Anyways. This post is about analysis of a specific item in League of Legends - Liandry's Torment.
Introduction
Obviously the very first thing we need to analyze Liandry's Torment is some exact information on what it is. You can find that information here, if you don't already have it memorized.
Our analysis here will be an attempt to figure out whether Liandry's Torment is something that you would ever want to buy, and under what circumstances you would want to buy it.
In order to perform this analysis, we need some alternatives. Here are a few possibilities that I've been considering...
1) Haunting Guise with Blasting Wand and Amplifying Tome
This one is kind of obvious. Instead of getting Liandry's, you get everything for it but buy something of equal value rather than getting the unique passive. You lose out on 100 health and the passive, but you gain 35 ability power.
This is the most direct possible comparison, as the difference in what you get in terms of damage is easy to measure: 35 ability power as opposed to Liandry's passive.
2) Abyssal Scepter
The item itself costs slightly less, but they are targeted at a similar goal - dealing damage while being slightly tankier, with part of the damage increase being from a reduction in magic resistance. In terms of only damage, you gain 10 AP and 5 'MPen,' while losing the unique passive.
Fairly similar in many ways, this is also a good comparison, although we will be disregarding the value of the aura.
3) Rabadon's Deathcap
Fairly close in price, but is the game's premier damage item for champions with high AP ratios. Will be a useful comparison to see at what point Liandry's Torment becomes better than this.
(For Deathcap, we will assume it is the only AP providing item you have. Obviously comparisons become more and more slanted towards Deathcap the more AP you are assumed to have.)
The General Case
Now let's try a general - also known as vague, unrealistic, and mostly useless - case for Liandry's as opposed to these other items, in terms of damage only.
Here are our assumptions...
1) Your opponent has 2000 health and 30 MR.
1) Your opponent has 2000 health and 30 MR.
This is a fair baseline, at least IMO. If the opponent has more health Liandry's passive obviously becomes more effective. How effective? We'll find out in a moment.
2) You are dealing 100 magical damage to your opponent every second, with an AP ratio of 1.
Again, seems a fair baseline. Changing the base damage and AP ratio around will obviously change the effectiveness of the different items.
3) You fire away until your opponent is dead.
2) You are dealing 100 magical damage to your opponent every second, with an AP ratio of 1.
Again, seems a fair baseline. Changing the base damage and AP ratio around will obviously change the effectiveness of the different items.
3) You fire away until your opponent is dead.
Pretty simple one, eh?
Results can be found here, in a nice spreadsheet. You are welcome to download and play around with it a bit - I know I did, just to see what happens, and some of the results are quite surprising.
EDIT: To download, rather than view, the spreadsheet, please go here. Apologies.
Results can be found here, in a nice spreadsheet. You are welcome to download and play around with it a bit - I know I did, just to see what happens, and some of the results are quite surprising.
EDIT: To download, rather than view, the spreadsheet, please go here. Apologies.
Results of General Case
We're going to look at two different numbers for each setup we are examining - time to death, and time to half health.
Deathcap: 6 seconds to half health, 11 to death
Deathcap: 6 seconds to half health, 11 to death
Abyssal Scepter: 7 seconds to half health, 13 to death
Haunting Guise w/ Blasting Wand and Amp. Tome: 7 seconds to half health, 13 to death
Liandry's Torment: 5 seconds to half health, 11 to death
This is somewhat surprising, especially if your original thought was that Torment was a terrible item, as it outperforms Deathcap in nearly ever way in this scenario.
However, as pointed out beforehand, this scenario is kind of silly, and not very useful. Let's try out some similar silly, not very useful scenarios...
1) Same as general case, but AOE damage.
Everything else stays the same, but Torment now gets the opponent to half health at 6 seconds, and kills them at 13 seconds. Not looking so great now, but still comparable with our other two alternatives.
2) Same as general case, but no disable.
Exactly the same as directly above, as we're assuming constant damage every second. Things would change around if the damage occurred at longer intervals, but for now we are not concerned with that.
3) Same as general case, no disable and AOE damage.
Torment now half healths at 7 seconds, kills at 14. Worse than everything else.
Now, these were fairly straightforward changes. Let's try some more of those, huh?
This is somewhat surprising, especially if your original thought was that Torment was a terrible item, as it outperforms Deathcap in nearly ever way in this scenario.
However, as pointed out beforehand, this scenario is kind of silly, and not very useful. Let's try out some similar silly, not very useful scenarios...
1) Same as general case, but AOE damage.
Everything else stays the same, but Torment now gets the opponent to half health at 6 seconds, and kills them at 13 seconds. Not looking so great now, but still comparable with our other two alternatives.
2) Same as general case, but no disable.
Exactly the same as directly above, as we're assuming constant damage every second. Things would change around if the damage occurred at longer intervals, but for now we are not concerned with that.
