Here, I will summarize the guides content: I have played many carry type heroes in the past, and I have confidence in my skills, and builds. I wish to share my knowledge to anyone, who is interested in viewing things in a different perspective. Enjoy!
What's a carry hero? In my opinion a hero can be called carry, if he deals physical damage with attacks, and can overpower several heroes. It's a simple definition, and many wouldn't agree with it, but it makes the upcoming parts easier to understand. This guide doesn't cover old fashioned Tank carry heroes that deal damage with radiance! Also no INT carries, because of the huge difference in their item builds!
Can any hero carry? YES! A techies with mkb, buriza, treads, butterfly, assault curias, heart is obviously a good carry hero. Is any hero good to carry? NO! The previous techies would be owned by a shadow fiend, that has the same items. Still, extreme situations may require a techies to carry, but there's no point in making builds for extreme situations. The heroes we can make builds for, have some kind of special ability, that makes them a better choice, than others.
What makes carry heroes special? Their fighting style. A carry uses attacks, to deal damage over time on heroes. In the previous sentence I wrote 2 key factors: attacks and time. In other words a carry needs stronger attacks, or more time, or both to be effective.
What is necessary for a carry to attack?
A stupid question, that needs to be answered seriously. To attack a carry must be in range (of the opponent), and must be able to attack (meaning not dead, or dissabled)!
A carry must be in range: Range can differ from melee to 600 on heroes. Obviously the longer the range, the better the hero is. My last sentence is only true for ranged heroes! Even though melee heroes are inferior in range, but they are usually better than ranged heroes with low range. Why? Heroes with low range (including melee) are balanced by better stats, or stronger abilities, but the main difference of ranged and melee, lies elsewhere. Melee can choose different items. While ranged heroes can have skadi and satanic (or mom) at the same time, melee can use Battlefury, Manta, Vladimirs and Bashers with more efficiency. Bashers get 15% chance to proc instead of the 10% for ranged heroes, but melee bash can also stun magic immune units. The damage type also differs, physical for ranged, and magic for melee heroes. Right now they are underused, but that may change in the near future.
In actual combat, the first thing we must do, is get in range! Melee and low ranged heroes have a big disadvantage here, and may need blink or invisibility to succeed. After you are in range you must maintain it. This can be done by stopping the opponents movement, or by going after him. Stopping the opponent is the best possible scenario for the carry. If you have to go after the enemy, you will loose time. Chasing is only possible, if the chasers move speed is greater than the opponents. Exceptions are heroes with low CD blinks. To achieve greater move speed, we must either decrease the opponents, or increase our own. Mobility is an important factor, when we are building carry heroes. The slower the opponent is, the less time we need to deal with him. Please note that the movement difference of the chaser and the prey has to be large enough for the chaser to attack once, before the prey gets out of range. Of course loads of IAS can help in this too, but increasing the gap between the movement speed is much more effective. For the reasons mentioned above, it is very difficult for melee heroes to maintain attack range. Of course that doesn't mater if the opponent doesn't (or can't) move.
A carry must be able to attack: If the carry is disabled or dead, he won't be able to attack. Silence cannot prevent a hero from attacking, but stun can. The opponent will disable, and kill the carry as fast as possible, since he is the main damage dealer. In order to survive the carry must either withstand the beating he gets, or he must make himself immune to disables. Another way to increase survivability is to make concentrated fire difficult for the enemy. With illusions for example. Or, if we cannot divide ourselves we might as well divide the enemy, with swapping skills. Divide and Rule! Dunno, who said that, but he was a really smart guy (edit: Julius Caesar). The carry becomes much more effective, when he deals with less opponents.
How to play against a carry?
In the previous parts I stated, that range, and the ability to attack is necessary to deal damage. If either of those two is missing, than the carry becomes useless. Against melee carries, it is better to do a hit & run, or stun and run tactic. For ranged heroes disables and concentrate fire is the best solution.
Melee heroes are harder to kill, since they get more EHP to be effective. Avoiding them until he is the last hero standing is favourable. Remember that a melee hero needs his teamates help more, than a ranged since they need support to pin an opponent down!
Ranged heroes on the other hand concentrate more on the offensive, and less on EHP, so getting him first is a must in most cases. If the carry is immune to magic, you must either use disables that go through it, or remove the immunity itself. Waiting for it to be end is a possible solution too, but not a good one.
Carry evading It needs strong teamplay, and it can be a double edged tactic. Namely: to avoid the carry completely! This tacitc is only effective in late game, when the carry is alredy well fed, and rich. As long as the carry is not a threat, there's no poitn in evading him. Running away form a carry is different form avoiding one. To avoid confrontation we must move to different lanes, and always do the same the carry does. If the carry is on the offensive, than we play offensive too. If he defends we defend too. This way we won't meet the carry, and the first one to destroy the ancient wins!
