Thanks to everyone who played in last night's Theme Thursday drafts. We managed to get two games in, and I for one had a blast. The first game we had was far less successful, and I haven't had Ms. Pirate rank those heroes yet. So let's put that one aside for now and instead focus on our second game. We decided on a hero pool consisting of Heroes That Ride. This was actually a rather large pool, as we identified 12 such heroes that meet the criteria. In the end we settled on Chaos Knight (Safe lane, position 1), Mirana (Middle, position 2), Luna (off lane, position 1.5?), Abbadon (off lane support, position 5), and Keeper of the Light (safe lane support, position 5). Yes, these positions and lanes make little sense. BUT WE RODE TO VICTORY ANYWAY! Check out the Dotabuff here!
Quick shoutout to everyone who played with us - [Cher] Jm J. Bullock, Greg Scherr, be a bee, and ES JAGO. It should briefly be noted that ES JAGO is a Dota 2 god, and sometimes plays with the likes of aui_2000. That's not a weird WLD joke, but factual. He has like 7,000+ hours logged on Dota 2, and is probably the main reason we won this game (despite the fact that he was playing position 5). But now for the thing you've all been waiting for - Ms. Pirate's rankings of how cool/adorable each of our heroes are. These rankings are entirely arbitrary and follow no known rubric - it's entirely based on me showing Ms. Pirate the heroes, and her making comments about them. She has never played Dota 2 before and does not really care to. BUT SHE HAS EXQUISITE TASTE. So, from 5 to 1, with one being the best:
5) My boy Chaos Night brought up the rear. Ms. Pirate enjoyed his fiery eyes and lava feet, but found a key issue with his horse - a rather unfortunate particle effect that makes it look like the horse is eternally pooping. She didn't like that at all, so Chaos Knight was the worst. She also pointed out that this dude is made of fire! What the heck does he need armor for? She thought it might be more appropriate for him to have a poncho. Volvo, please.
4) Next in the rankings we have Abbadon, wearing the Drowned Horseman set. The big drawback for Abbadon is how ridiculously close together his eyes are. She also didn't approve of Abbadon's slouching posture. On the plus side, Ms. Pirate enjoys that his horse is basically a seahorse. She likes seahorses, apparently.
3) Coming in at number three was Luna. Overall, Ms. Pirate found Luna herself to be boring, but her lion mount to be awesome. She liked that the lion's beard featured a chin braid, and that his ears, "looked cool." Not much to argue with there.
2) Coming in at number 2 is everyone's favorite wizard, Keeper of the Light. She referred to him exclusively as Gandalf, and she's not wrong. Her exact description was, "It looks like Gandalf got lost on the way to a May day party." Make of that what you will.
1) The winner of this week's Ms. Pirate Power Rankings is none other than Mirana! First off, Ms. Pirate did have some criticisms. Despite the arctic theme of the set, Mirana is wearing no pants and sandals. While this might excite people like Brian, Ms. Pirate was worried about her staying warm.
So how did this end up at number 1? This was far and away due to the mount. His name is Ormr the Lunar Dragon, and according to DotaBuff he is a steal at $0.13 on the Steam Market. This mount is pretty sweet. He combines some key elements to create a sort of lizard-dragon-lion, and it's very wonderful. According to Ms. Pirate, he looks like he would enjoy a good scratch under the chin, while still being capable of tearing off your arm. GGWP
As the reader may have noticed, Valve has recently reformed the way that the pick phase in unranked is conducted. The new “All Draft” mode involves the ban phase from Ranked All-Pick, where players may nominate heroes against which they do not want to play, and the server randomly picks from those nominated. Then the teams alternate selections from the remaining hero pool, losing money as a team if a hero is not picked. This brings a level of team composition strategy to unranked pubs, eliminating the “furiously spam click Invoker at exactly 0:00” scenarios that plagued unranked previously.
On the heels of my success with the Tread Switching: The Liberace Method article, I have decided to delve into the intricacies of hero selection in all-draft, which I will refer to as “drafting.” As a new concern to those of us who prefer the purity and elegance of unranked play, I will lay out some basic draft considerations and then run through the draft of a sample lineup that in my opinion will be successful.
