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General Guide by JAYZORZ

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League of Legends Build Guide Author JAYZORZ

A Mathematical Look at League

JAYZORZ Last updated on November 4, 2013
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Ability Sequence

Ability Key Q
Ability Key W
Ability Key E
Ability Key R

Not Updated For Current Season

The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.



Offense: 21

Honor Guard

Defense: 9


Utility: 0

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Hi guys, I'm Jawzeyy (formerly JAYZORZ).

I normally think that introducing yourself is irrelevant to builds, however in this case I think it will offer some insight, so I will briefly say that:

I'm a University student studying games tech and physics, with a strong interest in mathematics and science; all things logical. Wordsmithing isn't one of my interests, but hopefully it will be readable enough for everyone to understand.


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Aims of this guide

This 'guide' will look at the changes brought in by season 3 and what statistically and mathematically has changed due to this.

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1. Champions

The below chapters are focused on champions. Click here to go back to the contents page

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1.1 Impact on Carries

Carries, specifically AD in this context, have had an interesting development.

Thanks to the price decrease of Attack Damage, and a balancing price increase of Attack Speed, people that have innate attack speed buffs and/or scale extremely well off of raw AD have became quite popular.

Conversely, champions that benefit from attack speed have fallen off a bit, partially due to the cost increase and partially due to the limited build options. -> Mentioned in
Chapter #2.1 - Attack Speed Nerf

Furthermore, Adding to the point about carries with attack speed buffs becoming popular, this is why Nunu has became even more important this season, and why he is currently in a nerfed state on the PBE.

Example Champions:

Champions with Attack Speed buffs that scale with AD: Ezreal, Miss Fortune, Twitch, Draven, Varus, Graves and Sivir (ultimate only though)

Champions with Attack Speed buffs that don't scale (well) with AD: Kog'Maw and Tristana.

Champions that scale with AD but have no Attack Speed buffs: Ashe, Caitlyn, Corki, Vayne.

There are a few things to note about this above list. Caitlyn makes Nunu a safe pick, and her range allows kiting, which is why this combination is used a lot this season.

Graves and Sivir face problems of being short ranged without any (reliable) escape mechanisms and as such susceptible to the meta that is AD assassins.

Vayne is in an interesting category. She has low range, but escapes. Scales off AS but also AD. Without attack speed items though, it isn't a favourable pick, although her kit revolves around 3 hits, and may enable Sword of the Divine.

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1.2 Impact on Tanks

The impact on bruisers/tanks is fairly similar to that of carries.

Most notably, Health, similar to AD, has became cheaper, but Resistances, similar to AS, have gone up to balance this.

This means that many people will build health rather than resistances more-so than last season.

What's more is that armor penetration/reduction, thanks to The Black Cleaver, is now much more plentiful than before, so armor is less beneficial and as such is another reason why people may be amassing health rather than building armour that will just be shredded and ignored.

This should be indicative of champions that scale off health becoming more dominant, and they may have just done that. The most obvious and extreme example is Olaf -> more will be mentioned about Olaf, as he is a special case.

Other champions that scale off Health include: Sejuani, Shen, Vladimir and Volibear.

Why aren't these champions more popular? Well, Shen has always been popular.

Sejuani and Volibear are quite often underrated, most likely because their kits don't fit in with the current meta that well, but I wouldn't be surprised to see them soon.

Vladimir is one of my favourite champions, but the thing is he is often build more as AP than as HP soak, so the health cost just made his passive give him less gold worth when he buys AP.

Perhaps we will see him with a more prominent focus on health in the future.

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1.3 Olaf- Why he WAS a beast this season.

Everyone that watched the IEM Katowice will know 3 things: Gambit won, Riot shouldn't organise 'half-time' events and that Olaf is a beast and currently perma-banned in Korea.

Why is this? Well, He has always been a solid, reliable champion, and this season has done nothing but help him.

Remember, Health is now cheaper. Furthermore, Olaf scales directly with health from his W, Vicious Strikes (100 health= 1 bonus AD).

This isn't the only place he scales with health though, he indirectly scales with health on his passive, Berserker Rage and his E Reckless Swing.

Reckless Swing costs Olaf his own health, but if he has more, as it costs him a flat amount, it costs him less in terms of the amount of health he has available.

This also applies to Berserker Rage, as he will be at a higher health, when at an equivalent percentage, and as such be able to sustain and survive for longer.

What's more is, when he uses Vicious Strikes, his AD rises based on his health, and as such this makes his Undertow stronger.