3) Same as general case, no disable and AOE damage.
Torment now half healths at 7 seconds, kills at 14. Worse than everything else.
Now, these were fairly straightforward changes. Let's try some more of those, huh?
Changing Base Damages
If we lower base damage by 50%, Rabadon's is hit the least while Scepter is hit the most.If we increase the base damage by 50%, Rabadon's and Liandry's benefit the least, while Scepter and Haunting Guise and company are hit the most.
Examining either of these with the lower values of Liandry's, we find more or less the same thing - Liandry's is not particularly impacted by changes in base damage values.
Changing AP Ratios
An increase in 50% helps Rabadon's the most - its kill time is at eight seconds, while Liandry's only goes down to 10.
Greater increases further change the difference between Rabadon's and Liandry's - at 3.0, it takes 7 seconds for Torment to kill someone, while Rabadon's does it in five.
A similar decrease in AP ratio by 50% puts Liandry's Torment and Rabadon's at the same level - at or around 15 seconds.
Decreasing it even further, we find that Liandry's gets better and better the lower your AP ratio is, while Rabadon's and the others get consistently worse - with Scepter being hurt the least.
If you change Liandry's effectiveness by assuming either AOE damage, no disable, or both, you find that the difference in damage when you increase the AP ratio becomes greater and greater, while the difference between Liandry's and others when you decrease it is significantly less.
Changing Opponent's Health
As you increase the opponent's health, Liandry's obviously gets stronger, while it gets weaker as you decrease the opponent's health. Right?
Well, this is certainly true, but it doesn't happen in quite the way people expect. Halving the opponent's health to 1000 increases Liandry's kill time by three seconds, while increasing Rabadon's by five. Not such a huge change, really, when you think about it.
The real surprise, at least IMO, comes when you start increasing health. If the opponent goes to 3000, Liandry's kill time is 15 seconds while Deathcap's is 16. Increasing it again to 4000 increases Liandry's time by only three seconds to 18, while Deathcap goes to 21. Go one more time to 5000 and Liandry's goes to 20 seconds while Deathcap goes to 27.
As you can see, Deathcap's time increases linearly while Liandry's increases at a steadily decreasing rate. I'm sure that was no surprise at all to many of you who know a bit of math. The fact itself didn't surprise me, but the degree to which the change manifests itself is rather surprising.
Perhaps more importantly, Liandry's time to half health is even less impacted than time to kill. For instance, Liandry's gets opponent's with 5000 health to half in only eight seconds - only three more than when they were at 2000.
Well, this is certainly true, but it doesn't happen in quite the way people expect. Halving the opponent's health to 1000 increases Liandry's kill time by three seconds, while increasing Rabadon's by five. Not such a huge change, really, when you think about it.
The real surprise, at least IMO, comes when you start increasing health. If the opponent goes to 3000, Liandry's kill time is 15 seconds while Deathcap's is 16. Increasing it again to 4000 increases Liandry's time by only three seconds to 18, while Deathcap goes to 21. Go one more time to 5000 and Liandry's goes to 20 seconds while Deathcap goes to 27.
As you can see, Deathcap's time increases linearly while Liandry's increases at a steadily decreasing rate. I'm sure that was no surprise at all to many of you who know a bit of math. The fact itself didn't surprise me, but the degree to which the change manifests itself is rather surprising.
Perhaps more importantly, Liandry's time to half health is even less impacted than time to kill. For instance, Liandry's gets opponent's with 5000 health to half in only eight seconds - only three more than when they were at 2000.
What Does All This Mean?
Well, first and foremost, Liandry's is not a fundamentally bad item. If you assume constant DPS with a permanent disable - probably a slow - and a spell that is neither a DoT nor an AOE, Liandry's can outperform Rabadon's even if the AP ratio is quite high - the tipping point is right around .9.
(The only champion I know of who can perform this feat is Cassiopeia. Also, you have to take into account that Rabadon's gets better and better the more AP you have, so it is certainly stronger when you assuming you have more items, while Liandry's passive gets stronger only with more MPen and/or Rylai's for a persistent slow.)
It actually outperforms the most direct alternative - just sitting on Haunting Guise and buying a Blasting Wand and Amplifying Tome - very nearly all the time, and is better than Abyssal Scepter (discounting the aura and the MR/health to EHP conversion rate) except at very high base damages or AP ratios.
One other very important result - Liandry's does fairly well against health stacking (surprise, I guess?). Perhaps more importantly, Liandry's time to half health an opponent is largely unaffected as they build more health.
(The only champion I know of who can perform this feat is Cassiopeia. Also, you have to take into account that Rabadon's gets better and better the more AP you have, so it is certainly stronger when you assuming you have more items, while Liandry's passive gets stronger only with more MPen and/or Rylai's for a persistent slow.)
