FOR SCIENCE: The Worth of Your Runes (Patch 4.3 Vel'Koz Patch)

Welcome to the League Of Science!

Where we will keep you updated with all the math behind League of Legends. We will give you an overview of the current best builds (backed up by formulas) and if you have any League related questions, feel free to ask and we'll settle them ASAP, all to help you get up in the ranks!

Today we will be looking at the gold efficiency of your runes. But, in order to do this, we have to first find out the average cost of each stat.

To simplify things, we will only be looking at the Quints. If you want to know the costs of the other runes, just take the gold efficiency value for whichever stat you're doing it for and multiply it by the amount the rune gives (just follow the examples below if it still doesn't make sense).

So let's begin:

Let's look at the cost of some stats by looking at the in game items:

Ability Power
Amplifying Tome gives +20AP for 435g, so (435g/20AP)=21.75g per AP
Needlessly Large Rod gives +80AP for 1600g, so (1600g/80)=20g per AP
The average of these two comes out to (21.75g+20g)/2=20.875g per AP

Armor
Cloth Armor gives +15Armor for 300g, so (300g/15Armor)=20g per Armor
Chain Vest gives +40Armor for 720g, so (720g/40Armor)=18g per Armor
The average of these two comes out to (20g+18g)/2=19g per Armor

Armor Penetration
The Brutalizer gives +25AD, +10%CDR, and +10ArmPen for 1337g. At 36g per AD (refer below) and 19.3505g per %CDR (refer below), we get ((36g*25AD)+(19.3505g*10%CDR))=(900g+193.505g)=1093.505g worth of AD and %CDR. We get (1337g-1093.505g)=243.495g worth of ArmPen. So, (243.495g/10ArmPen)=24.3495g per ArmPen

Attack Damage
Long Sword gives +10AD for 360g, so (360g/10AD)=36g per AD
B.F. Sword gives +45AD for 1550g, so (1550g/45AD)=34.44g per AD
The average of these two comes out to (36g+34.44g)/2=35.22g per AD

Attack Speed
Dagger gives +12%AS for 400g, so (400g/12%AS)=33.33g per %AS
Recurve Bow gives 30%AS for 900g, so (900g/30%AS)=30g per %AS
The average of these two comes out to (33.33g+30g)/2=31.665g per %AS

Cooldown Reduction
Fiendish Codex gives +30AP and +10%CDR for 820g. At 20.875g per AP (refer above), we get (20.875g*30AP)=626.25g worth of AP and (820g-626.25g)=193.75g worth of %CDR. So, (193.75g/10%CDR)=19.375g per %CDR

Ionian Boots of Lucidity gives +45MS and 15%CDR for 1000g. At 13g per MS (refer below), we get (13g*45MS)=585g worth of MS and (1000g-585g)=415g worth of %CDR. So, (415g/15%CDR)=27.667g per %CDR

Kindlegem gives +200HP and +10%CDR for 850g. At 2.649g per HP (refer below), we get (2.649g*200HP)=529.8g worth of HP and (850g-529.8g)=320.2g worth of %CDR. So, (320.2g/10%CDR)=32.02g per %CDR

Stinger gives +40%AS and +10%CDR for 1250g. At 31.665g per %AS (refer above), we get (31.665g*40%AS)=1266.6g worth of %AS and (1250g-1266.6g)=-16.6g worth of %CDR. So, (-16.6g/10%CDR)=-1.66g per %CDR

The average of these four comes out to (19.375g+27.667g+32.02g-1.66g)/4=19.3505g per %CDR

Critical Strike Chance
Brawler's Gloves gives 8%Crit for 400g, so (400g/8%Crit)=50g per %Crit
Cloak of Agility gives 15%Crit for 730g, so (730g/15%Crit)=48.667g per %Crit
The average of these two comes out to (50g+48.667g)/2=49.33g per %Crit

Health
Ruby Crystal gives +150HP for 400g, so (400g/150HP)=2.667g per HP
Giant's Belt gives +380HP for 1000g, so (1000g/380HP)=2.63157g per HP
The average of these two comes out to (2.667g+2.63157g)/2=2.649g per HP

