The Fallacies of Item Efficiency

The Fallacies of Item Efficiency

It's come to my attention in recent months that the theories of "item efficiency" and "gold efficiency" are making a resurgence in popularity among League of Legends fans as well as theorycrafters. With this tick in interest, I've also seen many new problems rise in the system, which is what I want to talk about today. A lot of people are using the system (as I see it) incorrectly, and thats leading to many misleading assumptions in itemization theorycraft. No graphs, no charts, just a discussion of what I think are the merits and flaws of this system.

First, let's hit a quick review of the history of theorycrafting and gold efficiency. Strategizing the best way to play a game, also known as theorycrafting, has been in existence as long as games have existed, whether it be finding the fastest way to beat Super Mario Bros. or how to stay alive playing Pac-Man. But that was just the beginning -- the game that became best known for in-depth theorycrafting was World of Warcraft -- from its reputation, calculations in League of Legends don't even come close to the math needed to calculate DPS output in WoW. Despite it being complex, we should give credit to Warcraft for making it possible for having sites with dedicated theorycraft -- such as Reign of Gaming -- be popular in the present day. Theorycrafting, since that time, has grown from a niche interest to a word commonly used in gaming lexicon.

When theorycrafting first emerged in League of Legends during Open Beta and Preseason One, most players at the time had no idea what was going on, and the only way that people could agree with each other on the 'overpowered' status of items was using gold efficiency and item efficiency, which is where my Item Efficiency Spreadsheet came in. For the first time, people had a way to discuss items, and some key items such as Zhonya's (Rabadon's) and Rod of Ages quickly got nerfed or reworked. Through that time to the present day, many people, including much of the Riot balance team, has used gold efficiency as a metric in balancing items, both new and old.

But history isn't really what I wanted to talk about today. Since the beginning of item efficiency to the present day, the meaning and the usage of efficiency has changed from a metric of power to the holy grail of design balance in the eyes of the community. And that's not what it is. It's an effective balancing system, but it is heavily flawed in its approach to looking at items -- its one-dimensional, and really, you can only get an idea of whether an item is overpowered, underpowered, or balanced.  Item efficiency is best used as an indicator of intermediate items, as it is extremely hard to value the power of a unique passive such as Infinity Edge's unique passive.  Such things are better calculated through damage-per-second analysis because the gold worth of such a passive would be variable depending on the stage of the game and number of items you have.

 

In order to get a sense of whether is strong or not, you have to look at the big picture. In its original form, item efficiency only took into account primary variables. Secondary variables (regen, penetration, cdr, etc.) weren't included. Now, many people take total efficiency (primary and secondary) variables, look at the results, and get erroneous conclusions.  A recently popular speculation that has been going around discussion forums is that Spirit of the Spectral Wraith is an overpowered item because it has a ridiculously strong gold efficiency, when in reality much of its gold efficiency stats are secondary (spell vamp and mana regeneration).  Even Athene's Unholy Grail, a common rush items on many casters, is extremely overpowered from an efficiency standpoint but this doesn't necessarily transition to in-game superiority.  These items are balanced; just because they seem strong in one system doesn't mean they are overpowered in the waking world.

I'm tired of people putting item efficiency on a pedestal. Item efficiency is an inherently flawed system in design, yet we still use it as a metric because it's the best and easiest way you can approximate variables and the strength of items outside of the game, without actually playing it. At one point in time, it was the only thing theorycrafters used as a basis of analysis; now, the game has evolved so that we take many things into account and not just efficiency.  Sadly, much of the community has not kept up in the changes and with the recent surge in 'item efficiency' theorycrafters, I see a lot of these problems coming back into the spotlight.

While charts such as this one valuing masteries are applaudable in the effort undertaken to try to define masteries, gold efficiency isn't bulletproof enough of a system to do this correctly.  For example, the offensive mastery Frenzy is valued at less than 50 gold, but in the end-game it is one of the most powerful offensive options available to AD Carries.  Similarly, it's pretty hard to value how long reduced death timers are or the power of extra ward vision.  People are taking a niche system and overestimating its capabilities, when in reality we should be just using item efficiency for a "Fun Fact: X is pretty strong" type of analysis.

 

The Brutalizer's 10 flat armor penetration must be valued at 15g for this item to be gold efficient.

With the rise of new theorycrafters, we've also seen a warping of the current system.  Some people have the concept of "item efficiency" in their head, but it's often the wrong idea.  If you look at different items on the LoL Wiki, you'll find that generally the item efficiency explanations don't make a whole lot of sense, and in many cases they're even wrong.

Item efficiency is an imperfect system, and it's become even more imperfect as time has gone on.  It's best used for estimating what items might be overpowered and what isn't; it's not really a great indicator of what item to rush first or whatever, because oftentimes "gold efficient" items aren't giving you the right items.  It's not to be used to calculate how great every single element of the game is.  You can't solve the mysteries of the League of Legends universe with one set of calculations, let alone one that is based off the base cost of a Negatron Cloak.  In order to theorycraft, you have to look at every factor, not just the gold cost and stats.

