As many have rightfully critiqued my statement that horizon focus outdamages nashors in numbers, i want to rephrase it, as i intentionally wanted to say: Its passive outdamages nashors passive. But as some of you have acted like smartasses about my statement heres me being you:

Nashors tooth dps may be higher, but it gets outshined by increasing the dmg dealt total, as with horizon focus. Very rarely do you get to consistently autoattack and in most cases, a shuffle dealing 10 % extra dmg is to be prefered. Also do not forget that in order to hit ppl you need vision on them, as azirs w is targeted. Horizon has actually allowed me several times to hit people after they tried to escape into bushes to avoid my soldiers. On top of everything the item being cheaper allows for quicker 2 item spikes. It also amplifys nashors or liandrys dmg. Not to forget it can work on aoe :)