But that's not all, when Olaf uses Ragnarok, he gains free Armour and Magic Resist, meaning that his health is harder to take down, and that he gains the most expensive stats of being a tank in season 3 for free, and scales off the other stat (being health).

I swear Morello almost quoted this during the patch notes when Olaf was nerfed.

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1.4 Viktor

Time to tackle Viktor and his infamous passive The Hex Core.

First off, this item isn't terrible mathematically. Infact, it is well priced and offers decent stats plus gives a cheap and reasonably efficient early-ish/mid game item that others don't have as an option. That doesn't mean you should always get it, but nonetheless it is an option.

All upgrades have their merits:
Augment: Power: Gives you extra health and enables better trading
Augment: Gravity: Gives you more safety to play with CC and some CDR
Augment: Death: Gives you extra fire power and DoT

The problem however, and why most people dislike his passive, is that the MOST OFFENSIVE upgrade, Augment: Death only offers 99 AP at level 18.

99 AP isn't terrible, but for offering nothing else except a DoT on your E, it isn't alot. Especially when you consider other items you could build instead if you didn't have said passive: Deathfire Grasp, Zhonya's Hourglass, Rabadon's Deathcap, Void Staff

Comparing Augment: Death to Deathfire Grasp can place this into perspective.

Augment: Death offers 99 AP and 30% extra damage for your Death Ray.

Deathfire Grasp offers 120 AP, a 15% health nuke, 20% extra damage from all spells and some CDR

Admittedly, these are all much more expensive than the augment, however, this is irrelevant when at 6 items, and as such hinders Viktor's 6 item game by forcing him to have an early game item that can't be upgraded.

During the release of S3, Viktor's augments had an extra upgrade each which sounded really solid and I was excited because they would have made Viktor viable as a 6 item carry, but alas they have yet to be released.

TL;DR: His passive isn't terrible early game but hinders his 6 item build. An upgrade has definently been in Riot's mind and I think it is the right direction for Viktor.

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2. Items

The below chapters are focused on runes. Click here to go back to the contents page

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2.1 Attack Speed Nerf

All the viable attack speed items for carries are:

Berserker's Greaves, Phantom Dancer, Runaan's Hurricane, Statikk Shiv, Sword of the Divine and Zephyr.

Berserker's Greaves: These are still fairly standard on carries that want to auto attack as often as possible.

Phantom Dancer: Doesn't give as much movement speed as before and has a unique passive so stacking isn't as cost efficient as previous. Also costy and reliant on some AD unless champ scales off AS.

Runaan's Hurricane: Seems like a great item, particularly on people that scale off on-hit and attack speed like Kog'Maw and Vayne. This sadly doesn't hold true in practice. Kog'maw OUTRANGES this item, and Vayne's W, Silver Bolts, is completely counter-intuitive of this item.

This item is still great for Varus however. Similar range, he scales off AS and AD and has an on-hit, health-based ability.

Statikk Shiv: Overall, a fair item. Great for players that like to kite, so as to get the passive more frequently. Better on people that have range and can kite rather than close range targets, or slow champs without great escape mechanisms. This once again, means it isn't the greatest for the 2 champions most noted for scaling off AS: Vayne and Kog'maw.

Sword of the Divine: Allows 3 fast hits that are guaranteed to crit, then this item accounts for nothing. Great synergy with Infinity Edge. A strong choice for Twitch thanks to Spray and Pray and Vayne thanks to Silver Bolts.

Zephyr: This item seems like a great choice, but it offers so many assorted stats and costs significant money that it seems a little off. This item seems more suited towards someone that scales off AS and being tanky like Irelia, or possibly Graves, as opposed to any squishy carry.

As such, this demonstrates that there are very limited choices, and that many of these choices are niche and as such a champion can't be based fully off AS.

Blade of the Ruined King now also gives AS, which helps it significantly, and is dominating due to it's nature of dealing health based damage, the health meta and the fact it is an item that deals on hit damage, and regular damage, whilst uping attack speed and granting sustain.

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2.2 Armour Penetration

This also applies to Mpen, with the respective stats changed and items changed. More or less the same. (i.e. Void Staff instead of Last Whisper)

It's not breaking news that flat armour penetration is now subtracted after % armour penetration, which makes flat and percentage intuitive as opposed to last season.

The common build for people wishing to bypass armour is The Black Cleaver and Last Whisper.

Click the spoiler to see the maths of The Black Cleaver and Last Whisper subtracting armour.