Health Regen
Rejuvenation Bead gives +5HP5 for 180g, so (180g/5HP5)=36g per HP5

Life Steal
Vampiric Scepter gives +10AD and +10%LS for 800g. At 35.22g per AD (refer above), we get (35.22g*10AD)=352.2g worth of AD and (800g-352.2g)=447.8g worth of %LS. So, (447.8g/10%LS)=44.78g per %LS

Magic Penetration
Sorcerer's Shoes gives +45MS and +15MPen for 1100g. At 13g per MS (refer below), we get (13g*45MS)=585g worth of MS and (1100g-585g)=515g worth of MPen. So,
(515g/15MPen)=34.33g per MPen

Magic Resist
Null-Magic Mantle gives +20MR for 400g, so (400g/20MR)=20g per MR
Negatron Cloak gives +40MR for 720g, so (720g/40MR)=18g per MR
The average of these two comes out to (20g+18g)/2=19g per MR

Mana
Sapphire Crystal gives +200MP for 400g, so (400g/200MP)=2g per MP

Mana Regen
Faerie Charm gives +3MP5 for 180g, so (180g/3MP5)=60g per MP5

Movement Speed
Boots of Speed gives +25MS for 325g, so (325g/25MS)=13g per MS

Spell Vamp
Hextech Revolver gives +40AP and 12%SV for 1200g. At 20.875g per AP (refer above), we get (20.875g*40AP)=835g worth of AP and (1200g-835g)=365g worth of %SV. So, (365g/12%SV)=30.4167g per %SV

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Now that we have the costs of all the stats, we can finally calculate the gold efficiency of each rune!
Note: Some of them are currently too hard to calculate and we will save them for another day :(

AGAIN THESE ARE ALL QUINTESSENCES TO SAVE TIME, JUST PLUG AND CHUG NUMBERS FROM ABOVE TO CALCULATE COSTS OF OTHER RUNES!

Attack Damage: (35.22g*2.25AD)=79.245g

Attack Damage per Level: (35.22g*0.25AD)=8.805g per level, 158.49g at level 18

Ability Power: (20.875g*4.95AP)=103.33125g

Ability Power per Level: (20.875g*0.43AP)=8.97625g per level, 161.5725g at level 18

Attack Speed: (31.665g*3.4%AS)=107.661g

Armor: (19g*4.26Armor)=80.94g

Armor per Level: (19g*0.38Armor)=7.22g per level, 129.96g at level 18

Armor Penetration: (24.3495g*2.56ArmPen)=62.33472g

Cooldown Reduction: (19.3505g*1.67%CDR)=32.315335g

Cooldown Reduction per Level: (19.3505g*0.14%CDR)=2.70907g per level, 48.76326g at level 18

Critical Chance: (49.33g*1.86%Crit)=91.7538g

Health: (2.649g*26HP)=68.874g

Health per Level: (2.649g*2.7HP)=7.1523g per level, 128.7414g at level 18

Health Regen: (36g*0.43HP5)=15.48g

Health Regen per Level: (36g*0.11HP5)=3.96g per level, 71.28g at level 18

Hybrid Penetration: (24.3495g*1.79ArmPen)+(34.33g*1.4MPen)=43.585605g+48.062g=91.647605g

Lifesteal: (44.78g*2%LS)=89.56g

Magic Penetration: (34.33g*2.01MPen)=69.01g

Magic Resist: (19g*4MR)=76g

Magic Resist per Level: (19g*0.37MR)=7.03g per level, 126.54g at level 18

Mana: (2g*37.5MP)=75g

Mana per Level: (2g*4.17MP)=8.34g per level, 150.12g at level 18

Mana Regen: (60g*0.41MP5)=24.6g

Mana Regen per Level: (60g*0.065MP5)=3.9g per level, 70.2g at level 18

SpellVamp: (30.4167g*2%SV)=60.8334g

So the runes that cost the highest gold are the most gold efficient. Of course, it also depends on how effective your champion is with these stats.

Hope this helped!

Add me in game if you have any questions, or feel free to ask here.
IGN: Knows Gogeta SS4

FOR SCIENCE: The Best Gold Income Item (Patch 4.3 Vel'Koz Patch)

Welcome to the League Of Science!

