Views: 1815 ADC Maths P.2: Vayne, LW and IE
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Welcome to the second edition of ADC maths, brought to you by yours truly. This post proves to be an altogether shorter affair than the previous one. For a look into the mathematical process behind this, please visit ADC Maths P.1.
Introduction
Maths
Results
Discussion
Closing Words
Carrying on from the previous post, I compare the numerical value of building
Last Whisper or an alternative item 3rd. In this case, that item is Infinity Edge. Prior items are:
. This Vayne possesses the standard 21 masteries in offense and AD marks. I compared building options against the Sejuani and Nautilus from the previous post.
This time, I have a few predictions to make. What is it that LW and IE do? They both bring AD to the table, however it is the %pen and crit modifiers which are significant. Both serve to amplify a portion of your damage. In the case of %pen, it serves to increase the amount of damage you get out of your AD and BotRK, the amount depending on the enemies armour. IE increase both your chance to crit and the damage you can get from crits. As I mentioned last week, I incorporated crit into my calculations by determining the Expected Average Damage. Notably, IE does not affect the damage from BotRK's passive, as such, builds which use BT should favour IE more than those with BotRK.
I expect that IE will be superior as the 3rd item as the damage contribution from crits is very high. With the AD values from the build, the EAD with IE has a greater than 100 point advantage over LW (355 vs 246). Even with LW benefiting the damage from BotRK, can it be expected to provide the same power boost? I expect not, although results will probably be close again. Of course, there is an element of chance which may serve to widen the gulf or breach it when put into practice.
I do not expect the presence of Randuin's Omen to alter the relative strengths of the items as neither item contributes attack speed. However, higher armor opponents will favour building LW, and high health opponents might be expected to do so as BotRK's passive becomes stronger. However, the damage contribution of BotRK's passive is relatively small compared to the damage you get from crits, meaning that I doubt the effect of high health will do much to the conclusions.
As mentioned, the majority of the maths can be seen in the previous post, however I shall explain how I took account of Silver Bolts. This was pretty simple, I created an extra column with a formula to give a progression of 1,2,3 and repeat and set up the previously empty true damage column to calculate the damage from the passive when silver bolts proc'd. That was then added into the total damage, true damage is unaffected by damage modifiers like
Havoc
or
Executioner
.
Rather embarrassingly, I made a number of silly errors when converting Ashe's tables for Vayne. It's reminiscent of doing exams :/ A pity this maths does not in anyway prepare me foreFP2. But I digress. Due to some laziness some of the cells which should have held cell references actually used absolute values, specifically, the LW built 3rd was calculated with the crit chance and crit rate as if IE was built, meaning that LW was ridiculously overvalued. Then, IE was ridiculously overvalued, why? Because the LW tables had empty BotRK columns. Finally, just I began typing this up I realised that I had gone and used %current health damage for Silver Bolts instead of %max health. Derp. I'm now quite certain that everything is correct. God, I hope I don't do stuff like during my exams, such a loss of time.
I used the Sejuani as a basic model, her health and armour are 3628 and 198 respectively. Building IE 3rd, it takes 14 basic attacks to kill her, 7.97 seconds, with a mean DPS of 455. If LW is built first then it takes 15 basic attacks, 8.54 seconds, with mean DPS 474. Wait, what? I explained in the previous blog that I felt that averaging the damage from each attack gave a more accurate representation of DPS than health/time because damage is dealt discretely. With Ashe, this was fine. With Vayne, every 3rd attack gets a huge damage spike. It just so happens that the LW table ends on a Silver Bolts proc which is entirely overkill, thus bringing its DPS ahead of IE, despite taking longer to kill Sejuani. Ignoring that last proc puts IE in a healthy lead by about 25 DPS. However, if Sejuani had a teeny bit less max health it would result in both builds killing her in the same amount of time, so IE's lead is marginal.
