Creep control techniques
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Last-hitting is a technique where you (or a creep under your control) get the 'last hit' on a neutral creep, enemy lane creep, or enemy Hero. This is the only way to get gold from creeps apart from Hand of Midas, Devour, Death Pact, or Demonic Conversion, and gives much more gold than otherwise when done to towers or Heroes.
Creeps are your 'safest' bet on using last hits to gain a good chunk of gold. This is the primary source of gold in Dota 2. It is always desirable to get a last hit on a creep, although when laning with a carry as a support it is a good idea to give most of the last hits to the carry. It's ok to take a few if your carry might miss them. Supports should focus on harassing enemy Heroes and denying your own creeps. However, Supports DOES not necessarily mean that they should give you every single creep for the full babysit duration. If you think supports must give you every single creep, then you have some reflection to do.
Auto-attacking refers to the usually less desirable technique of simply letting your Hero attack at will. Because this decreases your chances of getting last hits, especially if your damage per second is low, and it pushes the lane forward, this is not beneficial. In the late game, however, Heroes often do enough damage per second to simply auto-attack and last hit. Auto-attacking can be useful in any case if you wish to push a lane forward, since it kills enemy creeps faster. This is especially useful for killing towers. In the early game, however, pushing towards an enemy tower is considered dangerous, as it leaves you far from your own towers and makes it much easier for enemies to gank you.
Heroes also give gold when you kill them. Everyone who did damage to an enemy Hero within 15 seconds of their death gets an assist. If you were the Hero who delivered the last hit you will get the kill and the bonus gold for it. If your tower or one of your team's creeps gets the last hit on an enemy Hero, the gold is split between all Heroes who got an assist. If only one Hero hit the enemy before your tower or creep killed them, that Hero gets the credit (and the gold) for the kill. If no allied Heroes assisted in the kill, the gold is split evenly among all five Heroes on your team.
Towers give a global bonus of gold when razed, but they also give a hefty amount of bonus gold to any hero who manages to get the last hit on one.
Denying is the act of preventing enemy Heroes from getting the last hit on a friendly unit by last hitting the unit yourself. All allied units can be denied once they fall below a certain percentage of health: creeps and siege units at 50%, heroes at 25%, and towers at 10%. Illusion and summoned units act as creeps in these instances. This prevents your enemy from gaining the full bounty of gold and experience from the kill.
Attack animations and missile speeds
It is important not to push your lane too much, but try to keep the lane creeps fighting in approximately the middle of the lane so you never are too far from the safety of your tower. Creep equilibrium is generally maintained by balancing last-hitting and denying, and on occasions attacking your own creeps before the deny point or attacking the enemy creeps to push. This technique is also known as static farming. Creep pulling can also help maintain equilibrium.
This is always situational though being pushed might be a bit safer but if the enemy lane is able to slowly chip away at your tower you should push harder. Also access to the side shops might be hinderance on occasions.
Creep Blocking is a tactic that makes the equilibrium of the lane lean towards your side. This is accomplished by physically blocking your creeps' path with your hero so they take longer to reach the middle of the lane. Since your creeps move more slowly, they will meet closer to your tower, making it safer for you to farm, and more risky for the enemy.
Creep blocking is generally most useful for the first creep wave at the start of the game. In the middle lane, being able to stand on your side of the river - not in the river - to last hit is valuable. The high ground allows you to see your opponent's side of the river, and for ranged heroes avoids the 25% miss chance of last hitting uphill.
For the "long" or "safe" lane, creeps sprint until about halfway between the Tier 1 and 2 towers. This makes it much harder to creep block all the way from the barracks.
Pushing is the act of damaging enemy creeps through auto-attacks or through abilities. Pushing is used to move the creepwave towards the enemy tower, or simply away from the allied towers. Late-game, pushing is used to move creepwaves towards the enemy base to win the game.
Pulling is the act of redirecting route of your lane creeps towards neutral camp (usually easy camp, as it is the closest one to lane). This can be done when it is not the best time to push and you want your carry to farm more safely, making the enemy offlane hero having harder time gaining experience or last hits. Pulling creeps is not recommended when enemy creeps are about to push, as it will hurt your tower or carry (tanking creeps) more.
It is also a good habit to stack easy camp before pulling, because only 1 stack is usually not enough to clear the creep wave and you'll end up having so called "double wave", which will eventually make you end up by the enemy's tower. You can also repull again from easy camp towards medium/hard camp, using the same techique when neutral creeps are about to die, to prevent double waving.
Pulling is usually done by a support, while carry should stay at the lane and farm lane creeps (which gives more gold/exp). It gives support quite a good chunk of gold/exp, without leeching it from your carry.
Roles and last-hitting
Depending on your role in your team you should focus on different things.
Carries should focus most of their attention on getting last hits.
Supports should focus on denying creeps and harassing enemy Heroes so that their carries can last hit without being harassed. Do not throw away the last hitting entirely as a support, because there are some last hits which are impossible for a carry to get (for example, the creep is being killed faster than a carry could possibly get in the attack range).
Supports can also creep stack to help their carry farm.