 

What can we do to improve the problems encountered by item efficiency?  The solution is not to abandon it, but to integrate it into your research.  If League were balanced on a one-dimensional metric such as this, the game would be extremely imbalanced.  As such, when we look at items we should consider: Is this item actually strong ingame?  If not, is that why the item is so efficient?  Questions such as these should guide your research in itemization instead of relying wholly upon one system. Efficiency has its merits in approximating value, but it cannot be used to pinpoint precision in actual usability.  Use common sense, make good judgments, and you will be able to see why the game is balanced as it is.

 


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Comments

  • #29 Itachi

    Could anyone provide me with a link to the file with the calculations behind the chart of gold value of Masteries or a link to the article it comes from? I am having some trouble locating it and I have several questions such as does the value represent the first point or the second point in masteries that give more for their first point such as Resilience.

  • #30 Itachi

    Nobody? Please? D:

  • #28 gouv1

    Hey,

    Can you please stop using this design for the parts of your articles? I always wonder if there is something to be found by clicking the title (In other articles it's used for spoilers/math so I tend to always click on it)

  • #26 elguero

    I've been using "Damage efficiency" instead for quite a while;

    I use it for Ranged AD carries, but It can be applied to the other damage types, too.

    It still uses the whole "400 Gold for 10 AD, so 1 AD = 40 Gold, or 1 AD/gold", but instead of it being a linear approach, I use that base value as the "Attack Damage Gold Differential"

    And you do the same thing to Crit Chance, Attack Speed, and Armor Penetration to get their respective "X Gold Differential"

    Once you get those, you just get the complete differential for DPS on an ADC:

    Damage = AD*AS*(1+CritChance*CritDMG)*(Armor*(1-PercentPen) - Flat Pen)

    Variables here, you use AD, AS, CritChance, Flat Penetration, and Percent Penetration. (Keep CritDMG and Armor Values as Constant as per individual analysis)

    Then complete Partial Derivative, and you get an Expression for d[Damage]/d[gold] , and this value can then be used as a "Damage to Gold Efficiency", which I find as a MUCH better measure.

    Of course, there's no simple expression the average user can use, so I guess that's why it's less practical.

  • #25 PedestrianA

    This reminds me for the days when items with bad stat synergy but perfect gold efficiency got nerfed over and over. Yes I am talking about gunblade, now even for the champions it is specially designed for has to think twice getting it.

    Also, it is probably one of the reason we have league of warmogs on the scene, even with warmog being super underpowered.

  • #24 pldl

    I remember the old Aegis of Legion. That was cost-efficient even if the added stats only applied to you. 

  • #23 tgo007

    For 4 months now, winrar's spreadsheet has wriggle's lantern costing 2000 instead of 1600 lol.

  • #22 FleurDeLiz

    We could have used this post several months ago when Gunblade and Atma's got smashed purely because "they were too efficient".

  • #21 KultoDeSkaro

    So, you're not going to give us any real counterexamples? You stated Athene's and Spectral Wraith, but you didn't give any convincing explanation as to why gold efficiency is deceptive on them, other than the fact that spell vamp and mana regeneration are "secondary stats." Are you suggesting that secondary stats are bad? Is there something else about those items that makes them bad? And what about the brutalizer? Are you somehow suggesting that it isn't a great early item?

  • #27 elguero

    It's deceiving in the sense that players could be fooled into thinking that a "more cost efficient" item could provide more damage than a less "cost efficient" item, for example.

    However, not every stat scales linearly with Damage, so even though an item may appear to be 'more efficient', even at the same cost, it may not necessarily provide more damage.

    In that sense, Gold efficiency is a bad approach to maximize your 'bang' for you buck.

    (ADC, for example, scale with 5 different stats: Attack Damage, Attack Speed, Crit Chance, Crit Damage and Armor Penetration. Each stat scales differently depending on the current stats of the champion building it, so it's not always 'efficient' to purchase the most cost efficient item right away, simply because you can obtain more damage by building onto another stat instead. Most common example is the PD vs BT rush.)

     

  • #20 registermyaccount

    Why did Xin Zhao fall over?

    BECAUSE HE WAS IMBALANCED.

  • #18 B3hr7

    To me, gold efficiency and item efficiency heavily depend on the champion due to different preferences of items, as well as their role. For example, Twin Shadows on Jungle Diana is considered extremely gold efficient and it uses many of the stats well, while for Mid Diana it's considered a cheaper alternative to Lich Bane. Both items are awesome on Diana regardless, but there are different circumstances. Lich Bane gives more kill power, but is most expensive. Twin Shadows is more utility oriented and is cheaper (plus it's built from a Kage's Pick). Both items are considerable on both roles, but sometimes Jungle Diana doesn't want to stomach a Lich Bane and simply work on a cheaper Twin Shadows, and vice versa on Mid Diana. Or perhaps even Mid Diana wants a Twin Shadows to take advantage of sitting on a Kage's Pick, and Jungle Diana got fed really hard and wants to murder people with Lich Bane? Such is nuances of figuring out what items you want to get, and there's no clear cut answer for some champions, it just depend on the circumstances of the current game you're playing.