Spoiler: Click to view

Below is for people that want help accounting for a %ArPen or %ArReduction on a champion(s) that they play, but would like a mini-tutorial and/or need help with the maths.

Spoiler: Click to view

Something further to note, if you have sufficient ArPen so to make a targets armour Negative (i.e. Your armour penetration is more than their armour), you will effectively do TRUE damage to the target.

You, however, will NOT do bonus damage based on armour penetration making their armour a negative value.

Spoiler: Click to view

For mathematical purists:
Spoiler: Click to view

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2.3 The Rise and Fall of Items

I mentioned the attack speed items, and how these are quite niche; Now I will mention items that have gotten much more popular and items that have gotten much less popular.

Warmog's Armor: This has went from an item that was rarely ever gotten to an item that is now fairly staple. Mostly due to the health buff, it costs less and keeps you sustained forever, particularly if you get it early.

It features a passive similar to that of the Force of Nature from season 2, except rushing FoN was not often smart, as it just offered health regeneration and magic resistance. Warmog's offers health and health regeneration, making it, in my mind, far superior to its predecessor.


Guardian Angel: Guardian Angel was nerfed pretty hard. The prices of resistances went up so the GA lost some resistances that it used to offer. It now costs what it used to, but has a cloth armour taken out of the recipe and offers 18 less armour.

Furthermore, the UNIQUE passive changed from 750 health to 30% of health, meaning this item is now better for tanks than it was previously, but worse for carries -> It will revive the player with 750 health if they have 2500 total health.


The Black Cleaver: This is barely even the same item it was before. Before it was extremely niche, and only good on carries that benefited from AD and AS, like Vayne. Now this item is good on pretty much every AD champion in the game, including bruisers, assassins and carries.

Shredding armour allows more physical damage to be dealt to the target and as such this item is often picked up to counter tanks, or to deal near true damage to squishies.


Sunfire Cape: Like Warmog's, this item has become more popular. This is taken on quite a lot of dive champions, due to the large health pool and the fact it offers armor to compliment the health offered, along with a non-neglect-able UNIQUE passive.


Last Whisper: This has always been a fairly common item for dealing with tanks, but now that it synergises with The Black Cleaver and combines to reduce 57.5% of armor (with Weapon Expertise ), meaning that armour counter-play is much more readily accessed, and taken on most assassins to amplify their damage significantly. It is eventually built on carries too, so they can deal with tanks on them.


Trinity Force: Unfortunantly, this item was one of the items worst effected by the changes, but thankfully, it is currently buffed, being 297 gold cheaper. It also made champions that this was core for less common, although they might just replace this with Iceborn Gauntlet, as it is superior on many champions for the price tag.


Tear of the Goddess items: Both of these items were helped enormously by the changes. Most notably, the 2 items that Tear of the Goddess turns into now evolve, giving an extra (very potent) ability. Both of these are great and quite good on a wide range of characters, compared to last season where Archangel's Staff was niche (only really for Ryze maybe Anivia and Karthus), and Manamune was only good on a few people too (eg. Yorick, Urgot)


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Difference between MPen and MR Reduction

This also applies to ArPen and Armour reduction, just thought I would write it about magic resistance this time, as the last section was based on armour

Flat MR reduction and Flat Magic Penetration both have a universal goal, to remove the effectiveness of opponents (low) magic resistance, thus allowing magic damage to do more damage through not being reduced by as large of a number.

They both effectively reduce the targets' magic resist, either through directly affecting the stat or by ignoring part of it.

Where they differ however, is that Flat MR reduction is a debuff that must be applied to the opponent in order for them to take the extra damage. Flat Magic Penetration, however, is a statistic that always applies when calculating magic damage that you deal.

This means that, for a specific example, Abyssal Mask only increases the effectiveness of magic damage within 700 range (excluding the AP offered as a result of the item) due to the aura procing the debuff within 700 range. That been said, if they are further than 700 units from you, but within 700 range of another holder of Abyssal Mask, they are applied the debuff and would take the same damage anyway.

This means that if you have sufficient range (such as Teemo's Noxious Trap), this items passive won't be of much effect. Though, regardless of the enemies position, magic penetration will still effect it equally, meaning that MPen is a better choice for people with global, or long, range.

Due to this, Abyssal Mask should only be obtained on people that are likely to be within 700 range so as to use the benefits of the aura.

NOTE: Magic Penetration/MR Reduction affects all magic damage, even those that do not scale with AP or that scale with both AP and AD. Common examples include Dr. Mundo's Infected Cleaver and Ezreal's Trueshot Barrage.