It actually outperforms the most direct alternative - just sitting on Haunting Guise and buying a Blasting Wand and Amplifying Tome - very nearly all the time, and is better than Abyssal Scepter (discounting the aura and the MR/health to EHP conversion rate) except at very high base damages or AP ratios.
One other very important result - Liandry's does fairly well against health stacking (surprise, I guess?). Perhaps more importantly, Liandry's time to half health an opponent is largely unaffected as they build more health.
When Is Liandry's Efficient?
The big question. I'm fairly certain the answer is most of the time.
More importantly, however, I'm sure you'd all like to know when Liandry's is better than alternatives. I don't have a straight answer to that, but here are some guidelines as to when to get it...
1) You need a way to safely and consistently apply the debuff.
This is the biggest of all concerns. If you cannot safely apply the debuff, Liandry's is more or less a worthless item. If you cannot consistently apply the debuff, you are better of getting ability power (unless you are more concerned with getting opponent's low than killing them - see guideline three).
To apply it safely, you need either range or tankiness. To apply it consistently, you need some sort of low CD ability or a long-term DoT.
Some examples of champions that fit both considerations: Cassiopeia, Mordekaiser, Malzahar, Lux, Amumu, Cho'gath, and Sejuani.
2) If you buy only a single damage item, Liandry's is great in that slot.
More importantly, however, I'm sure you'd all like to know when Liandry's is better than alternatives. I don't have a straight answer to that, but here are some guidelines as to when to get it...
1) You need a way to safely and consistently apply the debuff.
This is the biggest of all concerns. If you cannot safely apply the debuff, Liandry's is more or less a worthless item. If you cannot consistently apply the debuff, you are better of getting ability power (unless you are more concerned with getting opponent's low than killing them - see guideline three).
To apply it safely, you need either range or tankiness. To apply it consistently, you need some sort of low CD ability or a long-term DoT.
Some examples of champions that fit both considerations: Cassiopeia, Mordekaiser, Malzahar, Lux, Amumu, Cho'gath, and Sejuani.
2) If you buy only a single damage item, Liandry's is great in that slot.
IMO the competing item here is Abyssal Scepter. Torment is better for overall damage, while Scepter is great if you need the MR and the aura. Either one is a good choice, but the better choice is largely going to depend on the situation you are in.
The two also complement each other, which makes it very tempting to switch a single damage item build to a two damage item build while being slightly less tanky. (I really like doing this with Amumu or Malphite when I'm ahead.)
3) If you care more about getting an opponent to half health than killing them, Liandry's is excellent.
There are many cases where getting an opponent to half health is very nearly as good as killing them. If you can consistently force opponents to back, you can take objectives quite easily while they are down a person.
This strategy lends itself particularly well to certain poke and AOE compositions.
4) You don't always need a consistent disable to make Liandry's good, but it helps.
Liandry's loses a lot less effectiveness if you don't have a persistent slow or other disable to go along with it than people seem to think. While Rylai's/Liandry's is still very good, if you only want Liandry's you don't have to get Rylai's to make it worthwhile.
5) If you have very high AP ratios you are probably better off skipping it in favor of something else.
This goes doubly if you have high AP ratios on AOE or DoT spells.
6) Surprisingly, the opponent having more or less health doesn't really affect the decision.
One surprising negative result is that, while Liandry's is certainly better when the opponent stacks health, it is not significantly better at killing people at higher health than simply stacking ability power.
If the above guidelines don't lead you into buying Liandry's, do not buy it simply because the opponent is stacking Warmog's. It will not be making more of a difference than getting something more suited to your champion and the composition you are in.
And there you have it. Liandry's isn't bad, and is actually a perfect item for certain champions, situations, and/or compositions.
In unrelated news, I just started doing this, so please kick me in the teeth if I did something wrong. I won't mind.
EDIT: A list of spreadsheets by champion...
Comparison of Abyssal Scepter and Liandry's Torment as single-damage items on Amumu.
And, as per usual, I am terrible and forgot the pun of the day...
ReplyDeletePun of the Day: When a clock is hungry, it goes back for seconds.
And it seems as though Google Docs is not good at sharing the actual spreadsheet with people.
ReplyDeleteApologies on that.
Will be moving it around to somewhere else in the next few minutes.
And done. Again, apologies on that.
ReplyDeleteSome additional information, for those interested...
ReplyDeleteThe original spreadsheet I used had a fundamental flaw in it - I was using the damage from Liandry's over a single second as the damage for over .5 seconds.
Obviously fixing this had an impact, but it was not nearly as large as I originally thought it would be when the error was uncovered. Liandry's is now much more comparable to Abyssal Scepter, but still brings people to half health at least as fast as Rabadon's in most cases.
At a request from people elsewhere, I am also beginning to do a number of spreadsheets on specific champions for specific decisions. I have added a link at the bottom of the original post to the first spreadsheet.