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Cost Efficiency


doxthefox
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Introduction:

Today I shall introduce a concept called cost efficiency. Written in standard Shablagoo wall of text style with a scientific method twist, it is rather lengthy, but I assure you that it is very informative, but there is a tldr for those who don’t like reading. Now what exactly is cost efficiency you say? Cost efficiency is basically actual worth of an item by taking only base stats into consideration. A tier 3 item such as Argus Crystal for example consists of 100 int (ignoring passive for arguments sake), and is comparable to getting 16.66 temporal platings (the cheapest purest int item in the game).

 

Purpose:

Everyone has argued over which items are better than others and they normally understand why through playing the game enough that certain items are terrible, while others are perfect. Below I have posted some prime examples of items that people commonly buy and have broken down their efficiencies. The purpose of this analysis is to show which items are worth buying and which are not.

 

Calculations/Analysis:

Gravity Edge gives 70Int/20 dam/6%ms/35% true damage converter for 3600.

A breakdown of these stats gives us

285 (Temporal plating) = 6 int à 70/6 = 11.66 * 285 = 3325

325 (Quantum Spade) = 10 weapon damage à 20/10 = 2 * 325 = 650

No items for flat movement speed, but let’s say 4% = 350 (Old Shoes, might be 450 I forget)

 

We can conclude that although the 35% Unique True Damage doesn’t have a price, the total price of [3325+650+450 =] 4425 makes this item already cost efficient even without it’s passive.

 

Now let’s compare it to another famous int item known as the Argus Crystal, which gives us 100 int/ 20% bonus magic damage at 4150.

Applying the same principle we can see that

285 (Temporal Plating) = 6 int à 100/6 = 16.66* 285 = 4750. Thus it is already cost effective even without it’s passive.

 

The only known counter to true damage is obviously health and nothing gives us as much health as an Organic Carapace, which gives you 60 strength and 650 health (and 2.5% health regen for no damage taken after 5 seconds) for 4350.

When we break it down we can see that

475 (Emerald Mox) = 180 health à 650/180 = 3.611 * 475 = 1715

285 (Cybernetic Implants) = 6 strength à 60/6 = 10 * 285 = 2850

1715+2850 = 4565. Thus Organic Carapace is cost ineffective without its passive (requires 1 kill @ 300 gold to break even)

 

Another famous item used to counter casters for tanks is the Lifetech Nanosuit, which gives 450 health and 15% spell resist for 2700 and of course the volibear passive of being under 35% health a health regen of 30% of max health over time. Basically it’s supposedly the perfect blend between health and spell resist.

A breakdown of these stats yields.

475 (Emerald Mox) = 180 health à 450/180 = 2.5 * 475 = 1187.5.

425 (Mirror Plating) = 8% spell resist à 15/8 = 1.875 * 425 = 796.88

Thus, as we all expected it is extremely cost efficient at 1984.40 even without it’s passive.

 

 

Of course I cannot complete this small section without including the item known as Pyre for my Agil friends. At 3200, this item gives us 25% weapon speed, 30 Weapon damage and the newly acquired 6% of the enemies CURRENT health.

Let’s start the breakdown.

325 (Quantum Spade) = 10 damage à 30/10 = 3 * 325 = 975

425 (Focus Prism) = 8% weapon speed à 25/8 = 3.125 * 425 = 1328

1328+975 =2303. Thus Pyre is cost inefficient without it’s passive. Including’s passive though, the breakeven point can be found.

 

3200-2303 = 897 à 897/325 = 2.76 * 10 = 27.6. Thus, we need to average greater than 27.6 damage from the passive to be cost efficient (the item is very cost efficient against tanks who max health obviously, though I’m too lazy to provide the math at the moment).

 

Now my friend Aellectris (shout outs to Iliketrees) pointed out a while ago that one of the worst items you can possibly buy is a superheated mantle. A superheated mantle gives us 350 health, 7 armor (and 40 spell damage/second for everything in a 5 unit radius) for 2400.

475 (Emerald Mox) = 180 Health à 350/180 = 1.94 * 475 = 923.6

315 (Neosteel Vestments) = 2 armor à 7/2 = 3.5 * 315 = 1102.5.

At 923+1102 = 2025, it appears as though Aellectris is right about the cost effectiveness about the item statistically, except… the item is built from a gold per 10 item. This item costs 800 and gives us 5 gold for every 10 seconds.