There are some basic concepts to Dota2 drafting that will help you create a lineup that will allow your team to win games.
1. Hero balance – You generally want a good mix of heroes in your lineup in terms of farm capability. There is only so much farm on the map, and certain heroes do more with that farm than others; similarly, some heroes need farm while others don’t. You want two or maybe three core heroes who can really use quite a bit of farm (I’m assuming we’re not playing at Liquid.gh levels of efficiency here), one or two more who can use some, and then a support or two who can survive with very little.
2. Draft order – The order in which you select your heroes matters as well. You don’t want to “give away” too much if what you want to do, so picking heroes who don’t tell you much – let’s say Mirana, who can play any position, or Ogre Magi, who’s useful in a variety of drafts – are good early picks. You don’t want to pick a very niche hero like Huskar first, because the other team could pick Huskar counters and make your game no fun (you’re picking Huskar – your goal is to make their game no fun).
3. Enabling your overall strategy – Certain strategies require certain drafts, and so you want to pick heroes that enable that strategy. If you want to play Naga, for example, you might not take other heroes who require lots of farm (see point 1), and moreover, you may want to ban or pick for your own team heroes who can effectively deal with durable illusion spam, like Lion.
For the purposes of this article, let us assume that there will be two bans, which is fairly common for all-draft games.
The first ban will be Witch Doctor. Someone always nominates some random hero, and then that hero gets banned. You’re sitting there on the pick screen going through the heroes you hate and maybe those who hard counter your preferred choice, and then you see “Witch Doctor has been nominated for banning.” “Who bans Witch Doctor?” you think, but the bans are announced and the answer to that question turns out to be: someone in your game. Alchemist, Lone Druid, Lina, and a variety of other nominees manage through, but no one’s playing Witch Doctor tonight.
The second ban is Slark.
For a first pick, you want to make sure that you don’t reveal too much, and you don’t pigeonhole your draft into playing a strategy made suboptimal by the opponents’ (and your teammates’) subsequent picks. Decent supports can be picked here, and our first pick will be Pudge. Pudge can create pressure all over the map and create lots of space for you and your allies. Some people may think he’s going to be your mid hero, which adds an element of uncertainty to what you’re planning to do. He fulfills all the requirements for a good first pick. Our Pudge will roam as our position 4.
Your second pick will be Juggernaut. You were lucky to get Juggernaut for a second pick – since he just had an arcana released, he is in high demand, but you were able to select him to help your teammate unlock the orange form of his Bladeform Legacy. Juggernaut can only be played as a farming core (sorry LanM), but he can go mid or safelane. What’s more, he has very few “counters” and can play a variety of styles, including coming online early for teamfights, and can group up and push with Healing Ward.
For the third pick we show our hand a bit, with Invoker. Usually chosen before the third round, we are able to land him. Invoker is only played mid, but like our other two picks, can be played in a variety of styles depending on how the rest of the draft phase progresses. He has also had a very high rate of success in the Dota2 Asian Championships, so assuming that our teammate has been watching that event and can execute on the level of SumaiL or Miracle-, we’ll be in an even better spot. Our selection of Invoker means that he will play as our 2-position, and our safelane farming core will be Juggernaut.
Our fourth pick will shore up our offlane, which requires that a hero have the ability to stay alive in a potentially dangerous position, and potentially scale with some farm if in a good place to find some. We select Phantom Assassin, because she can farm from a great distance with Stifling Dagger, and will be able to escape danger with Blink Strike. Phantom Assassin can also come online with very few items – really only Phase Boots, Aquila, and a Blightstone – so she can contribute throughout the game. Remember: PA was picked as a support just a few patches ago; here, she will be our position 3 offlaner.
