Bruiser Mathcraft: BotRK is King

In my last article, “Bruisers: The Science of One Damage Item,” I discussed the three main “one hit wonder” bruiser damage items: Iceborn Gauntlet (“IG”), Trinity Force (“Triforce”) and Blade of the Ruined King (“BotRK”). AD carries have received a lot of attention in regards to maximizing DPS, and I referenced an A DIFFerent View article about Bloodthirster versus BotRK to help conceptualize BotRK’s damage.

However, defensive bruisers, as a class that specializes mainly in tanking and that used to almost solely build Triforce for damage, has not received the same depth of analysis. To remedy this, I bring you:

Bruiser Mathcraft

IG falls in an obvious place because of its lower damage proc compared to Triforce, but how do BotRK and Triforce directly compare? Is one of them strictly better than the other, or are they heavily situational?

Setup

First, I’m going to present an amended version of the chart you’ve likely seen several times to show BotRK’s passive damage. This chart shows health (“HP”) amounts and the corresponding BotRK passive damage, the damage needed (including the extra attack damage BotRK has over Triforce) for a Triforce proc to equal BotRK damage and the base damage a character needs in order for these two damages to be equal.

HP	BotRK Passive	Damage Needed	Req. Base Damage
1,000	40	50	33 ⅓
1,100	44	54	36
1,200	48	58	38 ⅔
1,300	52	62	41 ⅓
1,400	56	66	44
1,500	60	70	46 ⅔
[. . .]	[. . .]	[. . .]	[. . .]
2,000	80	90	60
[. . .]	[. . .]	[. . .]	[. . .]
3,000	120	130	86 ⅔

As you probably already guessed, an autoattack with a Triforce proc will almost always do more damage than a BotRK autoattack. This table gives some useful information that we can use in later calculations: BotRK’s passive does 4 more damage per 100 HP and 40 per 1,000 while you need 2 ⅔ base damage per 100 HP and 26 ⅔ per 1,000 for a Triforce proc to keep up.

Application

BotRK and Triforce are both a pain to calculate damage for because they’re dependent on two variables that widely vary: enemy HP and character base damage. In order to make things both easier and more practical, I’m going to compare these items using Jax and Irelia, two of the most common and prototypical Triforce users from previous seasons.

Jax, mainly because of his low cooldown W (Empower), is able to proc Triforce’s effect almost every time it’s up. Irelia, on the other hand, has longer cooldowns and cannot proc consistently. While I will be calculating the extra attack speed from Triforce, I am not going to consider Jax’s passive because it makes things considerably harder and I want to give Triforce a handicap (more autoattacks helps BotRK since faster attacks will not get you any more Triforce procs). Take this as a small substitute for the utility Triforce brings, if you wish; you’ll soon see, however, that this does not impact the results.

Scenarios

             

First, let’s look at Jax and Irelia’s base attack speed, attack damage and how they increase throughout the game. Note, the client rounds off numbers to display them but, just like in your rune pages, the unrounded value is used in actual calculations.

	Irelia	Jax
Base Attack Speed	0.665	0.638
Attack Speed per Level	3.2%	3.4%
Base Attack Speed at 18	1.027	1.006
At 18 with Triforce	1.3357	1.3078
Base Attack Damage	59.3	59.675
Attack Damage per Level	3.3	3.375
Base Attack Damage at 18	115.4	117.05

For the sake of simplicity and easy endgame analysis, the base values for level 18 will be used, but, with the data I’ve shown you, it should be easy to scale to whatever level you want to look at. And remember: BotRK only depends on an enemy’s health while Triforce uses your base attack damage, so this is the best case damage for Triforce. BotRK is therefore better at comparatively lower values of HP earlier in the game.

Scenario #1: Sustained Damage

The first scenario is a moderate, 10 second period of sustained damage against a target. This is likely to occur in duels against other bruisers or tanks. For squishier characters, you’ll only see this scenario if you are able to effectively stick to them.

