Gentleman Gustaf here with a quick preparatory post for my upcoming AD Carry series. In calculating dps for AD Carries, there are really 5 separate statistics: AD, AS, Crit, Pen, and splash damage. Typically, AS and Crit or AS and splash damage are bundled together. There are two similar items, which give both AS and Crit: Statikk Shiv and Phantom dancer. This post will be a brief comparison of Phantom Dancer with the new Statikk Shiv.
What is Statikk Shiv?
Statikk Shiv is part of the AoE damage proposed for auto-attackers; it gives less AS and Crit Chance than PD, but gives an interesting passive. Every 100 charges (10 attacks or 2000 units moved), it releases a chain lightning spell that does 100 damage to up to 4 nearby targets. This damage can crit, taking into account the user's crit chance and damage. However, this passive does not have full multiplicativity. The chain lightning is magic damage, and so does not scale with Armor Penetration. Moreover, it has a base damage of 100, and does not scale with AD. As such, it is stronger the fewer items you have.
First, let us see how it fares in a full build. Let us assume that the average AD Carry has about 100 AD at level 18, with a base attack speed of .658 and a scaling attack speed of .03%/lvl. Also assume 15 AD, 4% attack speed, and 5% crit damage from masteries, as well as 15 AD from runes. Assuming an Infinity Edge, a Last Whisper, and a Bloodthirster, this gives an AD of 341, with a 25% chance of crits for 2.55 damage. Now we can add either PD or Statikk Shiv, giving us attack speeds of 1.35 and 1.28 respectively. This gives a dps of 852 for PD, and 743 for Statikk Shiv, with an additional 22 dps for each target hit by the lightning. Assuming the minimum number of targets hit (1), this gives a compared dps of 852 to 764 (rounding), and assuming the maximum gives a compared dps of 852 to 830. Even adding in additional damage from Shiv (movement also charges it, so kiting will give more damage) does not make a huge difference, changing the lower bound to 775, and the upper bound to 873. Below is a charts, detailing dps comparisons of PD and SS assuming standing and auto attacking:
The following chart shows the same comparisons, but assuming kiting.
As we can see from the above charts, our basic summary of SS from above is accurate: it is stronger than PD as a first or second item, but loses its scaling efficiency as the game goes on. As such, I would prefer Statikk Shiv on champions who have weaker mid games but solid late games, like Tristana and Varus, as it can shore up their weaknesses, and their late game strength will make up for the item's slightly lower dps. It also has obvious benefits like AoE damage for pushing/counter-pushing over Phantom Dancer. Moreover, given that it is cheaper by about 300 gold, and builds from Avarice Blade, I think practically speaking, Statikk Shiv is probably the better purchase, especially given the importance of the midgame. Only on champions who really need the late game strength (Ashe) or who are low range (Vayne/Sivir) would I consider PD over SS. Well, that and Draven, because depending on where his axes go, you can't actually control your kiting run distance that well. Just be careful of 1v1 duels with AD Carries who went for PD.
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