Rapid Firecannon vs Statikk Shiv

Why is it that I always seem to see guides and players picking Rapid Firecannon over Statikk Shiv? (and even sometimes Phantom Dancer, but I won't go into that)

The way I see it is, they both cost the same, use the same items to build and give the same movement speed and critical strike chance but here the the pros of each one:

Statikk Shiv: +5% attack speed. Energized Attack hits 5 targets near your primary target. Deals +50% extra damage to minions. Can critically strike, damage scales off of critical strike damage.

Rapid Firecannon: The on-hit damage scales better than Statikk Shiv's base damage. +35% range for energized attack (up to +150 range. Works on structures.

Now, damage-wise, RFC does more damage (100%-133%(scaling off of level) of Statikk Shiv's damage to non-minions) but if Shiv is used on one minion, that damage is 220% what it normally does, which out-ranks the 100-133% when using RFC: Damage vs non-minions: RFC wins. Damage vs minions: Shiv wins.

However, if you were to crit (which you would 30%-100% of the time, depending on your build) then Statikk Shiv would (assuming critical damage was at 200%) deal 150% more damage than RFC - which cannot crit anyway. Assuming that you have Infinity Edge (250% critical damage), you will be critting 50%-100% of the time and the damage would go up to 187.5% of that from RFC, this just gets larger if you have other sources of crit damage. Crit: Shiv wins. Non-crit: RFC wins.

If the energized attack hit more than one target, the TOTAL (not single targeted) damage would become 200%-500%(scaling off of targets hit) - compared to 100%-133% from RFC - that of what Shiv would normally hit for, if this was a crit, it would deal 400%-1000% (2002.0; 5002.0)(scaling off of targets hit) TOTAL (I repeat, not single targeted) damage than RFC, if one had Infinity Edge that damage would be 500%-1250% (2002.5; 5002.5)(scaling off of targets hit) TOTAL damage dealt. Multi-target: Shiv wins. Single-target: RFC wins.

If the target was out of range and the +35% attack range allowed the auto attack to land, that would be an up to RFC, however, for poking, shiv is likely to deal more damage (critical strike damage X multiple targets hit) and for sustainable damage, shiv would also win as it gives 5% more attack speed and you don't have to get closer after the first shot (however, when attack speed is low, the reposition might not be such a bad idea, contradictory to that statement, however, the 5% attack speed increase would help with this issue; if only ever so slightly) Situation win for either item as explained above.

For sieging a tower, I would have though shiv would be better, it would allow one to push the wave into the tower to START the siege faster and when it is there be able to kill further waves quickly to keep the siege going for longer, thus indirectly increasing the total damage done, RFC, however, can deal direct damage to the tower, however much that is, and can be used on most champions from outside tower range (not requiring minions to avoid taking damage), however, when minions are not present, towers take less damage, further mitigation the actual damage dealt Looks like shiv would win in most circumstances, but RFC has the potential to deal small amounts of damage with less setup required.

Summary, I don't see why Rapid Firecannon is purchased so consistently over Statikk Shiv, what do you think? Up-vote this thread if you like what I've done, thanks.

[slayer-jinx-wink]

TL;DR: RFC has larger range and works on towers, why does those two facts out weigh Shiv being able to crit (which deals more damage than RFC), being able to hit up to 5 other targets and giving +5% attack speed over RFC?

P.S. if I got any calculations wrong, please politely point them out, I wrote this at a very late hour of the night. Thanks!