I have been attempting to branch out with the heroes that I can play, especially learning how to play carries (as my preferred position is usually a position 4/5). One of the recent carries I have been trying to learn is Troll Warlord. While browsing through the builds, I noticed that all the builds recommend phase boots over power treads. Troll is not a particularly positioning based hero, so the only reason I could think of for building phase over treads was due to his innate abilities to increase attack speed – therefore phase must provide more damage per second. However, treads provide certain benefits that phase do not, such as extra health, mana or damage when you need it. I decided to investigate further the thought that phase provide more DPS than treads on Troll. Here are my findings.
Caveat – I am not a mathematician by trade and many of these numbers are rounded up or down. If the maths are completely incorrect, I apologise. If they are a little off, then this is probably due to rounding.
(aps) – Attacks per second
(dps) – Damage per second
Things to remember – Attack speed increases are increases in percentage. So an item that gives you 100 attack speed gives you 100% attack speed (doubling your attack speed).
Before Battle Trance
w/ Str. Treads and only Treads at lvl 16 – 1.248 (aps)
w/ Phase and only Phase at lvl 16 – 0.96 (aps)
Adjusted for fervour (which adds 34% attack speed at lvl 4 per stack) over 5 seconds – Remember 2 attacks are required in order to begin the stacks.
w/ Strength treads at lvl 16 – 0.96 base + Treads (30%) = 1.248 (aps), after 2 attacks (approx 1.6 seconds – 64%) – 1.574 (aps), after 3 attacks (at 2.1 seconds – 98%) – 1.9 (aps), after 4 attacks (approx 2.7 seconds – 132%) – 2.23 (aps), after 5 attacks (at 3.1 seconds – 168%)- 2.57 (aps)
The remainder of the 5 seconds will be filled by about 5 more attacks at 2.57 (aps) – approx an attack every 0.4 seconds. So we’ll take an average attack speed across the 5 seconds according to the number of attacks.
With some rounding, that’s 1.25+1.25+1.57+1.9+2.23+(6x2.57) / 11 = average of 2.14 (aps)
At 90 damage that’s an average of 193 dps.
Now for phase boots – 0.96 base, after 2 attacks (approx 1.9 seconds – 34%) – 1.28 (aps), after 3 attacks (approx 2.7 seconds – 68%) – 1.61 (aps), after 4 attacks (approx 3.3 seconds) – 1.94 (aps), after 5 attacks (approx 3.8 seconds) – 2.27 (aps)
This is about an attack every 0.45 seconds so there are a remainder of 3 more attacks to fill the 5 seconds up. So to take an average - 0.96+0.96+1.28+1.61+1.94+(3x2.27) / 8 = average of 1.7 (aps)
At 90+24 damage (114) that’s an average of 193 dps. (welp!)
This so far doesn’t take account of bash chances over the 5 seconds. With treads at 10% chance to deal an extra 50 damage, you have a 1.2 likelihood of getting a bash. With phase, you have a 0.9 likelihood of getting a bash. As we are talking over 5 seconds we the distributed dps is 10. So we need to add 11 dps for treads and 8 dps for phase.
Treads – 204 dps
Phase – 201 dps
Pretty much nothing in it. We should also consider that the damage of a hero sits between a low and a high number i.e. Warlord’s damage at lvl 16 is more like 81-99. Given this, the two are basically the same.
Battle Trance at lvl 19 provides a bonus of 180 attack speed over 7 seconds. Max attack speed is 400 (AFAIK). So we need to reconsider the numbers for when trance is activated.
w/ Strength treads at lvl 16 – 0.96 base + Treads + BT (210%) = 2.01 (aps), after 2 attacks (approx 0.9 seconds) – 2.34 (aps), after 3 attacks (at 1.3 seconds) – 2.66 (aps), after 4 attacks (at 1.7 seconds) – 2.99 (aps), after 5 attacks (at 2 seconds – 168%)- 3.32 (aps)
3.32 (aps) is approx 3 attacks every 1 second, which means we can fit in 10 more attacks.
So to work out the average – 2.01+2.01+2.34+2.66+2.99+(11x3.32)/16 = 3.03
Which means the average damage with treads along is 273 (dps).
Now for phase boots – 0.96 base +BT (180), after 2 attacks (approx 1.1 seconds ) – 1.76 (aps), after 3 attacks (approx 1.6 seconds) – 2.1 (aps), after 4 attacks (approx 2 seconds) – 2.43 (aps), after 5 attacks (approx 2.35 seconds) – 2.76 (aps)
2.76 is approx 3.35 attacks every second which means we can fit in 8 more attacks.
So to work out the average – 1.76+1.76+2.1+2.43+(9x2.76)/13 = 2.53
Which means the average damage with phase is 288 (dps)
We need to take into account bash chance with the 10 extra dps it provides. Treads provide a 16 extra dps and Phase provide a further 13 -
Treads – 289 dps
Phase – 301 dps
Again, pretty much nothing in it.
Agi Treads – I often sit on STR treads as I prefer the survivability. However, if you were to sit on agi treads, then the numbers would just about favour treads. This is because you would add an extra 8 attack speed and an extra 8 damage.
Without the attack speed or bash considerations – the extra 8 damage would provide a total dps of:
Agi Treads w/o BT – 209 dps
Agi Treads w/ BT – 296 dps (with further bash chance and more attacks, this will come out as higher than phase boots)
Move Speed – Phase provide extra move speed for chasing. How useful this is depends on the heroes you are against. For example, if you are vs a Luna then chase will be important due to her high mobility. If you are vs a Necrophos then move speed is less of a consideration due to lack of mobility. You’re move speed at lvl 16 will already be above 400 due to points in rage. Phasing through heroes and creeps is a consideration if this is something you are having trouble with.
Survivability – Str Treads provide a further 152 hit points (about the equivalent of a lvl 3 nuke). If you are facing heavy nukers then treads may be a good option. Eventually you will want to get a BKB anyway, but that’s going to come about 25 mins into the game, if you’re lucky. So that’s 10-15 minutes of game time where you will be more vulnerable to nukes without the extra HP.
Lock Down – Although we can treat bash chance as further dps, we can also consider that this provides lock down in duelling situations. Despite the lack of chase treads provide compared to phase, then further lock down they provide may make up for this in terms of increased chance to bash.
As always in Dota, your item choices should depend on the situation. Boot types are no exception even when a certain type is considered standard. This shouldn’t be news to anyone, but it is often overlooked in actual play. What I hope to have shown is that Power Treads are just as viable and, in some situations, more viable than Phase Boots on Troll Warlord.