Introducing a Nautilus with a Randuin's Omen (again from last week), I do not expect any leads to change because neither item contributes attack speed. Indeed, that is just what I find, both build paths require 14 attacks, 9.38 seconds. However, the gap in actual damage is somewhat reduced, being 380 and 375 for IE and LW respectively.
Given that LW is favoured more as armour increases (obviously) and as health increases (because of the synergy with BotRK's passive which IE lacks), I subbed in arbitrary values of 300 and 5000 respectively on Sejuani to see just what happens. LW pulls ahead marginally, to the same magnitude as IE pulls ahead in the previous example. Of course, these values are not likely to be seen together in game.
Based on these results, I conclude that it is technically better to build an IE before LW, however the results are so marginal as to be negligible against tanky foes. I would prefer to take the gamble of crits over the certainty of penetration, but that's my preference. However, IE is notably stronger against squishy targets. Unless you spend pretty much all of your time attacking a tank and never touch anything remotely squishier (I believe bruisers will qualify as sufficiently squishier) then IE is clearly better.
Comparing these two items is notably easier than comparing LW and BotRK on Ashe in the first blog. There is no need to consider how much attack speed is actually getting used, or the benefits of having more lifesteal and a unique passive. Both LW and IE serve to increase the damage of each attack, and IE is generally stronger than LW. However, both are strong and I would recommend getting both where possible.
That was quite a bit quicker to do, about two and a half hours, compared to nearly ten previously. I have noticed an almost dogmatic approach to LW, "build it when several people have high armour". Results last week suggested that the LW is weaker than generally considered, but did not contradict that approach, although "high armour" might be considered higher than most would think. However, on Vayne at least it seems that delaying it in favour of an IE is actually stronger. This may lead to some questioning the validity of my results. If you feel that there is something wrong here and LW is a lot stronger than I have credited it, feel free to raise the issue, I want this to be accurate. I am however quite confident that I have not missed anything that could significantly change the results. I am entirely comfortable saying that it does not make a huge difference whether LW is built 3rd or 4th on Vayne, and pretty happy to say that going IE 3rd will most frequently be the right choice, unless you hate to gamble.
Table of Contents
Introduction
Maths
Results
Discussion
Closing Words
Introduction
Carrying on from the previous post, I compare the numerical value of building
Last Whisper or an alternative item 3rd. In this case, that item is Infinity Edge. Prior items are:
. This Vayne possesses the standard 21 masteries in offense and AD marks. I compared building options against the Sejuani and Nautilus from the previous post.This time, I have a few predictions to make. What is it that LW and IE do? They both bring AD to the table, however it is the %pen and crit modifiers which are significant. Both serve to amplify a portion of your damage. In the case of %pen, it serves to increase the amount of damage you get out of your AD and BotRK, the amount depending on the enemies armour. IE increase both your chance to crit and the damage you can get from crits. As I mentioned last week, I incorporated crit into my calculations by determining the Expected Average Damage. Notably, IE does not affect the damage from BotRK's passive, as such, builds which use BT should favour IE more than those with BotRK.
I expect that IE will be superior as the 3rd item as the damage contribution from crits is very high. With the AD values from the build, the EAD with IE has a greater than 100 point advantage over LW (355 vs 246). Even with LW benefiting the damage from BotRK, can it be expected to provide the same power boost? I expect not, although results will probably be close again. Of course, there is an element of chance which may serve to widen the gulf or breach it when put into practice.
