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There are many posts in this forum discussing the effects of artifacts. Here, I want to discuss them more objectively. I will compute the effects of artifacts in 16 hours in terms of equivalent armies. More precisely, effect = equivalent armies in 16 hours with the artifact equipped/used - equivalent armies in 16 hours without the artifact. The formula to convert money to armies is "army = money / mercenary cost".

Remarks:
* Only artifacts that need to occupy a slot are taken into consideration. I treat Smelt/Crafter Double as such artifacts.
* I skipped some artifacts for which I do not know how to calculate. If you know how other artifacts work, I would love to calculate their effects.
* The effect depends on level, techs, advancements, and play style. The data I give below is taken in the middle of the level Scandinavia. So, even if the effect of one artifact is better than the other one below, it may not apply to your situation. But, if one artifact is significantly better than another, then the former one should be at least slightly better than the latter one for everyone.
* You are encouraged to share the effects of your artifacts on your level and with your techs and advancements. So, we can compare and find universally good artifacts.
* I will only compute the effect of rare artifacts. You can do it for other rarity if you like.
* Some artifacts may have combos. In other words, the effect of A+B may be better than the effect of A + the effect of B.
* The unit of the effect is "billion equivalent armies per 16 hours".

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Effects
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Speedy Crafters: 15.40
Time Warp: 3.31
Craft Double: 3.11
Inspire Mercenaries at 10B camp: 1.41
Quadruple Strike at 2B territory: 0.72
Army Camp Boost: 0.66
Tripe Strike at 2B territory: 0.60
Territory Money Boost: 0.54
Efficient Crafters: 0.49
Bonus Money Boost: 0.37
Supercharge Army Camp: 0.21
Field Hospital at 2B territory: 0.18
Damage Territory at 2B territory: 0.18
Supercharge Mine: 0.10
Mine Boost: 0.03
Speedy Smelters: 0.00
Smelter Double: 0.00
Efficient Smelters: 0.00

Combos:
Speedy Crafters + Time Warp: 19.68
Speedy Crafters + Time Warp + Craft Double: 24.09

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Conclusion
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We can see that Speedy Crafters, Time Warp, Craft Double are much better than other artifacts for me. The best combination of artifacts occupying the slots for me is Speedy Crafters + Time Warp + Craft Double.

Edit: Fix some calculation errors.

Edited 8/10/2021 02:59:41

SC: 15.40 = Super charge armie Camp?
TW: 3.31 = Time Warp?
CD: 3.11 = ???
IM at 10B camp: 1.20 = inspire Mercanaries
QS at 2B territory: 0.96 qutrro Strike
TS at 2B territory: 0.80 Tripple Dtrike
ACB: 0.66 Armie camp boost ?
TMB: 0.54 = Terittory Mones bost
BMB: 0.37 = Bonus money bost
DT at 2B territory: 0.24 = Damage teritory
FH at 2B territory: 0.24= Field Hospital?
MB: 0.03 = ???
SD: 0.00 = ???

can u help me? Correct me?

I have updated the post. It gives the full names of artifacts now.

I've done the calculations myself using my current level data. The numbers and conclusion are very different from yours. Quadruple Strike is by far the best. Bonus Money Boost is the best passive artifact for me, even better than Speedy Crafter, which is radically different from your numbers showing Speedy Crafter being 42 times better than Bonus Money Boost.

I guess these numbers really differ by a lot depending on the level, playstyle and advancements.

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In the following calculations, we assume that all artifacts are at Rare rarity, and all items are sold together with a Rare Items Values artifact (which is an artifact that I have).

I'm near the end of the Afro-Eurasia Gargantuan level.

The unit of the effect is "billion equivalent armies per 16 hours".

