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FREEAGLELAND26781 Posts
So last hitting under a tower at early levels can be difficult. Due to random damage ranges, sometimes frustratingly so. Rarely in a game will you have a laning phase devoid of your allied protector firing searing projectiles at enemy minions. So next time your support is pulling a neutral camp (hopefully stacked) or the enemy team is just shoving their creep wave in your face, perhaps some simple math will help those of you who are more mathematically inclined.
Tier 1 tower
Damage range: 100-120
Average damage: 110
Let's take a look at last hitting ranged creep under a tower first, since that's much (on average) easier to do than last hitting melee creep.
Ranged creep
300 HP
2 HP regen
0 armor = 0% reduction
If a tower hits a full HP ranged creep twice the ranged creep will have between 60-100 HP left, and on average said creep will have 80 HP left. Always hit a ranged creep once before the tower gets two hits in. If you and the tower start attacking a ranged creep at the same time, hit it once and let the tower hit it twice. Then hit the creep again to pick up the last hit. This rule of thumb stands for almost every hero, since no ranged hero has enough base damage to one-shot a full HP ranged creep and there are only a handful of melee heroes that can do so if assisted by a Quelling Blade.
So what about when ranged creep with missing health come into your tower range? First, you must consider your hero's damage. To keep things simple, we will be looking at said hero's average damage (base plus any damage-boosting starting items you may have). Call that average damage x. Note that some of what I write below may seem trivial or obvious; I'm just listing that information to be inclusive.
+ Show Spoiler [Math part] +So if the ranged creep has between...- 260 and 300 HP, hit the creep once if you won't bring it below 220 and let the tower hit it twice before finishing it off. If you will bring it below 220 with one hit, go to next bullet point.
- 220 and 259 HP, hit the creep once, let the tower hit it once, and then finish off the creep if you have over 55 base damage. If not, let the tower hit it twice before finishing off the creep.
- 220-x and 219 HP, hit the creep once and let the tower hit it once before finishing it off if you have over 55 base damage. If you don't, hit the creep twice before before the tower hits it once, and then last hit.
- 111 and 111+x HP, let the tower hit the creep once before finishing it off. Note: may overlap a bit with previous bullet point if x > 55.
- x+1 and 109 HP, finish off the creep by hitting it twice if you have over 55 average base damage. If you don't and the creep has close to 109 HP, you either need to hit the creep three times to kill it before the tower focuses it or let the tower shoot it once and hope that the tower damage for that shot is in the lower half of the range.
- 1 and x HP, last hit the creep before the tower can hit it.
Rule of thumb for ranged creep: Always hit once before tower hits twice when at full HP. If tower hits it twice and you can't kill it in one hit, you need to hit it once beforehand. If creep is damaged already, deal whatever the creep has in life minus 110 in damage before the tower hits it twice (let the tower hit it once).
Now for melee creep. Generally harder to last hit.
Melee creep
550 HP
HP regen .5
2 armor = 10.714% reduction = .89286 ~= 0.9 damage multiplier for simplicity
If tower hits a full HP melee creep 5 times that's 98 damage on average per hit, resulting in the creep having 60 HP left. At early levels, you can pretty much always get the last hit if you hit the creep once between 5 tower shots. In order to "on average" last hit a full HP melee creep after five tower shots, your hero needs to be able to deal 68 damage with one attack. This is doable for many melee carries with Quelling Blades, and impossible for ranged heroes (with the sole exception being Luna, but that's the very high end of her damage).
Now for melee creep missing some HP. Again, let's define your hero's average base damage as x. Let the tower hit the creep down to around 250 HP, then assess the situation.
+ Show Spoiler [Math part] +So if the melee creep has between...- 201 and 250 HP, let the tower hit the creep twice before last hitting it. If you don't have over 60 base damage and the creep is close to 250 HP, hit it once before letting the tower hit it twice, then finish the creep off.
- 200-0.9x and 200 HP, hit the creep once and let the tower hit it once before finishing it off if you have over 57 base damage. If you don't, hit the creep twice before before the tower hits it once, and then last hit.
- 99 and 99+0.9x HP, let the tower hit the creep once before finishing it off. Note: may overlap a bit with previous bullet point if x > 57.