For our final pick, we have our core positions selected, and one roaming support. The best option is someone who will help the Juggernaut lane, potentially set up some kills, and be in a position to survive buying wards and smokes with what meager income he or she is allowed. Shadow Demon can work here, as can Dazzle. But it’s Twenty-Serpentine, WLDers! When our opponents think “zig,” we “zag.” Our fifth pick is Sniper. Our opponents will have no idea what our lanes will be, which creates a strategic advantage right from Strategy Time. Our Sniper will start in the jungle – having taken Take Aim as his first level skill, creeps will have to walk farther to hit him and he will be able to kill nearly an entire camp before healing up at the shrine. Between using both shrines, he can farm three or possibly even four camps before heading back to the fountain to heal. And Sniper can scale better than Shadow Demon, which means we will have a huge advantage going into the late game. Position 5 jungle Sniper is the pick that ties the entire draft together.
So there is a relatively foolproof method to drafting successfully in the new unranked All-Draft. If you can get three of your friends together, and then either SumaiL or Miracle-, you should have no problem executing this draft and cruising to that sweet, sweet unranked Dota2 victory screen.
Happy April Fool’s Day, Everyone!
I first want to thank Sam “The Plaid Pirate” for giving me the opportunity to share with you, the reader, the secrets of tread switching. I’ve uncovered these secrets through hours of playing Dota, hearing casters refer to tread switching, and then Googling “tread switching” to find out what they meant. If you follow Dota on Reddit, you may know that tread switching is one of the very basic tricks that all the 9k Redditors know, like countering entire heroes with one item (BKB), and only losing because of the Peruvians on your team. Understanding tread switching will add somewhere around 2,000 to 3,000 MMR to your solo account – you’re welcome! (therefore my actual MMR in the absence of my tread switching ability is somewhere between 300 and negative 700)
More seriously [No, probably not more seriously – Ed.], tread switching is one of the many game mechanics in Dota that is completely unexplained and likely emerged from players’ actual play, rather than being an express design decision of IceFrog. It gives you some more efficiency in resource use (hp and mana), and critically makes you feel like a professional dota player. The esteemed gamer Sean “Day” Plott explained in one of his “Day Dailies” that esports and gaming are great because you can watch what professionals do and then do that very thing in a game against your own peers, and feel good about yourself, even if you’re never going to win GSL or an International. So really, tread switching is about positivity and feeling good about yourself! Tread switch, WLDers - you’re worth it!
Here’s how it actually works: when Dota adds or subtracts attributes (STR, AGI, INT) from a hero, it maintains the same percentages of hp and mana that the hero had before the attribute change (throughout this essay I will use the term “attribute” to refer to STR, AGI, and INT, and “resources” to refer to hp and mana). This is why, for example, when Undying throws a couple Decay stacks on you, you have “full” health, even though you’ve only got 200 hp. What’s interesting about this is when you combine 1) Power Treads’ ability to quickly move around attributes with 2) the expenditure of resources, mainly (though not exclusively) mana.
An example: Say you are Dragon Knight (a STR hero) and have 300 mana without Treads, and you’d like to cast Level 1 Dragon Tail – a spell that costs 100 mana. You do so, and you now have 200 mana, or 67% of your previous total. This, I think, is fairly straightforward.
Since you’re playing DK, you buy Treads. In STR form, they add the normal +25 attack speed and +45 movement speed, but also 180 health, some health regeneration, and +9 damage. But you want to stun your opponent, so you switch to INT on your treads, which among other things not relevant to our example adds 108 mana, so your total mana pool is now 408. You cast Dragon Tail, which costs 100 mana, and you now have 308 / 408, or around 75% of your pool. Here’s where the magic happens: when you switch back to STR, Dota maintains your percentage of expended mana, and you have 225/300 instead of 200/300. Free 25 mana!
This works in all sorts of examples, too, some of which I’ll mention in the next section. It doesn’t seem like much, but when you’re dealing with spells that have low cooldowns and low mana costs, it can add up and really improve your efficiency.
What follows is a brief explanation of how you can learn to do this. It is how I went about learning tread switching, and so it is almost certainly the objectively correct one. Behold: The Liberace Method.