Quadruple Strike at 75B territory: 36.00
Tripe Strike at 75B territory: 30.00
Inspire Mercenaries at 127B camp: 15.24
Field Hospital at 75B territory: 9.00
Damage Territory at 75B territory: 9.00
Bonus Money Boost: 8.15
Speedy Crafters: 7.24
Time Warp: 5.65
Territory Money Boost: 3.24
Craft Double: 1.73
Efficient Crafters: 1.57
Army Camp Boost: 1.49
Supercharge Army Camp: 0.92
Mine Boost: 0.92
Supercharge Mine: 0.50
Speedy Smelters: 0.00
Smelter Double: 0.00
Efficient Smelters: 0.00

Conclusion: Just looking at my numbers, it's tempting to conclude that Quad Strike is the best. However, there's only one 75B territory on the map. The second most expensive territory on the map is 14B.

As you can see, for one-time use, Quadruple Strike is the best for me. For multiple use, Inspire Mercenaries, Bonus Money Boost and Speedy Crafters are the best for me.

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But the above calculations assume that all artifacts are at Rare rarity, which is not the case for me. Using the rarity of the artifacts that I actually have, here's the numbers:
Bonus Money Boost (legendary): 32.62
Speedy Crafters (rare): 7.24
Territory Money Boost (epic): 6.48
Army Camp Boost (epic): 2.97
Damage Territory (common) at 75B territory: 2.25
Mine Boost (rare): 0.92
Craft Double (uncommon): 0.87
Efficient Crafters (uncommon): 0.79
Supercharge Mine (uncommon): 0.25
Speedy Smelters (uncommon): 0.00
Smelter Double (uncommon): 0.00
Efficient Smelters (uncommon): 0.00
I don't have other ones

And yep, I'm equipping Bonus Money Boost, Speedy Crafters and Territory Money Boost right now, which are my best 3 artifacts according to the numbers.

Here's some thoughts about similarities between my numbers and functor's numbers, and potential reasons behind the differences.

Similarities:
-Speedy Crafters and Time Warp are good passive artifacts for both of us.
-Inspire Mercenaries and Quadruple Strike are good active artifacts for both of us.
-Mines, smelters, army camps are trash for both of us.

Differences:
-The numbers for some active artifacts are disproportionally large for me.
-The two Money Boost artifacts work very well for me. They don't work well for functor.
-Crafting works very well for functor. Crafting still works decently for me, but not as extremely well as it is for functor.
-And of course, the biggest mystery is the Bonus Money Boost vs Speedy Crafters comparison.

Potential reasons behind the difference:
-Obviously my active artifact numbers are heavily affected by the design of the map. Having a stand-alone 75B territory messed up the numbers a lot.
-I maxed my Increased Money from Bonuses advancement, but my Increased Item Sell Values advancement is only at 30%.
-Expecting a 2-3 day level time, I didn't upgrade my mines much because I don't expect them to have a lot of time to pay me back. As a result, my smelters are kind of useless because there're not enough ores to feed them. Almost all of my crafters work on materials being bought from markets, which decreases the actual profit by a lot. And I cannot work on any late-level recipes because the relevant bars are either too expensive to be bought from markets or simply not being available in the markets.
-I'm near the end of the level now, but for of reasons stated above I'm still working on early-level recipes. So, my bonus and territory income reflects end-level income, while my crafting recipes reflects early-level income. Meanwhile, functor's data is from mid-level Scandinavia.
-In the tech tree, I focused on the "Increase size of caches by 50%" line and the "Decrease the cost of mercenaries by 15%" and didn't care about anything else. So I'm missing out some techs that help with ores and crafting.
-Given that functor's data was from mid-level, maybe it consisted of lots of paths going towards hospitals and other useful targets while not a lot of bonuses were being completed?

While I've listed a lot of potential reasons for the difference, it still feels weird that Speedy Crafters is 4060% better than Bonus Money Boost for one player, and being actually worse than Bonus Money Boost for another player. 4060% is a lot. Not sure if the reasons I've listed above are adequate to explain a 4060% difference.

