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Thoughts: Effects of Artifacts, related to Time: 8/30/2021 14:39:04

Level 25
Composing a draft about... Thoughts on the effects of artifacts, but related to time and not specifically armies.

There's a lot to talk and think about, and calculations take time. So I'm just going to dump some text here and update more later. Feel free to add input, give feedback, etc. This started with me wanting to ask here on the forum if BMB was actually better than Mine Boost; but this turned into a thing where I wanted to talk about actives. And if I'm going to do theorycrafting, calculations, and other stuff, may as well share with the community as well, eh?

I read a post that functor wrote (see below) about the different effects of artifacts. The measuring standard that was used was armies ("billion equivalent armies per 16 hours"). Armies are indeed meaningful, because ultimately a lot of WZI revolves around reaching a state of the game where the armies that you generate (along with effects of Hospitals, Joint Strike, etc.) must reach or exceed the map's army value. A lot of strategy that I see being advocated for and effectively used then involves Supercharge Army Camp earlygame and midgame, and Mercenaries and Hospitals midgame and lategame. Universally, SAC and Joint Strike are well-liked and for good reason.

But something about that post didn't quite sit right with me because a billion armies earlygame on a map can be worth something quite different than a billion lategame. Even when talking about the value of something midgame, we can't disregard its usage earlygame or lategame.

And another thought popped up; instead of using that measurement, perhaps using time instead? It's more meaningful if we're looking at how fast/slow each map can be completed using different advancements and artifacts.
i.e. If a map without any help can be completed in 3 days, and comparing two artifacts gives us different completion times of 1 day for one artifact and 2 days for the other, then we have a better idea of which artifact is "better". Instead of asking "How many armies is this worth?" we ask "How much time is this worth to me?"

We can then measure certain advancements and artifacts a bit better. In the future we can better map out when during a level that advancements or artifacts are the most effective, and which ones are effective when we consider idle vs active time and different playstyles. We can also then better determine at what point we should stop upgrading certain artifacts (especially certain actives!) if there are diminishing returns.

To support the above, let's humor this idea and take a moment to think about SAC in a vacuum, at its extreme.
At Insane, it will x20 a camp for 8h, and has a cooldown time of 16h.

Let's consider that we're playing a map where army count is the only thing that matters. No mines, mercs, etc. Just 1 army camp and you need to reach a certain value of armies to win. The win condition is that after a certain time has passed, your army value will exceed the value on the map.

In the span of 48h, you get about 24h of supercharge (3 charges per 48h). If you are sitting on only 1 camp, then in that entire span of 48h your armies are being virtually generated at x10 speed, and we can consider your time is accelerated x10. At its peak and ideal conditions then, constant usage of SAC accelerates us at x10 time.

But is this actually useful? WZI maps aren't like this, right?
Well, there's one state of the game where the peak and ideal conditions for SAC are there: earlygame, when you only have 1 camp and the only thing that you can do is use your armies to conquer territories. You can only reach midgame and other interactable features once you breach a certain army count; and into midgame, more and more camps and other features will change the conditions upon which you use artifacts.

Another post by graeme (see below) was discussing his quest for good active artifact usage, because the new update gives us access to a 4rth slot specifically for active. He correctly identifies that SAC is strong early, accelerating time at x10 in ideal conditions; and touches upon active artifact usage at different stages of the game, but he seeks a singular artifact to beat them all. But because he seeks a single active artifact (and at specific tiers) to solve them all, he can't come across a solid answer, because different artifacts are powerful at different stages of the game (and powerful with different playstyles).

So what's our solution then? We identify when artifacts are ideal to use, who uses them best (playstyle, active or idle), how to best squeeze an active for what it's worth. We can also try and find how high of a tier that we should upgrade each artifact to get the best use out of each one then. We use time that each artifact contributes to you to measure all of this.

At this moment, I might measure each artifact to have a value of accelerated time. But perhaps I might consider how many seconds worth of time that it's giving you with its usage.

24h = 86,400s
16h = 57,600s
8h = 28,800s
1h = 3,600s

Alternatively, I might potentially assign an estimated time value to each map; as some artifacts might be better measurable as a portion of a map's time rather than having a specific time value in seconds.

It'll take a while, but if I have free time I might examine each active artifact (and maybe even the passives), and see where we go from here.

List of Artifacts. (tentative. do I really want to do this?)

(( [value of all camps] - [original value of SAC'ed camp] ) + ( [ original value of SAC'ed camp] * 10) ) / [number of camps]

See below, if we calculated by if each camp has the equal value of 1 (and we can also see how the more camps we have, the less powerful SAC becomes). We also see that if we can frontload our upgrading into 1 camp, it delays SAC falling off in the midgame slightly.

(Camp #) = (Accelerated Time)
1c = x10.0
2c = x5.50
3c = x4.00
4c = x3.35
5c = x2.80
10c = x1.90
20c = x1.45
30c = x1.30
40c = x1.23
50c = x1.18

functor's post: Objective effects of artifacts

graemes' post: ‘Discount Hospital’ Active Artifact
Thoughts: Effects of Artifacts, related to Time: 9/1/2021 06:21:03

Level 56
Using accelerated time to evaluate artifacts/advancements is surely a better way. I shared a formula I once used in the following thread, and I am actually using a modified version of it myself.

However, the issue with accelerated time is that it depends too much on the territories that the player has conquered in a level. Even players with the same artifacts/advancements/strategy could obtain vastly different conclusion. For example, if the players do not have enough mercs caused by not Joint Strike enough, then the formula would tell the players that Inspire Mercenaries is totally useless, while in reality, getting mercs could help a lot for a player who did not waste armies.

Using equivalent armies in unit time also has a similar issue, but, players with similar artifacts/advancements/strategies and similar percentage of conquered territories should have similar results. Note that we are not supposed to take the data taken in the middle of a level to evaluate the effects of artifacts at the very beginning of a level.

Edited 9/1/2021 06:22:52
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