multiplier of: 1+(0.15+0.15+0.20+0.50+0.25) = 2.25

Without that last +20% tech, you would get a multiplier of 2.05, so the actual increase in multiplier is +9.8% and not the +20% you think you're getting.

The same general theme exists for reduction, where you get less reduction as you might think, but this time because the percentages are actually multiplied instead of added up. But some might say that this is more intuitive, so less players will wonder why two 50% reductions won't get you instant smelt times for example. But just for completeness I thought I should add this here. Increments are added (see JK_3's post) reductions are multiplied (so, two reductions by 50% result in a reduction BY 75% and TO 25%). Generally, you can assume that the game chooses the approach that helps you the least. But at the same time, prevents the game from being exploited. If reductions were additive, all those effects would be drastically nerved such that you were never able to reach 100% reduction.

Upgrades stack before they are multiplied with the base income

So if you have +15% from tech 1, +15% from tech 2, +20% from tech 3, +50% from your advancements and +25% from an artifact (just some random numbers), you would get a multiplier of: 1+(0.15+0.15+0.20+0.50+0.25) = 2.25

However, 20% bonus from watching ad is exception here, as it's 'real' 20% (that may be a bit misleading)

Without that last +20% tech, you would get a multiplier of 2.05, so the actual increase in multiplier is +9.8% and not the +20% you think you're getting.

It would be nice to see both numbers in game

With the Statistics advancement (on stage 2 I think) you get the Modifiers dialog on the Army Camp tab that shows you the current percentages. This won't give you the 9.8% number but if you are willing to spend some AP you get pretty close to seeing all those numbers. They can still be a bit confusing, though.