Oh BTW I have never used a territory army reduction artifacts like Quad Strike and I have no idea whether they work additively or multiplicatively with Joint Strike, so the numbers can be off by 25%.

another quite big difference can be what you use as "mercenary cost" to convert money to army equivalents. Is it the current lowest merc cost or the average, or what have you? This seems to be a likely reason, too, why TS and QS perform such drastically different to SC, because TS and QS immediately save armies while SC has to be converted with this division. And depending what you use as your merc cost, all money based artifacts can either be drastically nerved or buffed.

The minimum percent saved are as following assuming the the territory has 4 connections, we do not have a hospital yet, and we have maxed out JS:
Poor: 26.5% for Damage Territory, 28.75% for Triple Strike, 29.5% for Quadruple Strike.
Common: 27.25% for Damage Territory, 32.5% for Triple Strike, 34% for Quadruple Strike.
Uncommon Same as Poor Quadruple Strike for Damage Territory, 40% for Triple Strike, 43% for Quadruple Strike.
Rare: Same as Common Quadruple Strike for Damage Territory, 55% for Triple Strike, 61% for Quadruple Strike.
Epic: Same as Uncommon Quadruple Strike for Damage Territory, 85% for Triple Strike, 97% for Quadruple Strike
Legendary: Same as Rare Quadruple Strike for Damage Territory
Insane: Same as Epic Quadruple Strike for Damage Territory

Reason why I did not include how much armies saved for Legendary and Insane for Triple and Quadruple Strike is because they are already above 100% and it would be pointless to include them.

@Mathematician

All the reasons of the difference between BMB and SC you listed are probably contributing factors.
* I do not have Increase Money from Bonuses, and you max it out. This explains a 2x difference.
* I work on late-level recipe, and you work on early level recipe. Crafting Explosive Bolt gives me 56B/16h, but crafting Tin Can would only give me 10B/16h. This may explain a 5.6x difference. (It is not very accurate to compare recipes from different levels though.)
* My data is taken at about 50% of the level, and your data is taken at about 100% of the level. For simplicity, let us just assume that BMB scales with the percentage. Then, this explains a 2x difference.

From what I heard in global chat, the effects of QS/TS/FH/DT, just like hospitals, are calculated before Joint Strike. The numbers of these four artifacts in my post take this into consideration.

QS (rare) is still decent when we apply it to the 14B territory you mentioned. The effect would be 5.04. This is not high enough to be used for you at this moment, since you have BMB (leg), SC (rare), and TMB (epic). I can see that a QS (epic) would be a good replacement of TMB (epic). Another candidate is TW (epic).

A small correction: Time Warp is an active artifact.

@Phoenix

With the data of mercenary camps accessible to me in a level, I make a guess on the average mercenary cost of the level. You are right that the differences of average mercenary cost of different levels, and the deviation of guess and actual number, also contribute to the difference between BMB and SC observed by Mathematician.

Even though these don't occupy a slot, curious how hospital boost, item values weigh. @functor

Hospital Boost is useful if you're willing to do the swapping. Similarly, so are the Money/Resource/Army cache boosts. But none of them are deal breakers if you're too lazy to do the swapping. And sometimes I just couldn't be bothered, lol.

Item Sale Value boost is unquestionably excellent. I have Rare @ 16% and it gives great value. I have the Increased Item Sell Values advancement @ 30% ... so maybe when I get that to 100% the artifact won't have quite the same kick, but right now it nicely boost the value of my E Bolts, and it's only a quick swap at time of sale.

That said ... measuring HBoosts in Functor's system can be done b/c they both easily translate to armies. HB for # of armies saved by using it, but it's a % of hospital savings so not a fixed figure. And ISV based on what you're selling to get money which is then used to buy mercs = # of additional armies able to bought by equipping it.

Oh BTW I have never used a territory army reduction artifacts like Quad Strike and I have no idea whether they work additively or multiplicatively with Joint Strike, so the numbers can be off by 25%.

QS & TS work differently than JS.

