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Nashor's Tooth on fizz?

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So I've been trying to help my friend getting out of bronze since she plays way better than those in that "div" and her pc broke. It was all good until 17-3 then my so called team decided that they are just as strong as me and they went in one by one all the time. I posted this image and got offended pretty hard for having nashor on fizz. I think it's a pretty viable item and I have no idea why those tards attack it.
ITT: Discuss Nashor's Tooth
 

Vunjo

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First of all, you must act like a gamer, not like a meta league of legends player to make a different build. You obviously did that part well.

Then take in consideration what you're building on a certain champion. Most players will say that Fizz is a high burst assassin champion. Assassin champions require a lot of burst damage, which comes from simple items. As Fizz, you're building AP, along with magic penetration for the ultimate burst damage.
On the other hand, for continual damage you would require either cooldown reduction, mana regeneration, or so.
That would be start of building offensive items. Now we must consider few other things. How to be defensive, and how defensive should you be. It's pretty simple. If you're an assassin, and your job is to single out a single (or more) champion(s) in a matter of seconds (depending on class and build). For that matter, you do not need defensive items, in other words, you can almost go with a glass cannon build. On the other hand, continual damage requires more time to deal the same damage as a glass cannon. For this obviously you would require more defensive stats, because you simply need more time to kill the enemy, and you can't kill your enemy while being dead (Karthus: "I don't get it.").
So the meta build and gameplay for Fizz is a high burst assassin mage. This means players will mostly rush glass cannon items, with few exceptions such as zhonya/abyssal or so. People play this because it works fine, and it's pretty easy to play.
Now after all this chat, let's start with what you're doing right now. Nashor's tooth is the best described as continual damage item, hence it increases attack speed, and cooldown reduction mostly, while granting moderate ability power for burst damage. Why build Nashor's tooth on Fizz? The answer is quite simple. Fizz's W procs an on hit effect on each auto attack, scaling with ability power. Nashor's Tooth grants both attack speed, and ability power, meaning that it should be a great item for him. However, you should note few things first:
1.) Is it truly worth of building it? Does his W scale that much effectively?
2.) What is your role? Assassin, or bruiser? If you're an assassin you would not require that much continual damage such as Nashor's Tooth, because you are squishy, and would not land much more auto attacks (The team should focus on glass cannons first at least).
If you take a look at patch notes, you will see a change in Fizz's W that happened recently if I recall. Ability Power scaling fell from 35% down to 15% per auto attack. This makes very inefficient to build attack speed. Why? Because other auto attackers like Teemo/Kayle have much greater scaling damage (Teemo's 30%, and Kayle's 40%). + Both of them are ranged, meaning they will survive more without building tanky items, and thus directly auto attacking much more than Fizz would.
There's still another thing to consider when creating different builds, especially attack sped based. Each champion has a specific attack damage base. All attack speed increases are based on it, meaning that not all champions will benefit the same from the same attack speed item. Fizz has an above average attack speed base, and high above average attack speed increase per level. This means 2 things. First is that it's very efficient to build attack speed on Fizz because of his natural high base. The second is that he already has a decent attack speed on his own at level 18. This will be important in the next part.
Now we must consider the fact that there's a drop of efficiency when building stats. If you jump from 100 HP to 200 HP, you have doubled your effective defense. If you jump from 500 to 600 hp, you've only increased it by 20%. This means that the same amount of stats is not always efficient, it's based on your current stat, and you want to max out efficiency of the build. As stated before, it's very efficient to build attack speed on Fizz based on his base attack speed. However, overdoing it will not fix the problem. If we take a look at the examples already given, Teemo or Kayle both able to benefit from attack speed far more than other champions. Then again, overdoing the attack speed is not the solution. As stated few sentences above, for example:
Getting 0.2 attacks per second is efficient when you have 1 attack per second, then you've increased your attack speed effectively by 20%. If you're gaining 0.2 attack speed when you already have 2 attacks per second, it's but a lousy 10% increase. The conclusion of all this in short is, never overdo any stat. Almost. There's always an exception.
From the above conclusion it's obvious that it could be effective to get 1 or maximum 2 attack speed items on Fizz. But, we must always make sure that this specific stat is effective on the champion in all ways. The ability power scaling from the new patches is low. Before that, it was quite high, 35%, but now it's down to 15%.
To conclude: Everything depends on your build. If you're a glass cannon, getting sustain DPS item will not solve your problem. If you're a bruiser, it's helpful enough to increase your damage output. For Fizz, it's not that effective since the new patches, simply because the AP scaling is really low, the base damage of spell (30) is also low, Fizz is a melee champion, meaning he won't be attacking that easy without defensive item, and the easiest way (perhaps not the most effective) to play Fizz is as an assassin.
 
Level 16
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Mainly I build nashor becaus of my role since Q procs on hot effects such as nashor passive also the 20% reduction to cd is pretty sweet. I often come to the issue that in late game the tanks have too much health and I can't do anything with single bursts even with maximum possible magic pen so my solution was to combinate W and Nashor to continuously damage them, squishy champs die from the lichbane+w+q combo anyway and even if not I can continuously damage them with nashor thanks to the gapcloser. Many times I could only secure kills because I had nashor.
 
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