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Introduction
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.
Legend
(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.
Totals –
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
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.
Further considerations:
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.
Conclusions
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.
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Treads are almost universally more dps, even on insanely attack-speed-biased carries like troll. However, the mobility and lasthitting power of phase heavily weight the scales in phase's favour. Especially as a hero with an ability like whirling axes (melee) which requires positioning difficult to achieve with treads.
Also, trolls utterly negligible mana requirements mean that tread-toggling, while incredibly good combined with his low low low int (the lower your str/int the better tread toggling is), isn't at all necessary if you have a bottle, which you should if you are mid, which you should be most of the time.
The problem with your wall of mathcraft is that you can't quantify the benefits of phase active on troll who badly badly needs it as a sort-of-melee carry with a mediocre slow as his only "positioning" tool. Even if you stay in ranged form u need the phase cuz ur slow as balls.
Lastly, you are 100% NOT calculating APS right. APS = (1 + IAS as a decimal)/BAT. Which on troll changes depending on ur form. Agi is included in IAS. BAT = 1.7 in ranged, 1.55 in melee.
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Thanks for the feedback.
The tread switching I think should be for Agi and Str. A basi or bottle will cover your mana as you say.
You've shown a couple of more assumptions I've made in all of this. The most major is that I've based most of this on being in melee stance.
I agree as well about all the maths, in that it doesn't tell the whole story at all. This is why I've put a section on other considerations. Those other things are hard to quantify and should be considered on a game to game basis.
I disagree with your comment about move speed. In ranged stance you have average movespeed (300). In melee you have very high movespeed depending on your level of Rage. By switching between the two appropriately you should always be able to close the distance, especially as your ranged W has a slow.
Edit : Another thing I've left out is that bash is a PRD. This probably changes some of the results.
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Strictly speaking your BAT doesn't effect the balance between DMG and IAS in terms of DPS since BAT is basically a fractional multiplier to your dps. However, your method of calculating attackspeed is WILDLY off and heavily overvalues additional attackspeed (like treads).
Anyway phase are still just better 9 out of 10 times. 30% slow sucks dick (although it lasts ages).
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I personally prefer phase boots heavily for a lot of the already mentioned reasons, they also help you get kills that you would have had zero chance getting with treads.
Running up and slowing someone and then using phase to get in their face has gotten me a ton of kills on squishier heroes.
With treads you a lot of heroes simply have the slow wear off slightly after you get in their phase and then they escape in my experience.
The movespeed is simply so very valuable as troll and outweighs the sheer damage increase treads gives compared to phase boots when hitting a target.
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On May 17 2014 02:47 SiwuA wrote:
Thanks for the feedback.
The tread switching I think should be for Agi and Str. A basi or bottle will cover your mana as you say.
You've shown a couple of more assumptions I've made in all of this. The most major is that I've based most of this on being in melee stance.
I agree as well about all the maths, in that it doesn't tell the whole story at all. This is why I've put a section on other considerations. Those other things are hard to quantify and should be considered on a game to game basis.
I disagree with your comment about move speed. In ranged stance you have average movespeed (300). In melee you have very high movespeed depending on your level of Rage. By switching between the two appropriately you should always be able to close the distance, especially as your ranged W has a slow.
Edit : Another thing I've left out is that bash is a PRD. This probably changes some of the results.
Math this math that. We love math on liquid, but let me tell you from raw experience and loving the shit outta this hero.
Let's just talk about DotA in general first. Treads will win straight DPS, almost no question here.
Now let's talk Troll Warlord. I can tell you from very long experience with troll and heavy analysis and reanalysis after each patch, that Phase be awesome on Troll.
***WARNING*** Long Troll History
When he was first imported (circa. 6.77c) his skill Whirling Axes (Melee) was bugged; there was no cast time, he could just chase and cast w/out the stand-still-movement penalty of using spells. This powered with Phase, meant he had awesome mobility, with great Nuke dmg.
After the Whirling Axes was fixed 6.78, it felt rather clunky but still playable. Battle Trance duration was nerfed 3sec, and the cooldown was nerfed 10sec; but these nerfs were rather minor compared to the Whirling Axes nerf even though it was only a mechanical fix. Last, Shadow Blade dmg was nerfed in this patch, though this only affected Troll in the scenario's he got that item.
In 6.79, Whirling Axes (Melee) got a dmg nerf and that total ended him from play. Shadow Blade was nerfed again in this patch, it's cooldown increased, nerfing again situations he got Shadow Blade.