For example, for a 100M territory, with hospital benefit of 10M:
- For JS alone w/o TS or QS, you need the full 100M to capture it, then the hospital units are subtracted (brings it to 90M), then 25% of the remainder is credited back (JS savings 22.5M). Total savings = 32.5M.
- For TS or QS, you only need as many units after the subtraction for TS/QS. So for 48% Rare QS, you only need 52M to capture it, then from the 52M your hospital discount is subtracted (brings it to 42M), then 25% of that remainder gets credited back by JS (10.5M in JS savings). Total savings = 68.5M.

So you see that despite saving 48M from the QS, it also reduces the value JS returns (down from 22.5M to 10.5M), so it is diluted a bit. It would be pretty epic if the JS was credited from the original territory amount, but alas, WZI math is (almost always) executed so that players get the least possible benefit. If summation gives less benefit, summation is used (like when adding positive bonuses together such as sell values or army camp buffs, etc); if multiplication gives less benefit, multiplication is used (such as when calculating discounts on merc costs or crafting times, etc). And when the two are mixed, the order is arrange to give the least benefit, so in the case of hospitals and JS, it gives less benefit to take the hospital discount off first and then do the JS rebate then the reverse (take JS from total, then subtract hospital discount), so it is done that way. And the TS/QS is an extension of that, first take the TS/QS discount, then the hospital discount, then the JS rebate. Taking the hospital discount before the TS/QS would be higher benefit, so is not done that way.

Another oddity is that (so far as I'm aware) the units saved from TS/QS (and Damage Territory as well) are never accounted for in any of the stats. They aren't counted in total armies earned, army camps, mercs, caches, drafts or hospital counts. So they are just removed from the territory and lost in the ether, never accounted for.

Field Hospitals factor into the equation as well, don't recall exactly but likely after the natural hospitals are subtracted (b/c that would give the least benefit, but I don't have an example handy to verify it).

I suppose while we're on the topic ... DT works by simply reducing the armies on the actual territory by the % indicating. No relation to hospitals, JS, TS, QS, FH. What distinguishes DT is that it can be used on the same territory multiple times (but I wouldn't recommend this) and it can even be used on a territory you don't have access to but you do have visibility to (via FB, etc). So if you play Europe Huge, FB the whole map, you will be able to see the 404B territory, and you could instantly DT it to 307B with a 24% Epic DT, do it again in 16h and repeat as you see fit until it's small enough for you to capture normally. I don't recommend this ... but some have said they have had success with this approach.

Edited 8/8/2021 06:11:05

@megaol

Let us assume that we conquer 300 territories in 16 hours. Then the effect of Hospital Boost (Rare) is 3.48.

@krinid

The effect of Item Values (Rare) is 6.60.


* Note that the above effects are only for me, on Scandinavia. Your mileage may vary.

I’m beginning to get a sense that ultra-late game WZI is just a race to find the platinum market and the E-bolt recipe, then abusing Speedy Crafters + Item Values advancement and Item Values + Craft Double + Speedy Crafters artifacts to make ridiculous amounts of money.

Are we sleeping on Recipe Visibility and Market Visibility? Are these part of an ultra late-game build out where you don’t even bother to complete bonuses you just beeline straight for E-bolts?

The problem with recipe & market visibility is that it tells you that there's a recipe and market there, but not which recipes & what's in the markets. So you don't know if you would be beelining to a Fuse, Diode, Circuit (non-profitable garbage recipes), markets that sell copper, copper wire, barbed wire, titanium, thorium aluminum, etc (not platinum) . . . so you could never accurately ascertain the position of E bolts & platinum.

Change those Adv's so they reveal the content and not just the location, and they could add value.

