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Randuin’s Omen vs Frozen Heart – What’s your best option? Mathcrafted.


Hello, hello! DiffTheEnder here bringing you more rainbows in today’s mathcrafted analysis.

Tanky champions in LoL have always been one of the biggest nightmares to come up against in a game. You remember that fed Shyvana who could 1v4 and crawl out alive without taking an arrow to the knee? She probably had a Randuin’s Omen.

Why is Randuin’s Omen so good?

randuin

Randuin’s Omen has been one of the most popular items in the game for a long time. According to LoLKing’s stats – it’s more popular than a Doran’s Ring and is in the top 15 of all items built.
There’s a few reasons for this:

  • It’s a tank’s dream – it gives HP which is good against all types of damage with a huge armor boost to boot
  • It comes with an Attack Speed reducing passive which is extremely effective against auto attackers (both in its build path and final build)
  • It has one of the best item actives in the game with a powerful AoE slow
  • Cost efficiency – when given the benefits of its passive it’s a great buy in terms of gold spent.

The competition for the item slot that Randuin’s occupies usually is one of the following, and Randuin’s is preferred over them for some of the reasons listed (not a comprehensive list):

  • Sunfire Cape – Randuin’s provides more durability and is more cost efficient
  • Thornmail – provides no HP and no utility as compared to Randuin’s
  • Warmog’s Armor – Vulnerable to %HP shred and you’ll have no resists to scale off it
  • Guardian Angel – No HP and is very cost inefficient without the passive. Also provides no CC.
  • Frozen Heart – No HP and mana is a wasted stat to be paying for (manaless champions are king these days)

I want to have a second look at the above list of items, specifically the Frozen Heart. For those who have read my older works, you would remember my “Why Frozen Heart is the Best Item in the Game” article.

With the rise of manaless champions in the bruiser/tank role – Dr. Mundo, Shyvana and Renekton come to mind – Frozen Heart has all but been useless on these champions who make no use of mana and this may mean it is not the best item in the game and this is simply not acceptable. So it’s time to resort to the power of mathematics to prove that it is still an amazing item if not the best!

Patch Changes that buff Frozen Heart

Recently in patch 4.10, Riot has nerfed Randuin’s Omen:

  • Attack speed reduction on being hit reduced to 10% from 15%.
  • Movement speed slow on being hit removed.

Given the buffs to attack speed that ADCs got in the same patch – Randuin’s is significantly weaker than it was. This makes Frozen Heart a more viable option. Here’s what the item does for those of you who may have forgotten:

frozen

Here’s how the Frozen Heart was changed in patch 4.10:

frozenPatch

While the attack speed reduction aura was nerfed, it’s still much stronger than the Randuin’s Omen passive and more significantly the attack speed aura affects enemies even if they are not attacking you (which benefits your whole team and not just you!). The cost reduction and armor increase also take Frozen Heart up a notch.

The latest patch has Spirit of the Ancient Golem boosting all bonus HP by 25%, which means you’re more likely to have a higher HP amount for the 100 armor from Frozen Heart to benefit off.
With all of these changes happening – I set out to check if Frozen Heart is actually better than Randuin’s Omen now and as always resorted to rainbow graphs to compare them!

Factors in making a comparison

When comparing tank items, there is a greater level of complexity than when comparing other items. This is due to the fact that resists scale off having more HP. If you want more information regarding how there is no diminishing return on resist stacking (take a look at one of my videos here)

So the core difference between the two items (ignoring the passives/actives) is the following:

comparison tableWe’ll get to the passives and actives later. Let’s focus on the HP, armor and Attack Speed reduction first. Important to note is that Frozen Heart does not help at all against magic damage while Randuin’s does (with its HP), so for the next sections we will be focusing on comparing the item when faced against auto-attacking champions (usually ADCs).

