Templar Assassin is capable of high physical "burst" damage, such that her attacks are comparable to magical nukes. With a blink dagger she can quickly annihilate the enemy back line but also can go toe-to-toe with most carries. What sets her apart from other heroes is refraction. Refraction allows TA to eat a number of attacks and abilities after getting the first jump without fear of dying.
TA is strongest against fragile heroes, especially those without point disables, and those who fear high dps: Lina, Leshrac, KotL, Naix, QoP, Invoker, etc.
She is weakest against tanks, slows, and like other low-hp damage-dealers is not fond of easy disables: Axe, Spectre, Shadow Demon, Venomancer, Bane, Viper, Clockwerk, etc.
Item Progression: Bottle, Phase Boots, Blink Dagger, Magic Wand, Desolator, Daedalus
Because we have a built in defense, and because the strength of this hero is in assassinating people quickly, our item choices reflect that. If we can, we would like to avoid having to make BKB, drums, and these kinds of generic survival and fighting items. To play this hero strongest, we want to jump quickly into position and have every attack deal the highest possible damage.
Thus we prefer phase boots over treads. We do not necessarily care to attack faster, but we wish to move swiftly and have every attack deal more damage.
Desolator is especially strong on this hero because the armor reduction from Meld stacks (and every point of armor reduction is worth more than the previous one from a damage perspective).
Now on most agility carries, butterfly is the best item, even disregarding the evasion and bonus armor. From a dps perspective, it gives +60 damage and +60 attack speed. Compare this with daedalus which gives +81 damage and +35% dps. (60 attack speed is equivalent to 60% dps).
However, as discussed above, on TA we don't necessarily want to attack faster , but we would rather have every attack deal the highest possible damage, and thus we choose daedalus.
Other situational items such as Manta Style against Juggernaut, or Maelstrom against Phantom Lancer are still not recommended. We want to play our hero the strongest way it can be played and not take half-measures. However, if you are playing from behind and your team lacks fight control (such as a Tidehunter), then a BKB may be a more stable route.
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