And for the record, I try use to FBs and do my beelining in the mid-game, not the ultra late game. Yep, ignore bonuses to get the goods (recipe, market, enough crafters), then craft craft craft. And if not using FBs, just explore wisely. Start with tin cans, then upgrade to welding rods, rivets, bolts, structs, boiling flasks, e bolts as quickly as possible. On a good level (placement of items, ability to locate & get to the items), I transition directly from tin cans to e bolts, but some levels make this just too difficult and I need 1 or 2 intermediate crafting steps - which ones depends on what is available to smelt, available from markets & the profit margins or each.

Yeah I’d agree with this tweak to the visibility advancements. To be clear, I’m talking ultra-late game here, multiple Level 4 advancements, beyond the point anyone is at.

The issue with how the visibility advancements work now is that people are inevitably going to create a database of where these key recipes and markets are which really defeats the purpose entirely.

Adding some data from the middle of Europe 1066 (500/955 territories conquered) on first Ascension.

Summary:

Speedy Crafters:            0.55
Quadruple Strike:           0.43
Triple Strike:              0.36
Army Camp Boost:            0.27
Supercharge Army Camp:      0.24
Supercharge Mine:           0.20
Mine Boost:                 0.17
Territory Money Boost:      0.13
Time warp:                  0.12
Damage Territory @ 1.2B:    0.11
Field Hospital @ 1.2B:      0.11
Craft Double:               0.10
Bonus Money Boost:          0.06
Inspire Mercenaries @ 0.5B: 0.06

Efficient Crafters:         0.00
Smelt Double:               0.00
Efficient Smelters:         0.00
Speedy Smelters:            0.00

Some additional details for specific artifacts:
I used a price of $10/A for Mercenaries. This is a little bit arbitrary (and generally, on the cheap side), but makes the math easy to scale to whatever value you prefer.

Speedy Crafters:  
# 4 crafting tin cans, 1 item sell tech, 1 speed up tech
$36e6 * (1/ 375s - 1/500s) * A1/$10 * 16 * 3600 * 4 = A0.55e9

Craft Double:
$36e6 * (1 / 500s) * A1/$10 * 16 * 3600 * 4 * 0.06 = A0.10e9

Inspire Mercinaries:
# +15% extra mercs, largest I've captured so far has 496e6 available, hence the low value

Army Camp Bonus:
# +90% advancement, +45% tech
(A32.67e3 - A27.918e3) * 3600 * 16 = A0.27e9

Territory Money Boost:
# I don't know the actual formula to use here, so I guessed it is multiplicative and scaled based on the value difference for an uncommon
# 30% tech, no advancements
# 158.76e3 vs 141.785 for uncommon.
(A158.76e3 - A141.785e3) * 2.0 / 1.5 * 3600 * 16 * A1/$10 = A0.13e9

Bonus Money Boost:
# Similar to TMB, I scaled multiplicatively from the value of a common
# 20% tech, no advancements
# 149.923e3 vs 141.785e3 for common
(A149.923e3 - 141.785e3) * 1.4 / 1.1 * 3600 * 16 * A1/$10 = A0.060e9

Supercharge Mine:
# +40% output techs, +80+30% sell value (advancements, tech)
# Scales additionally with minimal time effort using ore sell cost artifact at sell time
$28.271e3 * 20 * 3600  * A1/$10 = A0.20e9

Mine Boost:
# +40% output techs, +80+30% sell value (advancements, tech)
# $208e3/s tot, compared to $141e3/s from bonus & territory
# Scales additionally with minimal time effort using ore sell cost artifact at sell time
$29.149e3 * 3600 * 16 * A1/$10 = A0.17e9