- 0.9x+1 and 98 HP, finish off the creep by hitting it twice if you have over 55 average base damage. If you don't and the creep has close to 98 HP, you either need to hit the creep three times to kill it before the tower focuses it or let the tower shoot it once and hope that the tower damage for that shot is in the lower half of the range.
- 1 and 0.9x HP left, last hit the creep before the tower can hit it.
Rule of thumb for melee creep: If the creep is full or has close to full HP, hit it once and let the tower hit it five times. Then pick up the last hit. If the creep has enough HP missing so that it's not close to full HP, let the tower hit the creep down first to the hit closest to 250 HP and then assess situation. If you can bring it down to the next 100 level (for instance, from 250 -> 190) with one attack, let the tower hit it twice before last hitting. If you cannot bring it down to the next 100 level with one attack, attack it once and let the tower hit it twice before last hitting.
Siege Creep
500 HP
0 armor = 0% reduction -- actually takes 50% extra damage from tower hits due to armor type
Last hitting siege creep takes a bit of luck. Since a siege creep takes an extra 50% from tower hits, the tower is doing on average 165 damage to it, with a range of 150-180. If the siege creep is full HP, let the tower hit it three times before last hitting it. Sometimes three hits from the tower will be enough to take out the siege creep, so that's where the luck factor comes in. If you have any allied creep attacking the full HP siege creep when the tower is hitting it as well, you're pretty much guaranteed not to get the last hit.
If you have a creep wave (or parts of a creep wave) attacking the siege creep with the tower hitting it as well, your best bet is to get two attacks off and then try to use the third to last hit. Generally speaking, when you combine the creep wave hitting with your attacks, you can get the equivalent of one tower shot's worth of damage in when the tower has hit the siege creep twice.
Note that the mathematics sections are a bit hard to remember in game. Obviously, once you've played enough you develop a feel for how to last hit under a tower. Yet even professional players have trouble with this aspect of the game due to the randomness caused by damage ranges. If you want to improve upon your last hitting under tier 1 towers, take what I've written into consideration.
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28089 Posts
Thanks Flamewheel. This is very well done, and especially helpful for us math guys to visualize the last hitting mechanics easier.
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thanks dude. This will help a lot!
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Another tips:
Ranged creep has mana. So you need to take that into consideration if you level up Manaburn.
Siege machine always survive 3 tower hits. If it dies in 3 hits that means your ranged creep attack it once. After 7 mins ( need confirmation ), creeps gets stronger.
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On October 13 2012 17:46 Prime`Rib wrote:
Siege machine always survive 3 tower hits. If it dies in 3 hits that means your ranged creep attack it once. After 7 mins ( need confirmation ), creeps gets stronger.
thats not true yo
usually it survives 3 hits but if u have bad luck it dies in 3 hits
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On October 13 2012 18:46 Dead9 wrote:Show nested quote +On October 13 2012 17:46 Prime`Rib wrote:
Siege machine always survive 3 tower hits. If it dies in 3 hits that means your ranged creep attack it once. After 7 mins ( need confirmation ), creeps gets stronger. thats not true yo usually it survives 3 hits but if u have bad luck it dies in 3 hits
Pretty much this. But in my experience, siege creep dies with 3 hits generally. I feel extremely lucky if I see a range creep don't die with 3 hits from tower.
Another mechanic is, towers tend to hit siege creeps last because siege creeps grab little aggro from towers unless you pull the other creeps out of the towers range. This means some other of your creeps hit the siege before tower hits 3 times.
It is pretty hard to impossible to take last hits of siege creeps under tower.
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As mentioned in the OP, the average damage from 3 hits is 165x3=495<500, but it varies from 450 to 540 (although do to the multiple hits, it is more likely to be close to the average value 495).
If they get attacked by other creeps, sometimes you get start autoattacking and get it after two tower hits.
Ranged creeps always die to 3 t1 hits afaik. Early on it will take 2 tower+2 own normally, later 2 tower+1 own.
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I always wanted a thread like that, thanks :-)
I knew about ranged and siege creeps, but not about melee creeps.
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Wow. And i always go by feel 
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If the siege creep takes any damage, even a single melee creep swipe, the tower will probably kill it. In that case you have to try to get 2 to 3 hits (depending how much your own creeps damage it) to have a chance.
