AP assassins nowadays buy Lich Bane for its sheer burst power. 50 base is stupid, but 75% AP is awesome when added to a burst. Combine that with the already high burst and you have a 99% chance of killing your target.

Lich Bane has become so strong, that it's already getting nerfed (although reasons are that its also not a burst dmg item, but a sustained dmg item, like Tri and IBG). It's also getting picked on many other champions like Kayle and Teemo. Even champions that cant use it a lot, AP with high CD, use it. But is it worth it on them? When there is another very good item that is Nashor's Tooth? Let's find out.

FIrst of all, you need to know the champions base CD of the skills, the way you use them, and the skill you spam the most. Then you need the champion's AS at level 18 (or whatever level you are thinking of getting the items) and stickness potential. These are needed to understand what is most dmging for X champion.

All assassins are bursters, meaning they won't w8 2 seconds before using their skills. To find out what is the most dmging item, think of your build. Do yoy get a lot of CDR or AS? Do you AA or do you go in and out in an instant. Do u find yourself dueling a lot?  These do matter for the item pick.

Lastly, for these simple formulas to work, consider your full build, or build you have, instead of just using the items separatedly.

To calculate the Nashor VS Lich power:

(AS at prefered level + owned bonus AS) * (lowest cooldown skill + owned CDR ) =(Nr. of attacks during CD                                                                                                                                     of most spammable skill.)                                                                                                                                   (Let's call it Value A)

(Value A) * 15 = Total Base and Scaling of Nashor during CD of skill.

Example: a level 18 DIana with Nashors and Lich Bane. She has ~1.3016 AS and 25% CDR (Lowest spammable skill is Q with 4.5 CDR)

1.3015 * 4.5 = 5.8572 attacks.

5.8572 * 15 = 87.858 base damage and 87.858% AP

Nashor DPS: 19.524 (+19.524% AP) per second

Lich Bane DPS: 11.111 (+16.667% AP) per second.

So as you can see Diana has more dps with Nashor than Lich Bane. But when does Lich Bane become better? Well, all you have to do is use the lowest CD skill with Max cdr and go for 5 AA during that time. Lets use Diana again.

AS * 3.6 = 5  so  5 / 3.6 = 1.3889

So with 40% CDR, Diana would need at least 1.3889 AS to outdmg Nashor. 

And a fun fact. Lets see how much AS would Nashor need to deal as much dmg as Lich if you can perma use it.

5/2 = 2.5 AS.  The cap for AS. So you can reach the same amount of dps (more cuz Nashor has 25 more base than Lich), but you'd end up sacrificing a lot of dmg. 

This post wasn't made to say one item is better than another, since currently 1 is used for burst and other for sustained damage. It's just to show that just because an item is never used, and another abused, doesnt mean they're better. So next time you want to buy a Lich Bane for Maokai, think if he wouldnt be best off with a Nashor.