 

Thus, 2400-2025 = 375 gold. 375/25 (you get 25 gold per minute) yields us 15 minutes. Thus the item will be able to pay for itself in 15 minutes without its passive. Since you generally get a gold per 10 item early and don’t evolve it to its final form for probably 15-20 minutes, it is indeed cost efficient even without it’s passive. Does this mean Aellectris is wrong though? A lot of you would like that I know =), but before we can make a conclusion we have to check out the other item that is rarely bought known as the Eternal Drive.

 

Now what is the Eternal Drive, O yea that’s right it’s the “other choice” we have from the gold per 10 screen. This item is popular amongst European’s noobiest Soedenone. Could this noob be onto something? Well, this item gives us 300 health, 15 weapon damage, 5 health regen, 1.5 energy regen, and a 20% max health percentage health over 15 seconds active for 2800. Wow that’s a lot of stuff! Let’s break it down.

475 (Emerald Mox) = 180 health à 300/180 = 1.66 * 475 = 791.66

325 (Quantum Spade) = 10 damage à 15/10 = 1.5 * 325 = 487.5

425 (Anabolic Circulator) 3 health regen à5/3 = 1.66 * 425 = 708.33

400 (Pulse Regenerator) .75 energy regen) à 1.5/.75 = 2 * 400 = 800

 

791.66+487.5+708.33+800 = 2787.49. That’s almost exactly the same as the cost at 2800 and that’s without considering the gold per 10 ratios or the passive. In the same 15 minutes you take to break even with a superheated mantle you can surely pay for this item and get yourself something else with the extra gold!

 

Limitations/weaknesses of this analysis:

Practically every item in this game has a unique passive that cannot be quantified with ease in terms of mineral worth. To actually quantify these results, I would require further details on the damage that some actives provide vs. flat (true) damage vs. armor vs. magic resist, which would be extremely complicated and time consuming. I leave that to men with much more knowledge about game mechanics.

 

Conclusion AKA TLDR:

Gravity Edge & Argus Crystal are OP, SHM is UP compared to Eternal Drive, which is a fair item, Organic Carapace is UP, Pyre is fair and Lifetech Nanosuit is OP in terms of cost effectiveness. This analysis can be done for every item though I only included the few items that immediately came to mind for the purpose of this statement. Obviously there are other must have items like a spell buffer, but an analysis would probably only prove what we already know, which is that it is an extremely cost effective item (OP).

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I think this is a good way to view item strength. However, an alternative interpretation of your calculations is that the base items (e.g. Temporal Plating) are either OP or UP. Still, we can make inferences about relative strength for items that have the same (or at least mostly the same) base stats. In other words, this is a good way to compare items like Organic vs. Eternal Drive or Argus vs. Gravity in determining which item is relatively stronger for its cost, but it's not a foolproof way to make valid comparisons of items that don't share the same base stats (e.g. Organic vs. Argus). Again, while it could be that one item is truly more cost effective than the other, an equally likely conclusion is that the base items being used to calculate cost effectiveness are not well-balanced (e.g., Emerald Mox could be more cost effective than Temporal Plating). However, this concern can be addressed if we have consensus relative stat values (e.g. x STR = y INT = z AGI).

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I think this is a good way to view item strength. However, an alternative interpretation of your calculations is that the base items (e.g. Temporal Plating) are either OP or UP. Still, we can make inferences about relative strength for items that have the same (or at least mostly the same) base stats. In other words, this is a good way to compare items like Organic vs. Eternal Drive or Argus vs. Gravity in determining which item is relatively stronger for its cost, but it's not a foolproof way to make valid comparisons of items that don't share the same base stats (e.g. Organic vs. Argus). Again, while it could be that one item is truly more cost effective than the other, an equally likely conclusion is that the base items being used to calculate cost effectiveness are not well-balanced (e.g., Emerald Mox could be more cost effective than Temporal Plating). However, this concern can be addressed if we have consensus relative stat values (e.g. x STR = y INT = z AGI).