The best part of the picture is the scepter he’s holding.
For whatever reason, I decided early on in my Dota “career” to learn to do it and incorporate it into my muscle memory so if I ever got better (spoiler alert: not going so well!) I’d at least have that little mechanic down. I used to play quite a bit of Starcraft II, and I always insisted on playing “the right way,” even if I did so poorly, so I would have a good foundation on which to improve (spoiler alert: it didn’t go so well!). That’s maybe not “fun,” and it’s incredibly nerdy and actually kind of embarrassing to type out, but that’s how I approach games like this for myself.
Step 1: Regen
An easy tip for Treads that I think most people know is to only use your Bottle to regen hp and mana when your Treads are on AGI. Since your hp and mana are then at a relative minimum raw value, Bottle’s +75 of the resource increases it by the largest percentage, which is then maintained when you switch back to INT. So if you’re playing Storm Spirit or Windranger, make sure you’re on AGI when Bottling! And, of course, AGI for the Fountain and Shrines as well.
Step 2: Spam Low-CD, Low-Mana Spells
The easiest way IMO to learn to tread switch for casting is to pick heroes who do it a lot, usually in situations where you’re not under pressure from the enemy team. My chosen hero was Slark.
Example: Dark Pact costs 40 mana at Level 4, on a 6 second cooldown. It does 300 damage to enemy units around him, and while he takes 150 damage, he also heals super fast when nobody can see him so it’s not that important. During that mid-game period when you’re AFK farming instead of teamfighting and your teammates are pinging you and All-chatting “Report slark jajaja,” going from camp to camp Dark Pacting them all down speeds up your farm a lot.
Slark is an AGI hero, so generally my Treads are on AGI. But when I cast Dark Pact, I switch them to INT, so the 40 mana is paid from a larger pool, then switch back to AGI for the damage and armor when I’m right-clicking the creeps that I’m farming. I keep my Treads on “S,” and have “Q” for Dark Pact, so my routine is S-S-Q-S. That’s “AGI to STR,” “STR to INT,” “Dark Pact,” “INT to AGI.” Now, if you’re really pro, you can have them on STR while the 150 health is counting down, so you can execute S-S-Q-S-S-[wait for the hp expenditure to complete]-S-S. But that’s above my pay grade, and I’ve watched Arteezy and EE play Slark on stream and they don’t even do it. But it is technically more efficient, I think.
This also ought to be done with Anti-Mage’s Blink – S-S-W-click on target location-S. Anti-Mage and Slark are heroes who don’t have huge mana pools early or much mana regen necessarily, so this actually keeps you out on the map quite a bit more than if you just stuck on AGI and did it. So pick heroes like that – even in a practice lobby – and just SSQS and SSWclickS around the map training your muscles to do this. Before you know it, you’ll be like this:
Step 3: Complicated (read: Fun) Stuff
I also buy Treads on Medusa because with Mystic Snake, you can have almost infinite casts of it. She’s an AGI hero, so stay on AGI most of the time, but then switch to INT when casting Snake, but switch back to AGI before it comes back, because it adds raw mana and when your Treads are on not-INT, you have a smaller mana pool and it will increase your mana by a larger percentage. Necrophos is another fun one because Death Pulse costs mana and heals hp, so you cast it while on INT, then when regenning mana and hp from what used to be Sadism, you should be on AGI because the regen is raw numbers and AGI treads provide the relative minimum for those resources.
But there are cooler examples, too. Clinkz is another hero who usually builds Treads, and with a Soul Ring and his ultimate ability Death Pact, Treads can extend his resources almost indefinitely (until you walk under a Sentry Ward and get Laguna Bladed). Soul Ring costs hp and gives raw mana, so you switch to STR Treads, use the Soul Ring active, then switch to INT Treads to cast Death Pact which gives you hp, then cast Invisibility. The calculations are complicated, especially when incorporating Death Pact’s weird treatment of hp, but you can do the whole thing at almost no cost. I use “X” for my Soul Ring, so it’s S-X-S-R-E, then I go fail a gank.