In 10 seconds with BotRK, both Jax and Irelia will have time for 10 autoattacks while they will have time for 13 with Triforce. Without an ultimate, Irelia will be able to proc Triforce 3 times while Jax will be able to proc it 4 times using only his W. I am setting up Jax this way because using his Q causes him to lose an autoattack. I will assume that both characters start the fight with a proc (which allows Jax to fit his 4th proc in).

HP	BotRK Passive + Extra AD	Triforce Proc Damage
1,000	400	Irelia: 519.3
1,500	600	Jax: 585.25
2,000	800
2,500	1,000
3,000	1,200

Both Jax and Irelia do more damage with BotRK than Triforce to targets that stay above around 1,500 HP during the fight. This does not include the use of BotRK’s active, which makes it far more likely that you will be able to stick to your target during this period in order to get the full number of autoattacks. In this situation, the active would do 208.525 damage for Jax and 207.7 damage for Irelia, which would put the amount of HP needed to below 1,000. Remember, however, that BotRK has a 1 minute cooldown, which is why I’m showing the numbers both with and without it -- it is not something you will always have available.

Scenario #2: Short Burst Damage

It’s not surprising that BotRK is far better in a sustained fight: it’s passive is incredibly powerful. But what about a short, burst exchange? This would be a situation where, for example, you jump on an enemy carry and they get away after only a few attacks. Since the procs will take up a larger percentage of attacks than the last scenario, this is far more favorable to Triforce. To further help the item, let us (generously) say that while BotRK gets off 2 autoattacks Triforce gets off 3 with 1 proc.

HP	BotRK Passive + Extra AD	Triforce
1,000	100
1,500	140	Irelia: 173.1
2,000	180	Jax: 175.575
2,500	220
3,000	260

In this situation, which is essentially the most favorable one possible for Triforce, BotRK does more damage if a target is above 2,000 HP. If you use BotRK’s active (which, again, has a significant cooldown), this value is lowered so much that BotRK will always do more damage than Triforce.

Conclusion: BotRK is King

If my title didn’t tip you off, here’s my conclusion: BotRK is the definitive bruiser item for damage in this patch. As I mentioned in my last article, IG has a niche for those who want more tank stats, crowd control and spamming ability, but BotRK is definitely the choice if you want to have a solid damage option. It has an incredible build path with linear power increases that gives you a useful active early on with Bilgewater Cutlass. In comparison, Triforce requires way more inventory space and has the particular stumbling blocks of no sustain through lifesteal and an annoyingly expensive Phage component. Even better, BotRK’s passive grants extra “life steal” on top of what it already gives you as a flat percentage.

In my opinion, BotRK’s active does a great job in covering up its weakness: for it to work you must be able to reliably autoattack a target. Using the active, it is far more likely that you will be able to stick to a squishy target and, if not, the use of the active has likely given you more damage than the burst of Triforce procs would have, anyways.

BotRK is even more valuable than you would think for another simple reason: everyone is buying health. With the buff to health this season, almost every champion is buying health in some way, and even AD carries are commonly getting a Warmog’s as a last item. This means that BotRK is more effective since targets will have higher HP values for longer in a fight, giving it more time to out damage other items. Aside from being legitimately good in a normal case, it excels even more based on the current state of the game.

BotRK’s damage is based on current HP. This means that you do less damage over time to a target. Because of this, getting fed in the early game makes Triforce a better snowball item if you get a lot of gold to get it quickly. However, with so many people stacking health and bruisers and tanks rushing for it, I believe that BotRK doesn’t experience a significant decrease in usefulness because of this. Just keep this in mind so that you can adjust for different situations like squishier teams.

The significance of this conclusion should not be underestimated: this item is outperforming an item that is 1,003 gold more expensive. Triforce does have arguably greater utility because of it’s movespeed and mana, but you pay a lot for it.

Start buying BotRK. It is a tragically underutilized item and, in its current state, seems legitimately overpowered.

Edit: This article was written before the Patch 3.02 notes were released. BotRK is getting buffed, going from 40 to 45 attack damage and 4 to 5% current health on its passive. The math is easily modified to account for this if you want concrete numbers. Obviously, I recommend the item even more strongly now.