 

This is true mathematically and I would have to alter my analysis if this were to happen for sure. There are also many other variables to consider such as the enemies base stats and enhanced stats from the items (thus why we counterbuy) and bonus stats like leavers bonus among many others. However, no matter what the mineral cost yields from the cost efficiency analysis, we can still see the gold difference when comparing each item in the same category as was the case with the SHM and the ED (erectile dysfunction dam straight) to show which items should be bought. There would still be a problem when comparing int/strength/agil stats obviously though, but I guess that's just another limitation. I'd say change the scaling of item prices to be more linear of course. Aside form all of that, if Red Hydra were to do something like lower the cost of an Organic Carapace (or change the base stats), change the passive of a GE to something that doesn't scale as out of control with int later game, [or buff Raynor the day of the next upcoming tournament without releasing the patch notes until after the tournament is finished with a 1k true damage ulti =)] I'm sure that the game would be a lot more balanced.

 

 

* In an unrelated note, I'd like to say FUK the sona that took my pentakill, I just realized I had an extra q after I ulti'd for the quadrakill! <3

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would be nice for you to continue this for other under used items

 

might i suggest guardian steel since i forgot that item even existed until last night. i might play around with it but the only hero i feel it is viable on is erekul.

Guardian Steel = 30 Strength 15 Int +4 Health Regen. (passive recovers energy = to 15% of received damage) @ 2235

285 (Cybernetic Implants) = 6 strength à30/6=5*285 = 1425

285 (Temporal plating) = 6 int à15/6 = 2.5* = 712.5

425 (Anabolic Circulator) 3 health regen à 4/3 = * 566.66

 

1425+712.5+566.66 = 2704.17 >> 2235. Thus, the item is cost effective even without its passive.

 

Further Elaboration on cost effectiveness:

An analysis would need to be taken for every item in the game to see how they rank against each other before we can say which are the best items for cost efficiency, but there’s another issue that may skews the stats now that I think about it some more. So, basically if I’m remembering this correctly health regen is based on your health and health is proportional to strength in some way. (Similarly you get armor from Agil stats and mana regen for int.) I’ve wondered for a while what the ratios were for each though I’ve been too lazy to do the math myself and if I needed a significant amount of each stat to equate to something simple like +4 health regen or not. Late game obviously no one ever runs out of mana not named Erekul/Grunty who need specific items anyway, but that's another story. I bring this up because I think that mana/health regen are terrible stats to include for cost efficiencies and that they skew my stats heavily because why would I need mana regen or health regen if I can stack health or mana. However, they might be more effective for utility early game where mana issues are huge. I’d prefer if someone with direct knowledge to explain the health/mana regen system based on base stats. A popular pub build back in the day was the 5 black ball build for the stats, which was very strong early and could be built into the marine friends or a synergizer (fun times) at the cost of movement speed of course.

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Not being able to quantify the effectiveness of a unique passive almost single-handedly refutes the whole point of this analysis. Quantifying the relative cost efficiency of an item by using the cheapest stat item is a fine theorycraft and has its place in justifying item costs but does not translate into making in-game build decisions.

 

On top of that, there are times where absolute stat value with poor cost efficiency will supercede relative stat value with high cost efficiency, since the absolute stat value of that item is simply too valuable and worth paying a premium on. This is why 9/10 times you see people go for Organic instead of Lifesuit when they need a tanky item, since 650 health + 60 strength is simply more health than 500, even if it costs nearly twice as much. This is a valid premium to pay; stat values should not cost the same per increment up to infinity. At some point you should be paying more for the additional increment instead of paying the same price since the idea of cost efficiency highly underrates the marginal utility between the cost efficient, relative benefit item and cost inefficient, absolute benefit item.

 

Think about lategame mineral overload, play style, hero, team comp, enemy team comp, item unique passive, etc... there are too many factors to make a silly blanket statement like "SHM is UP." It may be in terms of purely mathematical analysis, but the game isn't mathematical analysis, so its a logical fallacy to assume its UP in any facet other than number-crunching.

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Not being able to quantify the effectiveness of a unique passive almost single-handedly refutes the whole point of this analysis. Quantifying the relative cost efficiency of an item by using the cheapest stat item is a fine theorycraft and has its place in justifying item costs but does not translate into making in-game build decisions.

 

On top of that, there are times where absolute stat value with poor cost efficiency will supercede relative stat value with high cost efficiency, since the absolute stat value of that item is simply too valuable and worth paying a premium on. This is why 9/10 times you see people go for Organic instead of Lifesuit when they need a tanky item, since 650 health + 60 strength is simply more health than 500, even if it costs nearly twice as much. This is a valid premium to pay; stat values should not cost the same per increment up to infinity. At some point you should be paying more for the additional increment instead of paying the same price since the idea of cost efficiency highly underrates the marginal utility between the cost efficient, relative benefit item and cost inefficient, absolute benefit item.