  • #17 Canvasofgrey

    I find that item efficiency is also determined by the effectiveness of the stat on the champion, such as the argument between Black Cleaver being more efficient on auto-attackers to ability spammers.

  • #16 Cerbereth

    I don't think lolwiki is bad for gold efficiency they mainly just say whether item A is gold efficient or not or what value you need to place on a passive for an item to be gold efficient. It's handy for spotting the noob trap items, and it shows that some items deemed underpowered are actually still gold efficient.

    I think the problem with gold efficiency is that it doesn't take into account  the meta.  Warmog's is only 5 gold more efficient than Frozen Heart, but in this meta with armor penetration being very easy to come by the Warmog's is far more valuable than that number suggests. 

     

  • #12 PerKiller

    I believe that the point of this article is more; Statistics CAN be good, they CAN be helpful - but you have to read it with caution, and they have to be put in a context -- a context, which is each and every game; or even each and every situation in each and every game. Which means - theorycrafting is interesting. Theorycrafting can tell you which items to rush on LeBlanc, in those "standard" games/matchups. But it CAN also be completely pointless, in certain games/scenarios/situations. Which is why the term "item-efficiency" is a misleading one. Whilst "gold efficiency" kind of deliver on what it says, and nothing more, the term "item-efficiency" claims to tell you how effective (in general, and in any/all ways you possibly could imagine) an item is. Which is impossible.

    I do NOT think the point was: We have to develop better models in order to successfully put a metric value on each and every stat found in the game.

  • #11 ToastedTomatoes

    People are already whining about this post, but I understand where you are coming from.  It's all happened to us. You get into a game, doing well, buy a certain item that's maybe a little outside of what's considered traditional or optimal on a character by the community (but it fits your current setup because of team comp, enemy team comp, etc) and then. . .

    FLAME. You get people telling you how that item is soooo gold inefficient and you should have bought X instead, nevermind it was the perfect choice for you right then in that particular situation.

     

    That's all the author is trying to say.  Sometimes there are other values influencing why an item is a good buy besides outside-of-the-game theorycrafting.

  • #10 Silverbel

    I completely disagree with everything this post says. Simply refuting statistical analyses because "it doesn't play that way" is a vapid and shallow approach. People can use incomplete statistical analyses, but the correct answer is not to throw them out on grounds of being useless - but to embrace a more complete form of analysis.

    "Fun fact: X is pretty strong (because I say so) and Y is not (because I also say so)" is an incompetent approach. Athene's Unholy Grail is a statistically powerful item, but if you don't use those statistics (because you hoard mana and never use your skills, hence never getting any of the mana regen effect) that does not weaken the item. The fault is on you for not making the most of your items.

     

    Criticizing an analysis by saying "This analysis is incomplete" and then turning around and saying "So... let's not analyze anything, let's do LESS complete analysis" is total bullhonky.

     

  • #14 TheFaller

    i dont know if you read the same article as i did, but what he stated was that the item efficiency helps analysing an item, but its not the true and holy answer to how viable it is for the game it is being played

  • #9 Benegesserit

    So many items have unique passives or actives that aren't easily quantified

  • #7 Apollinarius

    The point of this article is lost on me. Are you arguing that secondary stats are worthless? Or are you arguing that the value of primary stats can be measured objectively, but the value of secondary stats is completely situational?

    Every single stat on an item has a numeric gold value that can be assigned to it. The lol wiki page is notorious for using the cheapest item in a category for its value calculations instead of the most cost efficient item. A great example is the Bloodthirster. You can get the value of a point of lifesteal by using the vamp sceptre as a basis, combined with the BF sword:

    10 AD is worth 344 gold, so 10% lifesteal is worth 456 gold.

    A charged BT has 100 AD and 18% lifesteal. The lifesteal is worth 821 gold, so 100 AD is worth 2379 gold. This means that actually, the BT is the most gold efficient item in the game from the AD perspective.

    Solving some basic equations, we can determine that 60 AD is worth the same as 22% lifesteal.

    A few more steps later, you can determine that 10 AD is actually worth only 215 gold and 10% lifesteal is worth 585 gold.

    This is why lifesteal Quints are so fantastic and why Vamp Scepter is such a great buy. It is also why getting flat AD without combining it into a T3 item as soon as possible is catastrophically bad for efficiency. This leads into why AD carries are super weak early game until they get their multiplicative Tier 3 items going. It is because the components of their items are incredibly cost-ineffective.

    The same math can be done for AP items. Hourglass active only costs about 300 gold when you use the NLR as a price indicator for AP. But when you compare it to the AP efficiency of other items, you realize that NLR is actually very expensive. Deathcap costs 100 gold more than two NLR and it gives the same AP even if it's your only source of AP. If you have any other source of AP, it outscales NLR by a huge margin.

     

    Last edited by Apollinarius: 2/28/2013 12:21:42 PM
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