There are probably countless more cases that I haven’t listed. Have fun, explore the hero pool, and find your own!
Follow these steps:
1) use a Bottle efficiently so you get the idea of flat regen having the most effect on AGI;
2) practice some spammy, low CD, low mana spell, like Dark Pact or AM Blink;
3) move on to more complicated heroes like Medusa or Clinkz;
4) say “yes” when PPD calls you to play for EG, to replace his carry who left for another team.
Thanks for Sam for the opportunity to write this. I hope I wasn’t wrong about too many mechanics, and someone was at least entertained a little, even if my advice was crummy. I love the WLD community and was excited to be able to contribute to it.
CherLiberace ([Cher] Jm J. Bullock]
This post comes to you, dear reader, from Friend of the Show Arian. This is the first of a three-part series on Attack Speed and Damage. Enjoy!
Ask yourself this: What is the most basic way of inflicting damage in Dota 2? My first answer to that question would obviously be Sniper. My close second would be the Auto-Attack. Casting spells interacts with the mana mechanic and spells also have different ways of dealing damage through their damage type. Each spell is unique and has a different twist to it. In short, spells are hard. Auto attacks, on the other hand, are literally just hitting a hero in the face. However, you would be mistaken if you think that Auto-Attacking is not convoluted – this is Dota, after all. Much like a martial arts, simply hitting someone in the face can become complicated very quickly.
To best understand the ancient art of Kung-Dota, I will try to break it down in following three sections: 1) attack time, 2) the relationship between attack speed and damage, and crits and bashes. We’ll only briefly touch on orb attacks, because they are slowly getting phased out of Dota. Armor is also hugely important but luckily that topic was already explained in detail by your favorite Coffee-Grinder. Since you now know that a load of mechanics is coming right at you, now is your last chance to run. For everyone remaining, stand tall, and let’s start learning some martial arts.
The attack time consists of the actual attack animation (also referred to as attack point), the so-called attack back-swing, and an idle period so the system can’t be abused (more on that shortly). Let’s take these one by one. The attack animation, according to Dota 2 Wiki, is the delay between when an attack command is issued and the damage is dealt. Let’s pretend we’re everyone’s favorite Ogre, Alchemist. If our theoretical alchemist decides to get punchy, . the animation is his arm punching right up to the moment the actual damage is inflicted. The ogre returning his arms to their original position is the back-swing, and the period between the end of the back-swing and the launching of the next attack is the idle period. Check out the picture below:
I know what you sly dogs are thinking. After I deal damage, why don’t I just cancel my animation and skip this boring, slow, back-swing bit? Well, IceFrog outwitted us newbs once again. The idle exists so you can’t improve your attack speed by cancelling your animation. If you cancel your attack mid-backswing, after your attack was launched, your idle period extends to the time your backswing would have taken to finish plus your normal idle period. This is also why people sometimes complain about bad attack animations. Some heroes have a very fast attack animation and backswing (Anti-Mage comes to mind), and a very long idle. That makes last hitting easier because the hero responds much faster to your attacking-command. Other heroes, like Zeus, have a very long attack animation and a short Idle. The Idle period makes it so that Anti-Mage doesn’t automatically have better attack speed than Zeus only because he has a faster animation.
Every hero has a base attack time, which is 1.7 seconds for most heroes. Base attack time is the default interval between attacks assuming 0 agility and no attack speed bonus. From base attack time, we can figure out a few important things: 1) we can calculate attacks per second 2) we can calculate how much time passes between each attack. For those of you who enjoy math (from Dota 2 Wiki):
How does this relate to the game itself? After the time between attacks is calculated, the length of your attack animation, idle period and back-swing is adjusted so they add up to whatever your time between attacks is. TLDR; This is why our buddy Alch’s animation gets faster and faster as he gets more items throughout the game. The lowering of base attack time explains the attack speed portion of Alchemist’s ult. His ult lowers his base attack time, meaning every point of attack speed he has improves his time between attacks even more, resulting in the ridiculous attack speed you sometimes see on that hero.