 

Think about lategame mineral overload, play style, hero, team comp, enemy team comp, item unique passive, etc... there are too many factors to make a silly blanket statement like "SHM is UP." It may be in terms of purely mathematical analysis, but the game isn't mathematical analysis, so its a logical fallacy to assume its UP in any facet other than number-crunching.

You are correct to some degree. For example in a pub you got 3v5. You probably don't want an Eternal Drive vs. a Superheated Mantle because the ED's aura's aren't nearly as effective when there's only 2 other teammates to give them to. However, in the case of the Organic Carapace. It is well documented that the item is significantly weaker than its predecessors. Even with mineral overload it would probably be recommended to get as a 5th or 6th item in most cases. However, there is a specific case where it does work, which is that of the Gravity Edge's true damage (against burst). Even though it's overpriced, you still need that massive health to counter the flat damage. It's kind of like getting a pair of Jordan's. You know it's overpriced but they're still good sneakers so you get them. Also, there are other items that provide great utility that you can't put a generic price on. Notice that I didn't even dare mention items like warp shard and lockbox. Furthermore, just because you have an overload of minerals, it doesn't mean that you should buy terrible items. All items should be bought depending on team comp, enemy comp and to counterbuy if possible. I would personally get a lifetech over waiting for an organic because the difference is what, like 1600 gold give or take. Why would I wait that long to complete a t3 item when I can get a very good mid game item in lifetech. Especially if I'm some tanky initiator like Drake that benefits from the health regen, spell resist, and the passive. Lifetech does well against pyre builds too since it's spell damage. In ranked LoL games I tell my allies all the time that just because they build a lot of hp, it doesn't make them tanky! You need Magic resist and Armor as well. I think Organic might work better against crit damage builds since that's true damage (I think), [don't focus the tank plz!]. Hell what about the pyre + GE builds. Isn't that 20 shots or less guaranteed to kill anyone mathematically at about 5% true damage a shot (guessing on that number, might be 2.5% at 40 shots). I ask the people then, what's the strongest damage build for Agil characters? Is it crit strikes, pyre + GE, or are there too many variables and not enough experienced players left to answer the question?

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I always felt that gravity and argus should be more expensive, especially the latter. But instead of upping the recipe price for argus for example, just change the components to two higgs bosons + recipe increasing the price to around 4750. Argus should be a late game item but I see a lot of people buy it as their first or second item. Gravity should be more expensive than nitro.

 

Either way, thank you for that informed post. I wonder if Yamato is cost effective.

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Another famous item used to counter casters for tanks is the Lifetech Nanosuit, which gives 450 health and 15% spell resist for 2700 and of course the volibear passive of being under 35% health a health regen of 30% of max health over time. Basically it’s supposedly the perfect blend between health and spell resist.

A breakdown of these stats yields.

475 (Emerald Mox) = 180 health à 450/180 = 2.5 * 475 = 1187.5.

425 (Mirror Plating) = 8% spell resist à 15/8 = 1.875 * 425 = 796.88

Thus, as we all expected it is extremely cost efficient at 1984.40 even without it’s passive.

That example shows quite opposite conclusion...

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I always felt that gravity and argus should be more expensive, especially the latter. But instead of upping the recipe price for argus for example, just change the components to two higgs bosons + recipe increasing the price to around 4750. Argus should be a late game item but I see a lot of people buy it as their first or second item. Gravity should be more expensive than nitro.

 

Either way, thank you for that informed post. I wonder if Yamato is cost effective.

Yamato Reactor =25 strength, 25 agil, 50 int, 15% cdr à increase ts/spell damage by 25% for 8 seconds @ 4700

 

285 (Cybernetic Implants) = 6 strength @ 25/6 = 4.166 *285 = 1187.31

285 (Temporal Plating) = 6 int @ 50/6 =8.33 *285 = 2375

285 (Fusion Blade) = 6 Agil @ 25/6 =4.166 *285 = 1187.31

No price on CDR… let’s say 500 for 10% for arguments sakes @ 15/10 = 1.5 * 500 = 750

 

1187.31+1187.31+2375+750 = 5500 (about 4700 without factoring the cdr price I made up) It is indeed cost effective even without it’s passive. The reason that it might appear to be underpowered is because it’s a class cannon build at that price and players often rush it on something like Ghost or Raynor. It’s not terrible but you’re probably better off getting an Argus Crystal/Gravity Edge since they’re cheaper options. At the same time, the cdr is amazing on characters like that so as long as the enemies can’t get to you then it might be really good. Obviously the brother of the item to consider is the Sunflare Gun if you want to go the CDR/INT route. I’ll do it when I get home. Also, can anything compare to the late game damage that Gravity Edge has to offer when paired with other crazy Int items?

