League of Legends: Ninja Tabi

League of Legends recently made the interesting decision to remove dodge from the game completely. I would imagine they thought it was too spiky a stat. Against Nasus, for example, if you managed to dodge one of his Q attacks it would basically take away most of his damage output. Fail to dodge it and you'd get blown up. There was one champion based around dodge and they remade how he works. There were glyphs with dodge on them and they took those out and refunded the cost to anyone who bought them. When they redid the mastery trees a few months ago they pulled dodge out of them. And then there's the one item in the game that had dodge on it...

Ninja tabi used to be the set of boots used against people who mostly auto-attack. For the low cost of 850 you got the level 2 speed boost, 25 armor, and 10% dodge. This changed to a set of boots that for 850 gives you a level 2 speed boost, 25 armor, and 10% damage reduction from non-turret basic attacks. That sounds like quite a mouthful of a restriction but I'm pretty sure it works out to only working against the same things dodge used to work against. The difference is now instead of taking full damage 90% of the time and nothing 10% of the time you always take 90% of the damage. In the long run it has the same impact on durability but it is much smoother in the short run. There's no getting lucky and surviving when you 'should' die. There's no getting unlucky and bursted out with your defenses having no impact.

But the question I have is should it ever be purchased? How does it compare to other defensive stats you can buy on items? How does it compare to other pairs of speed 2 boots? Now that dodge is gone we really can use the old 'effective health' formula to calculate how long someone's going to live. There is healing in the game (many teams will run someone with a healing ability and there is life leech) which will make mitigation better than it looks when compared to straight health but for now I'm going to ignore healing...

Going back to a previous post on the subject Z=X*(100+Y)/100 where X is your max health, Y is your armour, and Z is your effective health. If all the incoming damage comes from auto-attacks (maybe you're fighting a fed Tryndamere, for example) the formula changes to Za=X*(100+Y)/90.

Ninja tabi costs 850. Possibly the best way to compare is to scale up chain vest which is 45 armour for 700 gold. If it cost 850 you'd get 55 armour out of it. So compared to ninja tabi you're picking up an extra 30 armour but losing the modifier. When, if ever, do these two things line up as equals?

Z = Za

X*(130+Y)/100=X*(100+Y)/90


With Y=0...
1.3X=1.11X

With Y=100...
2.3X=2.22X

With Y=200...
3.3X=3.33X

This is a pretty obvious pattern. Until you reach a really silly amount of armour you're better off just getting more armour instead of shifting to a ninja tabi. EXCEPT! You do actually get the speed boost out of the boots. It really isn't fair to assign the entire cost of the item to the defensive stats since the speed is a very real part of the item. You're not getting one or the other. You're getting some set of boots no matter what you do. How much of the cost should we deduct for that? Well, tier one boots cost 350 on their own. Lets be super generous and assume the boot upgrade is only an extra 50 on top. Then the defensive stats on the ninja tabi only cost 450 instead of 850. In this case the chain vest is really only worth 29 armour. This isn't even a comparison. You can get 4 armour or the 10% modifier. But for fun...


Z = Za

X*(104+Y)/100=X*(100+Y)/90


With Y=0...
1.04X=1.11X

With Y=100...
2.04X=2.22X

With Y=200...
3.04X=3.33X

So, yeah... Even if you didn't have any armour at all you'd be better off with the ninja tabi. Looks pretty good! EXCEPT! All the incoming damage is practically never going to be entirely auto-attacks. Maybe against Tryndamere, Master Yi, or Nasus? (And against them you should be all over ninja tabi!) But what about someone like Gangplank who does a lot of physical damage with special abilities? I was thinking this was going to be a question but with the current valuations it isn't. Only getting 4 extra armour means as long as practically any incoming damage is auto-attacks the ninja tabi is better than buying a chain vest.