Here are a list of factors we have to take into account when comparing these items:

  • HP – how much HP you have before buying each of these items. The more HP you have, the more it benefits the Frozen Heart (since the higher armor would scale off the higher HP better)
  • Armor Penetration – the more armor penetration the enemy has, the more it favours Randuin’s Omen as ArPen affects the benefits of Frozen Heart (the 30 increased armor is affected)
  • Attack Speed – attack speed reduction is calculated as a function of the final attack speed value which is different to how attack speed is built. In other words, buying a dagger does not outdo the attack speed reduction from Frozen Heart.
  • Armor(pre FH/RO) and enemy AD – This is common between both items – but it affects the numbers in terms of how many attacks you can tank (just keep this in mind!)

Now that we know what we’re dealing with, let’s talk about how we’re going to analyse the numbers and what assumptions we’re going to make.

Assumptions and Methodology

The easiest way to display the results would be to assume that you’re up against one auto attacker who deals only physical damage and uses no spells. It’s a specific scenario no doubt, but it produces the purest comparison between a Frozen Heart and a Randuin’s Omen. The only key assumption to be made here is that the auto attacker has 21 points in the offence tree which nets them a 6% armor penetration bonus. For the purposes of the following graphs, the champion has 100 armor before building a Frozen Heart or Randuin’s.

Important Note: For the first set of graphs that you see below — I’m actually giving Randuin’s a 625 HP boost. “Why?” you may ask – because Spirit of the Ancient Golem would offer a 25% HP boost to that amount, so I’m trying to present the most one-sided case for Randuin’s Omen with the first set of graphs.

As mentioned before, the enemy’s Attack Damage and Armor does not affect the relative difference in durability between the two items, but I will try to show off a couple of graphs so you guys can see the impact on the results. What we’ll be comparing is “How many auto attacks can you survive against an ADC with ____ AD and ___Armor Pen and _____ Attack Speed” when building a Randuin’s Omen vs. building a Frozen Heart.

On with the results.

Initial Results

Firstly, let’s get the obligatory “How to Read” graph out of the way.

How to

Make sure to click on the images for a clearer full-resolution view and make sure to leave me some feedback on the graphs!

4 graph

 

Firstly, let me say a quick apology for assaulting you with 4 rainbow graphs, the alternative would be to produce a graph that looks like this and I don’t think that looks very reader-friendly. There are simply too many variables to graph using a simple line graph or even one Rainbow Graph!

These results don’t mean much without some interpretations — all they’re doing right now is probably giving you a seizure. So let’s skip ahead to the..

Interpretation of Initial Results

So what can we learn from the rainbows above? That Randuin’s Omen is an amazingly strong item that can take 2-5 attacks more than FH all the time?! Not quite.

I’ll repeat this again to make sure you guys don’t miss it — the above set of graphs are made with the aim of trying to make Randuin’s Omen seem as strong as possible, with the following factors being used to do so:

  • +625HP for Randuin’s with the use of Spirit of the Ancient Golem’s bonus
  • Not accounting for the 400 cost difference between Frozen Heart and Randuin’s Omen

This effectively makes it look like Randuin’s Omen is better in every realistic situation — and you’d be absolutely right. It definitely is better in a lot of situations but nowhere nearly as strongly as above in some other situations. Let’s take a more realistic look at the case at hand though.

Key Points

The above analysis is accurate for junglers who built Spirit of the Ancient Golem and then a Randuin’s.  However there are other possible situations, and these may be more realistic. There are a few key points I have yet to cover and they are as follows:

  • Frozen Heart is cheaper by 400 gold – we can account for this by adding a Ruby Crystal (400 gold and 150 health) worth of stats to the analysis to even out the comparison.
  • Something that would not be shown via the graphs is the ability for Randuin’s Omen to offer greater durability against magic damage as it offers more HP (which works against all types of damage!)
  • Frozen Heart offers a huge boost to your mana pool and CDR which lets you cast more and cast more often which can decide fights.

Notably, the first bullet point above is the one that can be graphed to show some drastic change in results. We can now graph the situation where we can show Frozen Heart most favourably with:

  • +150 HP from Ruby Crystal from the 400 gold you save from not buying a Randuin’s Omen
  • -100 HP (to bring it to 500HP) for Randuin’s Omen if you aren’t building a Spirit of the Ancient Golem.

This presents a much more convincing case for results and these can be seen below.

More Results – Frozen Heart makes a comeback!