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Your calculation for Lifetech is skewed because getting 1.875 Mirror Platings only grants 14.5% SR [(1-0.08)1.875]. To get 15% SR using Mirrors, you'd need to satisfy the equation [.85 = 0.92x]. To get that, you use [log0.92 0.85 = x]. If your calculator can't make a custom logarithm base, use [ln(0.85) / ln(0.92) = x], which comes out to 1.95; you need 1.95 mirror plating to give the same SR as Lifetech. So:

 

Mirror) 1.95 * 425 = 828.75

Emerald) 2.5 * 475 = 1187.5

Total) 2016.25

 

Lifetech) 2700

 

It's still cost-inefficient, but by about 32 minerals less than your original calculation demonstrates.

 

The reverse process applies to attack speed because they magnify rather than diminish; 3x 10% is better than 1x 30%.

 

1.25 = 1.08x; log1.08 1.25 = x; x = 2.90; you need 2.90 Focus to give +30% attack rate.

 

Quantum) = 3 * 325 = 975

Focus) = 2.90 * 425 = 1232.5

Total) 2207.5 (rather than 2303)

Pyre) 3200

 

Still cost-inefficient and more-so than your original calculation showed.

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Gravity Edge and Argus Crystal can be modified, nerfed but not changed the idea of " increase damage in some way/ Make enemies vulnerable to" I mean you can't get some way to do players undestructibles giving other useless. So if price should be higher or true damage should be 25% or any other effect I don't know, But don't work around the idea It lets the caster get kills late game. Nothing about posters above just like to clarify this point.

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The great diminishing returns effect, yet it isn't nearly as great as one would imagine now is it. How about this question then, crit damage or GE+pyre for maximum damage. Basic logic tells me that I should assume pyre beats HP, GE+pyre beats HP+MR+Armor (full on tanks), and crit/damage beats squishy.

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Shrink Ray has a value of 4144, which is 644 more than 3500, and its active can also be worth the price entirely depending on how much weapon damage your opponents have. It can technically be the most cost-effective item in the game, nearing 10k minerals in effective value against a really fed carry.

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Shrink Ray has a value of 4144, which is 644 more than 3500, and its active can also be worth the price entirely depending on how much weapon damage your opponents have. It can technically be the most cost-effective item in the game, nearing 10k minerals in effective value against a really fed carry.

 

Don't confuse cost efficiency for item selection. It is true that you might be able to lower the stats of an ADC with a shrink ray for a short amount of time but if they are itemized then they wIll probably kill you anyway. Here's a prime example. You build armor and the enemy does spell damage. The items are probably cost efficient but they are useless for the circumstances. Here's a better example. In lol most people rush liandrys torment because it gives good health good magic pen ap and percentage health based damage. However the enemy builds straight magic resist and spell damage. The effectivweness of the item goes down greatly as opposed to if the enemy built straight HP. Even so there are much better items that you can get that will make it more efficient unless you're going against an enemy volibear or something super HP based its not worth the price of admission.

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Don't confuse cost efficiency for item selection. It is true that you might be able to lower the stats of an ADC with a shrink ray for a short amount of time but if they are itemized then they wIll probably kill you anyway. Here's a prime example. You build armor and the enemy does spell damage. The items are probably cost efficient but they are useless for the circumstances. Here's a better example. In lol most people rush liandrys torment because it gives good health good magic pen ap and percentage health based damage. However the enemy builds straight magic resist and spell damage. The effectivweness of the item goes down greatly as opposed to if the enemy built straight HP. Even so there are much better items that you can get that will make it more efficient unless you're going against an enemy volibear or something super HP based its not worth the price of admission.

 

Good point, but I always thought that the idea of cost-effectiveness was that if you can maximize the value of your stats over those of your opponent's, you'll have a raw advantage that can translate into winning fights. Of course, AoS has more unique heroes with different playstyles/skillsets, so it's much harder to judge cost-effectiveness than in LoL, since Unix, as an example, benefits a lot more from twin paradox than other heroes.

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