I do not expect the presence of
Randuin's Omen to alter the relative strengths of the items as neither item contributes attack speed. However, higher armor opponents will favour building LW, and high health opponents might be expected to do so as BotRK's passive becomes stronger. However, the damage contribution of BotRK's passive is relatively small compared to the damage you get from crits, meaning that I doubt the effect of high health will do much to the conclusions.ToC
Maths
As mentioned, the majority of the maths can be seen in the previous post, however I shall explain how I took account of
Silver Bolts. This was pretty simple, I created an extra column with a formula to give a progression of 1,2,3 and repeat and set up the previously empty true damage column to calculate the damage from the passive when silver bolts proc'd. That was then added into the total damage, true damage is unaffected by damage modifiers like
Havoc
or
Executioner
.Rather embarrassingly, I made a number of silly errors when converting Ashe's tables for Vayne. It's reminiscent of doing exams :/ A pity this maths does not in anyway prepare me foreFP2. But I digress. Due to some laziness some of the cells which should have held cell references actually used absolute values, specifically, the LW built 3rd was calculated with the crit chance and crit rate as if IE was built, meaning that LW was ridiculously overvalued. Then, IE was ridiculously overvalued, why? Because the LW tables had empty BotRK columns. Finally, just I began typing this up I realised that I had gone and used %current health damage for
Silver Bolts instead of %max health. Derp. I'm now quite certain that everything is correct. God, I hope I don't do stuff like during my exams, such a loss of time.ToC
Results
I used the Sejuani as a basic model, her health and armour are 3628 and 198 respectively. Building IE 3rd, it takes 14 basic attacks to kill her, 7.97 seconds, with a mean DPS of 455. If LW is built first then it takes 15 basic attacks, 8.54 seconds, with mean DPS 474. Wait, what? I explained in the previous blog that I felt that averaging the damage from each attack gave a more accurate representation of DPS than health/time because damage is dealt discretely. With Ashe, this was fine. With Vayne, every 3rd attack gets a huge damage spike. It just so happens that the LW table ends on a
Silver Bolts proc which is entirely overkill, thus bringing its DPS ahead of IE, despite taking longer to kill Sejuani. Ignoring that last proc puts IE in a healthy lead by about 25 DPS. However, if Sejuani had a teeny bit less max health it would result in both builds killing her in the same amount of time, so IE's lead is marginal.Introducing a Nautilus with a Randuin's Omen (again from last week), I do not expect any leads to change because neither item contributes attack speed. Indeed, that is just what I find, both build paths require 14 attacks, 9.38 seconds. However, the gap in actual damage is somewhat reduced, being 380 and 375 for IE and LW respectively.
Given that LW is favoured more as armour increases (obviously) and as health increases (because of the synergy with BotRK's passive which IE lacks), I subbed in arbitrary values of 300 and 5000 respectively on Sejuani to see just what happens. LW pulls ahead marginally, to the same magnitude as IE pulls ahead in the previous example. Of course, these values are not likely to be seen together in game.
ToC
Discussion
Based on these results, I conclude that it is technically better to build an IE before LW, however the results are so marginal as to be negligible against tanky foes. I would prefer to take the gamble of crits over the certainty of penetration, but that's my preference. However, IE is notably stronger against squishy targets. Unless you spend pretty much all of your time attacking a tank and never touch anything remotely squishier (I believe bruisers will qualify as sufficiently squishier) then IE is clearly better.
Comparing these two items is notably easier than comparing LW and BotRK on Ashe in the first blog. There is no need to consider how much attack speed is actually getting used, or the benefits of having more lifesteal and a unique passive. Both LW and IE serve to increase the damage of each attack, and IE is generally stronger than LW. However, both are strong and I would recommend getting both where possible.
ToC
Closing Words
That was quite a bit quicker to do, about two and a half hours, compared to nearly ten previously. I have noticed an almost dogmatic approach to LW, "build it when several people have high armour". Results last week suggested that the LW is weaker than generally considered, but did not contradict that approach, although "high armour" might be considered higher than most would think. However, on Vayne at least it seems that delaying it in favour of an IE is actually stronger. This may lead to some questioning the validity of my results. If you feel that there is something wrong here and LW is a lot stronger than I have credited it, feel free to raise the issue, I want this to be accurate. I am however quite confident that I have not missed anything that could significantly change the results. I am entirely comfortable saying that it does not make a huge difference whether LW is built 3rd or 4th on Vayne, and pretty happy to say that going IE 3rd will most frequently be the right choice, unless you hate to gamble.
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