Fast-forward to 6.81 and surprise! Icefrog has implemented that "bugged" state of Whirling Axes (Melee) 6.77c as an innate mechanic....weirdo that guy.
What you have now is the former fluid play of 6.77c, but with nerfed dmg. Not so bad. So yea...grab phase.
TLDR: You can math all you want bro, but I know from experience. My own, and watching better players. Now that the former "bugged" state of Melee Whirling Axes w/no cast time is back, Phase is definitely the go to boots. It's been a long time coming, long time coming.
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No reason not to get phase, especially since you can bash while phasing. Tread switching is one of the most overrated things in the game. On most heroes, the benefits from phasing severely outweighs that of tread switching, since the heroes benefit more from the extra ms and no creep blocking.
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Get phase if your not constantly getting ganked and actually dying. I played this hero once after new patch in solo q and the axes unnerf cast time was very much needed, now you can solo kill much easier.
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Russian Federation40186 Posts
OP, your calculations are not only overcomplicated, but also operate off of false assumption that +%ias = +% as. It works more like that: %ias = %of bonus as relative to as (100), so in the end aps=(100+ias)/(BAT*100). So, if we take that troll's damage is x and he has no other attack speed items other than either str pt or none(dominator-bkb-daedalus being his main 3 damage options, this is very much possible) at lvl16:
Without battle trance:
With str pt:
IAS at lvl16=21+2.75*15+2+30=94
dps at lvl16=x*194/BAT
With phase
IAS at lvl16=64
dps at lvl16=(x+24)*164/BAT
Since fervor and battle trance will only shift it into phase boots bias we just need to see if it's more dps for phase boots:
Str pt vs Phase boots
x vs 131
So, if your attack damage without phase is less than 131, pt is worse than phase from dps point of view. And fervor stacks/battle trance only shift this further into phase boots favor. Add phase active and there is little visible reason to get pt on Troll.
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The problem of not having phaseboots for me is that i cant move through nonhero units. So even if the movementspeed isnt a problem (i have a ranged slow), the creepwaves/nonhero units will decrease my movementspeed by alot resulting in less and delayed damageoutput (maybe even killing my own teamm8's indirectly).
E: Undying basically has the same problem. Without phaseboots to move though the zombies (tombstone) he cant secure alot of kills/assists, making tombstone a less impactfull spell if you dont choose phaseboots over other boots.
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Hence if your the aggressor get phaseboots on most heroes, if your team is losing and your defending get treads.
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Is it better to play this hero mid or as a sidelane farmer? I've heard that he is a great midlaner but I wasn't able to solo kill almost anybody despite winning mid hard. On the other hand, i had great succes using troll offlane together with sd or lich. Disruption into whirling axes is a death sentence for most heroes and if you get basi you can do it over and over again.
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His solo kill potential against ranged heroes isnt very high unless you bait them into overextending. I'd prefer to run troll in a dual lane with some support. Kill potential is pretty high at lvl2 in a dual lane, and fast basi/aquala is very efficient in lane.
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On May 24 2014 00:37 HighTimeDotA wrote:
His solo kill potential against ranged heroes isnt very high unless you bait them into overextending. I'd prefer to run troll in a dual lane with some support. Kill potential is pretty high at lvl2 in a dual lane, and fast basi/aquala is very efficient in lane.
Very true. Very recently I saw a pub game where Artezy offlaned troll alongside PPD as Rubick and they completely destroyed the lane. The amount of damage troll does early on is easy to underestimate.
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What about skill builds? I assumed this patch 1-4-1-1 into 4-4-1-1 would be the best, but according to dotabuff only 4% of players build him like that. I suck at math so i won't do the DPS thingy, but MS+better bash seems overall better than AS. Also lvl1 fervor seems to be a sweet value point.
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mainly depends on if your laning or neuting or free farming. If your dual laning and trying to get kills 4-4-1-1 is the build to go if your jungling 1-4-4-1 would be better and allows for solo rosh with some lifesteal. not a fan of junling troll though since just killing heroes with him is much easier.
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When going 4-4-1-1, what do you max first? I assume Whirling Axes?
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Yep, recent unnerf of melee axe cast time makes him decent again.
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I remember a period when the Chinese went heart on troll. There's just no defending that build.
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What's wrong with it and what is troll supposed to do?
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EPT