Here’s what the 4 graphs above look like with the HP considerations listed in the previous section.

b 4 graph

You’ll notice now that in most realistic scenarios – the Frozen Heart is better against auto-attackers! Also note that the colour to value scheme of these 4 graphs is different to the one above (due to a different set of values). Here’s our point of confusion now:

Frozen Heart is both worse and better than Randuin’s Omen depending on the situation. How do you decide which to build?

Let’s get to some full on analysis of our results so you can take away something useful from this article!

By the Numbers

So Randuin’s Omen can range from being about 5 attacks better than Frozen Heart to being around 5 attacks worse depending on what else you built and what stage of the game you bought the item in. This is actually a surprising result! When initially setting out on this analysis, I fully expected Randuin’s Omen would win it by a mile as shown by the first set of graphs, but was surprised how even it was when looking at an alternate scenario where Frozen Heart shines.

What can this tell us about each item?

  • Both items are relatively similar in strength against auto-attackers
    • Which means that the choice of the item to be built falls upon the merit of the item’s ability to benefit other aspects of your game (eg. CDR or AoE slow)

So let’s take a look at factors in weighing up the decision between Frozen Heart and Randuin’s Omen.

General Decision Tree

Let’s talk about theoretical situations and how you might make a decision on which item to buy.

question

Randuin’s Omen is favourable:

  • If playing against a team with a lot of magic damage — you’d be better off with a Randuin’s Omen which gives you more HP to fend off against magic damage.
  • If you are a manaless champion – Randuin’s may be preferred although Frozen is not a terrible option (it’s decent at best)  if you benefit from the CDR.
  • If you are already maxed out on CDR.
  • If you are a champion who does not build many other HP items or has a low base HP.
  • If you are a champion who has resist bonuses (eg. Rammus) which scales off the extra HP from Randuin’s.
  • If you need the AoE slow to help lock down the enemy for your team to kill them

Frozen Heart is favourable:

  • If playing a champion that scales very well off CDR/armor and a larger mana pool (see: Malphite and Maokai) – a Frozen Heart is favourable
  • If playing a champion who isn’t going to be in the middle of the enemy team to activate Randuin’s Omen – Frozen Heart may be the preferred option.
  • If you have no way to draw aggro (eg: Taunt) or place enough pressure to draw auto attacks to yourself — Frozen Heart may be preferred.
  • If the enemy team has a lot of auto-attackers
  • If you naturally have a large HP pool

An important point to note is that Frozen Heart’s attack speed reduction is an aura.

Regardless of whether you want to help your team or not and regardless of whether you are making the worst decisions in the world, you will continuously be reducing every nearby enemy’s DPS from auto attacks by 15% whether you like it or not. It’s foolproof.

Unlike a Randuin’s Omen, there is no thought process required of when to use the active or complex positioning decisions that need to be made when using a Frozen Hear. It just works! (I know that sounds like a Steve Jobs sponsored commercial — it’s appropriate in this context though)

Build Path

I’ll keep this one short.  They both share Warden’s Mail as half of their build path and, as a commonality, it can be ignored. In essence then, this comes to a question of is it better to have a Giant’s Belt or Glacial Shroud mid-game and which is easier/better to build.

glacial vs giant

Here’s my thoughts on the matter:

  • Giant’s Belt – A basic component item.
    • Helps you against all types of damage and offers you a lot of build options if you change your mind.
      • Sunfire Cape, Warmog’s Armor, Frozen Mallet and Rylai’s – although you’re probably not going to be building Rylai’s
    • At a cost of 1000, it is the most expensive component in an item recipe possible (besides BF sword and NLR). It requires you to save up and go for a few minutes without increasing your strength.
  • Glacial Shroud – An all around cheap item that helps in various aspects of the game.
    • Offers a great boost in CDR, mana and armor
      • Which helps immensely on champions like Elise, Malphite and Maokai
    • Cheap components at 400 gold for a Sapphire Crystal and 300 for a Cloth Armor (Cloth5 – which is where the name comes from!)
    • Does not offer as much durability as a Giant’s Belt against physical damage unless you have more than 1900 HP.
    • The mana and armor if bought during laning phase can improve your combat ability as you can use more abilities and take less damage against an AD top.