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3. Runes

The below chapters are focused on runes. Click here to go back to the contents page

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3.1 HP vs Armour Runes

Recently, I was comparing health vs armour seals and quintessences. I thought I might as well add these in here.

Greater Seal of Armor 1.41*9=12.69
Greater Quintessence of Armor 4.26*3=12.78

Greater Seal of Health 5.35*9=48.15
Greater Quintessence of Health 26*3=78

Greater Seal of Scaling Health 19.44*9=174.96
Greater Quintessence of Scaling Health 48.6*3=145.8

These figures suggest that Health seals are not as efficient as flat health, and similarly scaling quintessences are not as good as scaling seals.

Thusly, I suggest against using flat health seals or scaling health quintessences.

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3.2 Value of Marks

I was also curious as to which marks were the 'best' to take mathematically. (By this I purely mean which cost the most in terms of gold, not which are actually the 'best' at dealing the most damage).

As such worked out how much they were worth. The results were quite odd, but reasoning for why the results are so variant can be found at the end of the chapter.

This section is big and contains a lot of information about how much runes cost. I will try to set it out as best as possible. Click the spoiler(s) to view sections.

Spoiler: Click to view

I have noted nested spoilers do work, but they start in the 'open' position, which may confuse readers. Sorry. I can't think of a better way to set this out though.

Furthermore, The costs are irrelevant to how strong the rune is. ArPen runes seem bad according to the above equation, but this is because either: Kindlegem isn't cost effective, or The Brutalizer is extremely cost effective.

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3.3 Scaling vs Flat Runes

Though this is maths, it really isn't hard. This is more so you can get an overall gauge of runes, and compare them quickly. I had many kinds of runes, but decided I should only include 'optimal' runes so to make it easier to read


Attack Damage: Scaling better than flat at level 8. At level 18, they are 2.3x as effective as flat.


Armor: Scaling better than flat at level 10. At level 18, they are 1.9x as effective as flat.


Health: Scaling better than flat at level 5. At level 18, they are 3.6x as effective as flat.


Mana: Scaling better than flat at level 6. At level 18, they are 3.0x as effective as flat.


Breakdown of the numbers: The higher level of equity, the stronger the flat runes are. Conversely, the lower level, the stronger the scaling runes are.

Similarly, the more multiples at level 18, the stronger the scaling runes are, and thusly, the lower multiples at level 18, the stronger the flat runes are (in comparison to the equal flat rune).

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Rumours- Smartcasting

This section doesn't fit into the above categories, I might make a rumour section in future, if I think of more. I just want to clarify something about smartcasting that has always bugged me.
Some people may disagree, but whatever.

Ok, I'm not saying it's bad, so don't get mad yet.

I'm just saying, it is a preferential playstyle, not an indicator of skill level.

There are 3 main playstyles when it comes to smartcasting, which I will detail in coming paragraph. These 3 playstyles include:

  • Not Smartcasting at all.
  • Smartcasting spells it is not detrimental to (double negatives because I'm a sadist)
  • Smartcasting all spells

*People I have notice who don't smartcast everything: EG Froggen, TPA Toyz, MRN Ecco, TSM Dyrus.

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Not smartcasting doesn't mean the player is bad, it may just mean they prefer accuracy than speed, or they just prefer to normal cast/are not used to smartcasting.

It may restrict mastering some champions, namely Cassiopeia, Ryze and Katarina.

Strengths: Accurate spellcasting, less chance of accidental mis-aim.

Weaknesses: Slower response time (by roughly 0.2s due to requiring to click)

Smartcasting every spell is a risky playstyle, which you trade all the accuracy for speed. It means you need to be precise at judging, particularly length. If you enable range indicators, it is pretty much the same as normal cast.

Strengths: Continuity, speed, ability to spam spells faster.

Weakness: Loss of accuracy/Misjudging

Smartcasting spells that it is not detrimental to enables you to be faster on spells that don't require accuracy, whilst still allowing you to be accurate on spells that do require aiming.

This is my personal playstyle, but it is not for everyone.

Strengths: Accurate where needed, fast where needed.

Weaknesses: Champion specific, will require changing every game. May forget to and cause confusion.

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I will add some more to this guide after I think about some more changes that impacted across seasons in a big way.

Tl;dr: AD is more cost effective. AS buffs on champions are more valuable. AD scaling is more important. Health is more cost effective. Health scaling is quite valuable as are free resistances.


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