Where we will keep you updated with all the math behind League of Legends. We will give you an overview of the current best builds (backed up by formulas) and if you have any League related questions, feel free to ask and we'll settle them ASAP, all to help you get up in the ranks!

Today we will be looking at these three gold income items:

So which one of these gives the most gold? By the way, no super minions are factored in.

Ancient Coin gives 2 gold per minion death. Minions spawn 6 at a time every 30 seconds, and on every 3rd minion wave a siege minion spawns. This would give an average of (6+6+7)/3=19/3=6.33 minions every 30 seconds. However, after 35 minutes into the game, siege minions spawn every 2nd minion wave, giving an average of (6+7)/2=13/2=6.5 minions every 30 seconds. Now, in the optimal case, you would be getting gold from every minion from every lane, but let's be more realistic. We're going to say that you got every minion from one lane and leave it at that giving you a whopping (2*6.33)=12.66 gold every 30 seconds before 35 minutes into the game, and (2*6.5)=13 gold every 30 seconds after 35 minutes.

TLDR: Ancient Coin gives 12.66 gold every 30 seconds before 35 minutes, and 13 gold every 30 seconds after 35 minutes (if you never get out of your lane and watched every single one of your minions die).

Relic Shield gives your ally kill gold, along with you yourself originally obtaining the kill gold. However, your ally getting kill gold does not matter, since if your ally hadn't gotten out of the way for you to use your Relic Shield effect, chances are your ally would've gotten the kill gold for himself. With that said, this is how much money the minions give: melee 19(+0.5 gold every 3 minutes), caster 14(+0.5 gold every 3 minutes), siege 40(+1 gold every 3 minutes). In an optimal case, you would be getting only siege minions, however, since you get a charge every 60 seconds and a siege minion spawning every 90 seconds for the first 35 minutes, it's impossible.

Let's see in a more realistic setting. Initially, you would have to begin by getting the first two melee minions giving you 19+19=38 gold for the first 60 seconds. Now, next time it's up you can save a charge for a siege minion and a melee minion giving you 40+19=59 gold. Of course, these numbers will slowly get higher as time in game goes on.

TLDR: Relic Shield gives 14 to 19 gold every 30 seconds for the first minute (19 if two melee minions are killed), then afterwards around 14(+0.0833 gold every 30 seconds) to 29.5(+0.125 gold every 30 seconds) every 30 seconds (optimal case if a siege minion and melee minion are killed on cooldown until 35 minutes). Of course these numbers should be toned down, since it's almost impossible to be getting Relic Shield off every cooldown on the right minions.

Spellthief's Edge grants 5 gold per spell or basic attack on a champion or structure. This can occur up to 3 times every 30 seconds. So that's easy (5*3)=15 gold every 30 seconds, plus the 2 gold per 10 seconds, so an extra (2*3)=6 gold. We end up getting (15+6)=21 gold every 30 seconds.

As we can see, in the best case scenario, Relic Shield would give the most gold. However, anyone who has bought these items can easily say that Ancient Coin is the easiest one to use on cooldown, since the effect is passive. Spellthief's Edge now grants the buyer more damage on hit (10 additional damage either with basic attacks or spells) which is a significant amount earlier on in the game.

We are also not considering what these items build into later on, which is for another day. However, these calculations tell me that Relic Shield grants the most gold.

TLDR: Relic Shield grants the most gold out of the three items in an optimal situation. However, in a more realistic setting, Spellthief's Edge would give Relic Shield a run for its money.

However, we were just looking at the gold each item gives and nothing else. Here is a list of what I prefer on the supports that I play:

Alistar: Relic Shield
Amumu: Relic Shield
Annie: Spellthief's Edge
Blitzcrank: Relic Shield
Fiddlesticks: Spellthief's Edge
Janna: Spellthief's Edge
Karma: Toss up between Spellthief's Edge and Ancient Coin
Leona: Relic Shield
Lulu: Spellthief's Edge
Lux: Spellthief's Edge
Morgana: Spellthief's Edge
Nami: Ancient Coin
Nunu: Relic Shield
Sona: Toss up between Spellthief's Edge and Ancient Coin
Soraka: Toss up between Spellthief's Edge and Ancient Coin
Taric: Relic Shield
Thresh: Ancient Coin
Zilean: Toss up between Spellthief's Edge and Ancient Coin
Zyra: Toss up between Spellthief's Edge and Ancient Coin

Play style:

Ancient Coin: Passive play style in comparison to the other 2 starts, I hate starting with Ancient Coin, but the Talisman of Ascension active is so good. Of course, you can sell your initial income item and get a Talisman later.