The Golden Rule
Now we understand the strength and weakness, of carry heroes. To make the the most out of our hero we must follow one rule! That rule is: Balance... Generally, when we pick the hero, he will have an ability, that a carry needs. No hero gets everything, therefore it is our role to balance things out with the correct item build! To understand the importance of balance, please observe the next picture!
Carry Tree: The name synergy tree fits this picture more, than the current one. Before I discuss the order of the branches please note, that this tree lacks some information. The frost attack from skadi, magic immunity from bkb, the range and move speed of heroes, and some specific skills only available for heroes. Frost attack isn't mentioned, because it doesn't have synergy with IAS, and because the HP and Mana it gives are more important. Magic immunity is situational, and doesn't really synergies with anything on the tree. There are too many skills, and the tree doesn't have enough room for them.
To make it simple I will start from the bottom. First there is the hero itself. After that the tree has two main branches. One for survivability, that buys us the time to deal the damage on the other branch. Balancing these two main branches are the most important! If the hero gets killed before he deals the damage, or if he can't deal enough damage to kill, than he fails as a carry hero.
The Left branch starts with BAT, that stands for Base Attack Time. For most heroes this is 1.7. The less BAT you have the better each point of IAS gets. IAS is Increased Attack Speed, that works like damage. Each point of IAS reduces the attack speed by X percent of the BAT. Heroes with lower BAT have better synergy with IAS than other heroes. Some spells can reduce the BAT of the hero. After IAS the bracnhes part again. The new left branch is damage, and effects that depend on damage, while on the right branch we have effects that have percentage chances to work. The right branch has orb- and bash- effects since they synergies well with IAS. Good attack speed is a must for carry heroes, so getting effects from the right branch can be useful in a different way. Disabling, slowing the target or increasing our damage via lightning. Total damage depends on IAS (and BAT) and the damage per attack. To get the most total damage we must balance, damage and IAS since BAT is given. Some heroes have abilities that synergies more with IAS than damage. These heroes should get unbalanced IAS/damage, if they can make use of the IAS. Raw damage increases Critical Damage and Lifesteal. Lifesteal can increase our time spent in action, just like bash.
To make it even more simple, look at critical strike! Critical strike's effectiveness depends on raw damage, and on the frequency we attack. In other words on damage and IAS! Bash, Maim and the rest effects on the other branch does not synergy with damage, only with IAS.
The Right Branch starts with HP. Our Hit Points is amplified by armor and spell resistance, but never forget that raw HP is the base! The rule is the same as before, balance physical and magic resistance to get the most cost effective build! Depending on the opponents damage potential, and structure this may vary in each game. Hood is great against a team of casters, but less effective against a pack of DPS heroes. Also the hero you choose may have better armor or spell resistance, than the average. If you get a lot of the same thing, your hero may become unbalanced.
Balance is the key. We must balance branches on the same level, damage and survability, IAS and damage, physical and magic resistance! Please note that although lifesteal is on the left branch it is still a 100% defence ability, since each attack increases HP.
Beware the trends
Balancing the item build needs some brainpower, but it's not difficult once you have the hang of it. Remember that every item of Dota is good for any hero. The only difference is that some items are more cost effective, than others. One of the most common mistake people do, is that they follow trends instead of their heads.
The bandwagon effect, also known as social proof or "cromo effect" and closely related to opportunism, is the observation that people often do and believe things because many other people do and believe the same things. The effect is often pejoratively called herding instinct, particularly when applied to adolescents. People tend to follow the crowd without examining the merits of a particular thing.
The reason for success depends on many things: Skill, Teamwork, Attitude. If a pro player gets an item for a certain hero, and wins, than other players will copy his build. This is natural, but never forget the reason why he got that item in the first place! Do not be fooled by trends! If you have doubts about the build, than test it. If you manage to get better results with your own item build, than it's highly possible that yours is the correct. If you can observe correctly, than the game's level you play in is not a factor. Remember that swimming downstream is always easier, than swimming upstream...
Even similar hero skills, can differ greatly. Generally it can be passive or spell based. Spells have limited duration, and different cooldowns. A spell may give temporary carry abilities. By now you should understand what a carry ability is, but if not please take another look at the carry tree. The target of the spell can be a factor in determining, if the hero should carry, or not. Abilities can differ whether, if they are stat-based, or not. Getting stats to balance the hero, is usually not the best solution, but some heroes have better synergy with stats, than others. Also heroes that have illusions, or abilities that work on illusions falls in to a very different category.
Spells: If the carry ability is temporary, than temporary item effects may work the best. For example, if the hero has a spell that gives temporary damage, than temporary IAS and magic immunity works spectacularly. Even if you manage to get constant IAS and survivability, the balance will be off as long as you don't get constant damage.
Passives are usually weaker, than temporary effects, but since they are constant, passives may be stronger in the long run. If we support passives with constant item effects, than the hero will be balanced properly.
