It costs 1218 AP.
This is very much.

And what is the full cost?
I mean, the cost of the 2% increments until the maximum 25%.

Worth it?
There are many cheaper more useful advancements.
How long does it pay off?

Next steps are 200, 300, 400 ... 1100 for final 25%, for total of 7718 AP.

Not totally sure about ROI but I estimate it to be around 55,000-65,000 AP earning required to break even as you ramp up over each level (eg: earning +5% when you first buy it, then playing more, getting 7%, until you finally can play levels to get the fully unlocked +25%). So it's a losing AP adv for a LONG LONG LONG time, so you should only pursue maxing this out if you're committed to finishing all Idle levels multiple times over.

Break even for 5% is 24360 AP. if you purchase the first advancement, you should purchase the next two upgrading to 9%, which has a break even at 19089 AP. From there upgrades return less, upgrading to max has a break even at 30872 AP.

Thank you very much the information guys.

20-30k AP need for break even?
Terribly long ROI then!
You have to complete lots and lots of idle levels for that.
Months...

So I stopped saving AP for that advancement, and bought the Auto-Upgrade Army Camps.
Well, it cost me less than 700 APs and I already earned 1200 APs with it in minutes with a few clicks!
What a ROI difference!
I think I did a good deal :-)

@DJ Storm

You've oversimplified the math to a point where it's not accurate. 30872 is what the ROI is if you have 7718 AP available right now and spend it all on that AP Adv to max it out before playing anymore maps.

However, for us real folk, you can't just instantly "upgrade to max" (costs 7718 AP) and start earning @ +25% AP. You need to earn 1218 AP, upgrade to 5%, play more maps to earn more AP, upgrade to 7%, play more maps, upgrades to 9%, etc, so you need to ramp up your % returns based on the maps you're playing. Bigger maps that return more AP will get you to higher %'s quicker, but will have thus returned lower bonus AP % compared to a slow step up of completing maps just big enough to get the next upgrade level.

Either of these methods reduces the efficiency and thus extends the amount of AP you need to earn to achieve ROI.

That and the baseline is better then you’re giving it credit for - had you put the AP into better army camps or whatever you would be earning AP faster.

Doing the math, the break even point for buying it all at once is: 30,872 AP (as previously stated)

Buying upgrades the moment you have enough AP with 100% efficiency is: 34,945 AP (anything less than 100% efficiency will obviously take more)

Given the dramatic decrease in AP for completing levels, I don’t know if it’s even possible to earn that much AP in the first place.

Unless the rumors of the maps resetting once you beat them all prove true. Can anyone confirm this?

Someone in GC confirmed that completing all maps resets the AP for each. I have 7 maps left to go, so still a while before I can confirm first-hand.

That said, I'm banking on this premise being true, and thus I'm on the quest to max out this AP Adv under the premise that AT SOME POINT IN THE DISTANT FUTURE, this will generate more AP than investing in other AP Adv first. If not ... the joke's on me.

That’s good to know, thanks.

The only problem I see is the math doesn’t factor in the AP received from beating levels faster by getting useful upgrades.

There's a lot of factors the math doesn't account for, like winning AP/artifacts from WZIB to improve completion speed of both levels & getting the next AP Adv level, people who buy +30% AP at end of level, outright purchase of artifacts, whether you complete only the next absolutely smallest level to get to the next AP Adv level vs completing the biggest level available, etc.

Lots of factors at play so a single best method isn't really clear.

Agreed. There are a lot of factors. In the long run, AP boost is likely worth it. It just happens to be the LOOOOOOOOOOONG run before it breaks even.

So LOOOOOOOOOOONG in fact, that most people will finish all WZI levels and stop playing anymore before they ever reach the ROI point.

Thanks for pointing out my mistake.
To fully max out Increased AP, you need 1218 AP to unlock, then 190.48 standard AP (translating to 200 AP at 5% increase), and so on up to 894.31 standard AP (translating to 1100 AP @ 23% increase), for a total of 6806.76 standard AP (7718 accelerated AP).
You should ask yourself: should I put the next 6800+ AP in increase AP advancement, or in something else? Unlocking and maxing out Increase draft sizes costs 3405 AP, half of the above amount. True, you will need only 2724 standard AP ( equivalent to 3405 AP @25%), but are you willing to grind through a dozen levels without IDS just to eventually save 680AP in the end? Replaying U.S. gives 840 AP, and IDS saves more time in 10-12 games than you'll waste replaying one.
Apply the same thought process to Mercenary Camp sizes, you'll find you'll rather spend AP there.
So, I will invest in Increased AP only when there's nothing else better to invest in.