Once the items are complete, you’re left with 400 more gold since Frozen Heart is cheaper. Frozen Heart also scales well to late game as it benefits off HP better than Randuin’s Omen as shown in the above graphs. Which is once again a win for Frozen Heart.

Overall, I’d say this is a definite win to the Frozen Heart as a Glacial Shroud offers more versatility and is easier to build than a Giant’s Belt and offers benefits every 300-400 gold if you’re shopping that often.

(I lied, it wasn’t short!)

Champion Compatibility

This is the one that Frozen Heart struggles with. There are very few champions in the competitive meta who make great use of the mana and CDR the item provides while needing the durability. Notable champions that are currently popular who can make great use of the item are:

  • Braum
  • Elise
  • Jax
  • Orianna
  • Thresh
  • Ryze

malphite

With the buffs to attack speed, Malphite is more effective due to his innate attack speed reduction and a Frozen Heart Malphite is every ADCs nightmare although I don’t expect to see him in LCS as a regular any time soon.

Randuin’s Omen however is applicable to all the above champions and all manaless champions such as Shyvana, Renekton and Mundo which makes it a better item as a “one size fits all”. This is a clear win for Randuin’s Omen.

Active vs Passive

Both of these items have amazing effects. Randuin’s has the ability to slow an entire team while Frozen Heart reduces every nearby enemy’s AA damage output. It’s extremely hard to weigh these up as it depends heavily on team compositions and the champion you are playing.

Several questions need to be asked when deciding which is better:

  • Do you need to slow the enemy team because they are highly mobile or do you need to reduce their damage output?
  • Is your team lacking CC to lock down the enemy?
  • Would a persistent 15% AS reduction be more beneficial than 2 second slow?
  • Is your bruiser/tank going to be in the back line or peeling?

For this reason, it’s near impossible to label either one of these items as having a better passive/active than the other.


Conclusion

As always, welcome to all the readers to who skipped to the conclusion. I’ll try to summarise succinctly!

This has been an exhaustive look at the two items. We’re nearing the 3,000 word mark which means it’s time for me to wrap up our journey through the various aspects of these items.

Against auto attackers – depending on whether you buy a Spirit of the Ancient Golem, or do not and buy a Ruby Crystal with the 400 gold saved by buying a Frozen Heart instead of a Randuin’s Omen – the champion with Randuin’s Omen may tank 5 more auto attacks or tank 5 less auto attacks than a Frozen Heart. In most realistic situations both of these items are similar in their effectiveness against auto-attackers.

Against everyone else – Randuin’s Omen wins by virtue of offering HP.

For champions – Randuin’s is equally effective regardless of what champion you buy it on whereas Frozen Heart is only fully beneficial to a few champions.

Build path – Frozen Heart wins this one since its components are cheaper and is stronger mid-game.

Item passives – A number of factors determine which of these is more beneficial. The one thing that is certain however is that Frozen Heart’s passive makes the entire team more “durable” due to reducing all nearby enemies’ attack speed and is also foolproof.

Overall – This seems like a copout summary — but it is indeed highly situational for when you build a Frozen Heart over a Randuin’s Omen, although I think that it should be built a lot more than it is currently.


DiffTheEnder’s Note (Author)

Thank you so much to everyone who showed immense support for my Bloodthirster article and motivated me to write this one. As always, I’m looking for any constructive criticism and even just messages saying whether you enjoyed it or didn’t!

Ideas for future articles or telling me stories of how you perhaps despise tasting the rainbow and M&Ms are the master race are all welcome. If you wanted to stay up to date with my latest project or want to harass me on a daily basis — ping me @DiffTheEnder.

Also a big thank you to Denise who helped make most of the graphics in the article — the real MVP!

Thanks again — looking forward to hearing what you guys think about the Frozen Heart and the article!

Until next time — DiffTheEnder


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DiffTheEnder

A prominent mathcrafter in League of Legends. He is notable for several analyses on damage output comparisons of items. One of his most popular works was on the comparison of the damage output of Rabadon's Deathcap vs Liandry's Torment. He is also the co-founder of Cloth5.

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