Stat based abilities are rare, but important. Abilities that give damage with percentage values only amplify damage from your base, and main attribute. Since these heroes have better synergy with stats, an item that gives the needed attribute will have a higher value, than usual. Heroes that deal their main attribute as extra damage fall into this category as well.
Heroes with illusions should get items that support their minions. If you don't do that, than there's no point in choosing a hero with illusions. Some passives and effects from spells work on illusions. If the hero you carry with has this kind of ability, but doesn't have illusions you should consider getting manta style. Especially STR heroes with passive IAS (or low BAT) and MS. Remeber that not every passive works on illusions, and that a spell on your hero may be dispelled when you split to create illus.
Theory and Reality
With the information, and Instructions I gave, you should be able to make a proper build. Here I will do a few example to show how it was done before. For this I will try to use heroes, from league games everyone is familiar with.
Sven gets: (bracers, boots) MoM, BKB and Treads. The masks MS boost with treads gives sufficient mobility. Storm bolt helps too. Since God's Strength is temporary, getting lots of IAS, and magic immunity for the time the ultimate is on, will make the hero effective. With Avatar on only physical damage can hurt Sven, but with his armor aura, and the lifesteal from MoM, this won't be a problem.
Luna gets: (wraith bands) Treads or Travel, HotD, BKB, Butterfly, Satanic, Buriza. Luna's aura is AGI based for her. So she gets wraith bands and Butterfly to increase damage. HotD synergies well with damage and IAS, while BKB is there so that Luna cannot be disabled. As long as Luna can survive the first wave of disables, she will regain her lost hp via lifesteal. BKB isn't as important for Luna as it is for Sven!
Terrorblade gets: (wraith bands, boots) BoT, SaY, Butterfly. Illusions benefit from wraith bands and SaY greatly. Their damage, IAS and mobility is increased. With treads they would only get the extra stats, but not the IAS. Maim will slow down any hero, so that you and your illus can focus him effectively. Illusions won't get the raw damage and IAS from butterfly, but they get the evasion, and the AGI. Since TB's illusions are usually ranged less survability works for him.
Ok, first I will define support since this word holds different meanings for different people. Support is help the carry receives from allied heroes. To be more specific, allies can support the hero by babysitting, by granting carry abilities, or by playing support tactics. Also disables that slow, stun or silence the target can be seen as support for the carry. If you are interested in support heroes and techniques read Jesper2's guide!
Babysitting is only necessary for heroes that have little lane presence in early game. The art of babysitting would take at least as much space, as this guide does. A babysitter can play defensively and offensively to support the carry. When played offensively the hero harasses the opponent non stop. Last hitting is left for the carry. In defensive style the carry is supported by the babysitter's healing abilities. In my opinion the offensive style is the best support since offence is the best defence. Good Babysitters are: Warlock, Viper and Drow.
Granting carry abilities are very useful. Heroes can get us all sorts of buffs. Armor, damage, IAS, MS, magic immunity and HP with healing abilities. These hero skills can make the hero effective with less items, therefore the item build must be changed so that the balance won't broken. To us this 'tactic' we must think beforehand, and need to decide which heroes should be picked. Also we have to be sure, that by choosing a hero with the extra ability, won't make the team less effective.
Support tactics are a form of global playstyle your allies must take so you, the carry can gain something extra. For example leaving the lane you are farming untouched. Or not killing neutrals, that will be pawned by you very soon. The best support would be to occupy the enemy, by pushing a lane far away from you, while you are farming.
Dota is always changing. Therefore the builds should change too, but the concept of carry heroes will never change. A carry's item build changes, if one of its components change, the hero changes or if a new better item gets in. If none of the previous happens, but you still change the build, than you have been fooled by the new, or the old trend. Realising our mistakes is a part of playing Dota. Be stubborn, but not stupid!
Item changes can be nerfs or the opposite. If an item from your build gets buffed, than the item build won't change, but if it's a nerf, than it's possible that a different item will be better, than the one that was nerfed. When an item outside of your build gets buffed it may also become better, than the the one you are using. Nerfs outside your build can make your hero stronger, but won't change your build at all.
Hero changes can be deadly for item builds. If the new hero differs greatly from the previous, than we have to rework our build completely. If it's a buff, than we might need less from something we had to get before the change. It's rare for a buff to affect the build, but possible. Nerfs on the other hand can be very strict on heroes. To save the balance we must get back, what the hero lost, because of the change.
New Items should change your build, if an old item can be swapped by a new, and the item build still remains balanced. Even, if it has the same effectiveness as the old build, if it's easier to finish, or has better components, than you should make the change.
Knowledge is power
In the last part of my guide, I will give some reading material for those who want more information. If you are interested in Images read: Item effects on Images, and Skills on Images. If you wish to learn about attacks, and damage, read: The Attack Speed Guide, the Orb Effect table, and the guide about Critical strikes and Bash. Also check out the guide about magic immune units! If you haven't found what you were looking for, please visit the Dota Wiki page, or the Mechanics forum! Hope you had fun reading!