Relic Shield: More sustain, build up gold between the two of you for those late game comps.

Spellthief's Edge: Aggressive play style, so fun! I'm more of an aggressive player so this is my favorite pick as of the latest patch (patch 4.3).




Add me in game if you have any questions, or feel free to ask here.
IGN: Knows Gogeta SS4

Bot Lane Synergy Chart

Lux and Ezreal Bot Lane Synergy

Let’s go ahead and talk a little bit more about our support, Lux. Lux is a long ranged mage who supplies a lot of burst at longer cooldowns early game. It is essential to be very conservative with her spells early or you will run out of mana.  While a safe pick, it’s definitely better to look at lux as very passive aggressive. She is capable of scouting ahead or even denying the enemy laners a pathway to easy CSing with her E – Lucent Singularity with this tool the enemy will always be on their toes. On top of this amazingly safe tool she has her Q – Light Binding which is far more aggressive and really is the spell that makes this whole lane. The bind is a 2 second root to which ever target it hits first and also binds the 2^nd target behind the first for 1 second.  Also a part of her tool is her W – Prismatic Barrier. This is an excellent tool for anticipated trades since it allows you to shield your whole team if positioned correctly. If missed it is very forgiving because lux can always reposition herself to let the shield loop to her teammates. Last but not least everyone’s favorite ultimate, Final Spark. Perfect for sniping down fleeing targets, securing buffs, and/or objectives. This laser is uninterruptable and activates Lux’s passive, after activated it also reapplies Illumination. This ultimate should always be used if caught in a really tight situation as it applies a ton of damage that could change the tide of a team fight.

                Now onto everybody’s favorite explorer. Ezreal is a medium ranged ADC, with long ranged poke damage. He is able to kite in sticky situations and supply burst to compliment his support lux. His Q – Mystic Shot can be used as a harass or farming tool. It applies on-hit effects and actually reduces the cooldowns of ALL of Ezreal’s abilities by 1 second. It’ll be your primary tool for following up on your support’s bindings. W – Essence flux is amazing, it supplies any of the teammates that you shoot it through with an increased attack speed buff! What’s even better is that you can use this as a harass tool in lane to harass your lane opponent THROUGH minions. If you find that you can’t seem to land any Q’s since they are standing behind their minions W is perfect for by passing that. Ezreal’s E – Arcane shift is his escape tool. Predominately used as a kite/escape panic button it can also be used to supply burst if you know you’ll be okay to go all in. When activated this skill targets the nearest enemy unit. Now onto your ultimate. Ezreal’s R – Trueshot Barrage is a global ulti that deals damage to each enemy unit it passes through. The downside is that for each subsequent target it hits the damage is minimized to as low as 30%. It’s very crucial to make sure that you don’t have a hoard of creeps in front of your enemies before you let this bad boy go.

                Most of this lane really is paced by your support. It’s best to wait for Lux to land a snare and play safely. Take advantage of the fact that that’s a free Q, W, E (E- If the opposing laners are low enough. You need to be careful about using your Arcane Shift because sometimes it might be necessary to save it as an escape option.), and R. Keep in mind that while Ezreal unleashes his full barrage of spells that Lux will also be using her ult simultaneously to his. This combo will melt faces against any squishy bot lane before they have the chance to run. What makes this lane so good is the versatility of Lux with Ezreral. Ezreal wants to poke, Lux will poke. Ezreal wants to disengage and kite Lux can help kite as well. Same goes with initiates. Lux does a good job of locking targets down for Ezreal that he can’t miss his skill shots. In terms of their weaknesses it’s best to have lux stay safe and in the back. She’s prone to being hard CC’d and an easy kill. Supports such as Annie and Leona will give you a hard time. In terms of synergy it’s a fun skill and kill lane. Have fun blinding and nuking your enemies J