Commentary

* In terms of relevant artifacts to use, I have ACB, MB @rare and SC, TMB, SAC @uncommon. The above math confirms my intuition that upgrading Speedy Crafters next is probably the best option, though SAC looks surprisingly strong too.
* I'm not sure how @functor got such a small value from Mine Boost - is this just a level difference? Mines don't appear to be particularly valuable in Europe 1066, so I haven't been focusing on them as much this level compared to crafting.
* The "value" for DT / QS / TS / FH are all inflated IMO since I don't really want to capture the 1.2B territory right now since it will bring significantly less total benefit than capturing multiple smaller territories.
* My main takeaway is that the active artifacts will be useful one day, but, since they only apply during certain parts of the level (apart from SAC, which is super strong at the beginning), they aren't worth upgrading for now.
* I've been favoring MB over TMB and BMB as an early game money generator since it also speeds up key techs. It also works nicely with hospital strategies where you only want to capture the minimum set of most valuable territories before upgrading them. The math seems to confirm that this is justified, at least at this point in Ascension.
* For comparative purposes, I beat Fort Harbor in 6days 1 hour real life time. I have 4 total hours of idle time, so play time tends to be about 18hrs / day (sometimes lower if I have other stuff to do).

EDIT: My math is almost certainly wrong on TMB and BMB calculations - should I just be scaling my common value by 4 for BMB and the uncommon value by 2 for TMB? That gives updated values of 0.20 for TMB and 0.19 for BMB, which makes more sense (though I would still favor MB for the tech speedup aspect).

Edited 8/8/2021 21:22:22

@EarlTrybicowyll

> In terms of relevant artifacts to use, I have ACB, MB @rare and SC, TMB, SAC @uncommon. The above math confirms my intuition that upgrading Speedy Crafters next is probably the best option, though SAC looks surprisingly strong too.

It is great that this helps to confirm the best artifacts for you. I would like to remind you that there are other good artifacts which do not need to occupy a slot constantly, and you may also want to have a look at them.


> I'm not sure how @functor got such a small value from Mine Boost - is this just a level difference? Mines don't appear to be particularly valuable in Europe 1066, so I haven't been focusing on them as much this level compared to crafting.

There are certainly level differences. But, I think the main difference comes from the play style. I usually do not get mines until I have upgraded hospitals a lot. My data is taken in the middle of Scandinavia, and at that time, I only had a very limited amount of early mines.


> The "value" for DT / QS / TS / FH are all inflated IMO since I don't really want to capture the 1.2B territory right now since it will bring significantly less total benefit than capturing multiple smaller territories.

One factor that you may have overlooked is the drafting. The limit of the sliding portion of the drafting is 15% of total armies earned (after the drafting). So, for every 1 army earned, either from army/merc camps or caches, we get 0.176 additional army from drafting. This will increase the scores of "boosting artifacts" by 17.6%. If we only care about the "boosting artifacts", then we can simply ignore it, since the same constant scalar is applied to all such artifacts. Meanwhile, for the "saving artifacts", such as DT/QS/TS/FH, they do not enjoy this 17.6% benefit.

Another tip I have is on where to use DT/QS/TS/FH. I do not think it is a good idea to apply them to a random territory. Instead, we can use them on important territories, such as the ones containing very good recipes, or some huge stack like the 401B one in the last level Europe Huge.


> My math is almost certainly wrong on TMB and BMB calculations - should I just be scaling my common value by 4 for BMB and the uncommon value by 2 for TMB? That gives updated values of 0.20 for TMB and 0.19 for BMB, which makes more sense (though I would still favor MB for the tech speedup aspect).

Your updated calculations 0.20 for TMB and 0.19 for BMB look more likely to be correct.

The issue with how the visibility advancements work now is that people are inevitably going to create a database of where these key recipes and markets are which really defeats the purpose entirely.

Careful, you! You going to get the levels regenerated again, then all the databasing is garbage.

Seriously though, sooner or later, the levels will likely be regenerated. So just enjoy the accurate data in the interim while you can.

Also, if the visibility items were more useful, people would actually invest in them & use them, and then we wouldn't need to database items. You could say that lack of good (efficacy as described in this thread), accessible (low phases) & affordable (doesn't cost too much AP) visibility Advancements at least partially drives the desire for databasing.

Careful, you! You going to get the levels regenerated again, then all the databasing is garbage.

Levels just got regenerated.