If you're unlucky, 3 tower hits may kill it.
Also later on there's creep upgrades and tier 2's, you can do 2 tower hits then last hit ranged creep with very little base damage.
Melee creeps confuse me sometimes, it can be hard to judge especially if they're half health.
Edit: also under basilius ranged creeps are 3+ hits. And if the opponent tries to hit your ranged creep under their tower to prepare for their own last hit, you can add in your own hit to screw them up.
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With melee creeps, let the tower hit 3 times, then judge whether or not you need to hit it once.
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Thanks for post. It's nice to know someone knows what they are doing
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LOL that luck with seige engines.
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This can also help with making the decision wether or not to buy a Quelling blade in order to help with lasthitting melee creeps(It doesn't really matter for the others from my experience).
If you are someone like Phantom Assassin, with a pretty low, stable base damage, I don't think that Quelling Blade offers much because you can get the 1 early hit -> lasthit on melee creeps nearly all the time. However, on someone like Faceless Void, with a much higher base damage, lasthitting like this is kind of lottery, just like it is to wait for just the final hit. This is why it might be worth consideration to buy a Quelling Blade with Void, enabling you to comfortably lasthit the melee creeps with just the final attack.
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I needed this thread badly. I've been so poor at getting tower-range last hits, I was planning to practice with solo custom games to try and figure this out. Thanks for your hard work, flamewheel!
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Thanks flame wheel, especially for the melee creep mathematics section. I was in dire need of that last hitting advice!
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FREEAGLELAND26781 Posts
On October 13 2012 17:46 Prime`Rib wrote:
Another tips:
Ranged creep has mana. So you need to take that into consideration if you level up Manaburn.
Siege machine always survive 3 tower hits. If it dies in 3 hits that means your ranged creep attack it once. After 7 mins ( need confirmation ), creeps gets stronger.
Other people have already posted that siege creep don't always survive. On average, they should be left with 5 HP, but roughly 50% of the time you're not going to get the cart.
Creep get stronger every 7.5 minutes, though by that point in the game you shouldn't be worrying about your damage output if you are a farming hero.
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Dota 2 needs more stuff like this. Great post.
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Another note should be that when you are under tower, ranged creeps draw agro when they are attacking you. So always try and get closer to them to hit them once becasue the tower will attack them over melee creeps.
I think it is because they can "always" hit you but I might be mistaken.
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Most of the time I try to do this by feel, but it's nice to have the math behind it. It's especially helpful when you know certain damage thresholds for how many times you should hit a creep. If you have > X damage, hit it once, if you have < X damage hit it twice etc.
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nice post! I knew about the 1 hit on ranged creeps, which i try to get in if playing support to help my carry. the melee creep education was helpful for me, too since usually i just try if i can kill it after 5 and if i dont i get get one hit in bofore the fifth tower attack. so very helpful cheer!
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melee creeps and sieges are annoying because half the time i have to attack melee once before and half the time i dont =(
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I don't really calculate, but this will surely be helpful to the people aiming to be better last hitters and get to that 500 gpm.
Normally, i just use my instinct and experience to last hit the creeps.
As you play, you pick up the skills and knowledge of knowing when to last hit.
So just keep playing and do your best
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Thanks, good post regarding last hit math. I always had trouble with last hitting under tower in Dota... even in the WC3 days >_<
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Its sometimes even better to hit the melee creep twice when lasthitting under the tower. You should check the creeps HP after 2-3 tower hits, it can be very useful.
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Good initiative, but as KIH suggested, if you have problems lasthitting under tower you should pay attention to how high the towerhits deal. It differs so some cases you need to hit more, and that means you need to do this very early (unless you have good AS, but you dont cuz its earlygame!)
In general dota is alot about making quick calculations of HP vs DMG, be it in teamfights or in lasthits or just harass, your most important skill is to quickly realize how high different dmgoutputs are.
Good work on the guide 
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Flamewheel made this super easy for all of you. I remember by the HP line and when I can get the last hit. I know if I have less then 62 dmg I hit the creep once. Black^ whoever he is playing for just clicks the creep. and checks hp but I found that too much trouble. Most meele carrys can just let the tower hit and then grab it b4 it dies.
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EPT
