Blade Trap is one of the most fascinating skills I've seen come to the game in a while, and I've been up day and night trying to figure out how to make it work.
When activated it attacks in a circle with two copies of your equipped dagger, claw, or one handed sword 4 times (5 if dual wielding), hitting twice per rotation for a total of 8 or 10 times per trap over the course of 4 seconds. At level 20 it has a damage effectiveness of 67.5%.
The only issue is that it has absolutely no base damage, and is entirely dependent on the weapons you have equipped.
Let's run through the damage on one of the better options: Rebuke of the Vaal. Rebuke has flat out out one of the highest DPS' of any weapon in the game, but comes with the downside of dealing damage split into every damage type, making it hard to scale. This isn't an issue for traps however, as we scale trap damage, and optionally crit and crit multi. At near max rolls, Rebuke has a damage of around 600. Multiplied against the 67.5% damage effectiveness, we get 405 flat damage. Blade Trap hits 2.5 times per second when dual wielding (10/4seconds), making it a 1,012.5 damage per second, which is roughly comparable to the 1,150 damage of Ice Trap, however this isn't taking into account trap throwing rate.
The big issue is that the damage from Ice Trap isn't counting any bonuses from weapons such as Wands. Blade trap doesn't have that luxury because its weapons are its base damage, and no weapon in the game is strong enough to bridge the gulf of not being able to additionally scale its base damage with weapons. You could theoretically run a +1 to cold spell skill gems wand with 90% increased spell damage and spell crit to drastically boost that 1,150 to several thousand just by way of 2 wands alone. In fact, 2 +1/90 damage/90 crit wands raise Ice Trap's damage from 1,150 to 5,332, or more than quintuple the average dps of a level 20 Blade Trap with 2 Rebuke of the Vaal swords. This isn't telling the whole story though, because Blade Trap technically deals its damage over time (not actually over time, but hits repeatedly over a period), meaning it stacks.
To make a direct comparison I took an endgame trapper tree with Slavedriver's Hand, which had a trap throw rate of 2.94, multiplied by 3 for cluster traps, for a total of 8.82 traps/second. For the aforementioned Ice Trap we're getting a total DPS of 47,028.
Now for the math for Blade Trap. Considering each trap caps at 2.5 hits per second, and the usual max traps on a standard trapper tree is 24, we're getting a max of 60 hits per second with all traps activated on a single target. We go back to the 405 flat base damage * 60, and we get a total of 24,300 DPS, or just about half that of Ice Trap with endgame weapons.
In order for Blade Trap to be competitive, it, at the very minimum, needs a damage effectivness of 120% or so, and even then will still be out damaged by a basic endgame Ice Trap setup.
More about Path of ExilePost: "Blade Trap needs a severe buff to even be remotely viable. [Math inside]" specifically for the game Path of Exile. Other useful information about this game:
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