Your Base attack time is also what determines the maximum number of attacks per second (some call it the attack speed cap). If your base attack time is 1.7 you cannot go lower than a certain value of attacks per second. Some heroes have a better base attack time, like Anti Mage, which means his maximum attacks per second is higher. It also means he gets more value out of buying attack speed/agility items.
For all the lazy, immediate-gratification-seeking readers, here are the magic words:
TOO LONG DID’T READ:
- Attacking Consists of Three stages
- You can NOT increase your attack speed with animation cancelling
- Your base attack time determines how much attack speed items improve your attack speed
- Your base attack time determines your maximum attacks per second
Folks, full disclosure here - I'm on the worst losing streak of my Dota career. I'm on a 7 game skid, and 5-15 over my last twenty. Losing might be what I do best, but that doesn't have to be your destiny. After some reflection, I realized that I often find myself as a solo support in my pub games. This, needless to say, is difficult. Almost immediately, it seems, the four carries on my team simultaneously crack their knuckles, lean back in their gaming chairs, and load up their chat wheel. We need wards. We need wards. We need wards. In response, I grin as I alt-left click the wards to proudly proclaim "I will purchase -> Observer Ward (out of stock 1:32)."
This post will help you place these hard-earned wards effectively, focusing on the (very) early-game from the Radiant perspective. Don't waste your wards folks, you worked too damn hard for those gold coins.
So, minute 0. You pick your favorite support, because you're a good person. You put other people's pleasure above your own. You want your teammates to achieve their best possible selves. Thank you, support player. You immediately buy a courier and two wards, because you rock. But what to do with those wards? In a perfect world, you could give each lane a vision advantage. Alas, IceFrog has only bestowed upon us 2 wards at the start. So immediately you are faced with some difficult choices. Here's my 2k advice - the safe lane ALWAYS gets a ward. Why? Your hard carry, your position one, lives there. By definition, he or she is the one that gets top farm priority, and is the one that's going to carry your little support azz to victory. Two, you're there! You're the position 5, so you're going to be babysitting the safe lane. Don't make the game harder than it already is - give yourself a vision advantage. You bought the damn ward, so treat yo self.
Please see the above screenshots for where I like to put the first ward of the game. Is this groundbreaking, or an abnormal spot to place a ward? No. Will it get dewarded? Doubtful. The reason it won't get dewarded is because supports on the other team are just as poor as you are. Some folks might be upset that your ward didn't provide vision of the rune. Too bad, teammates. 7.xx placed LOTS of runes around the map, and you controlling the action rune doesn't take priority over better protecting the carry.
However, we do want to help out our midlaner. I believe giving your mid a vision advantage is key for a number of reasons. In no particular order: 1) Midlaners generally believe that they're the most talented player to ever install the game 2) They need this irrational confidence because they're (usually) in a 1v1 matchup 3) A happy midlaner means a happy team 4) A happy midlaner is far more likely to help you out and gank your lane. Think of the midlaner as a quarterback on a football team. Can you win with a below average one? Just ask Super Bowl champion Trent Dilfer and the 2000 Baltimore Ravens. Would I much rather play on a team with Tom Brady? I mean, just look at that guy. Now he's got a ring for the thumb. What I'm saying is the mid lane is real freakin' important, okay? Help that guy or gal out as best you can. You want him/her on your side, not raging. You can even go along and give him the ward at the start of the game. Or, if you want to take matters into your own hands, put the ward on the Dire's side of the river:
This will give your Radiant buddy a much better time in lane, as he or she will be able to track the opposing mid's movements and hopefully crush the lane. Just don't put it under tower, and don't let the opposing team see you do it. If the creep quilibrium is as pictured, wait until Dire no longer has vision. It's a real bummer to have the mid dewarded.
Ok, ok I know what you're saying. What about the off lane? That hero is going to get ganked from the very scary jungle! And you're right, we left him/her out to dry. But these are the early choices that Dota forces you to make. There are not unlimited resources. Let's look at the decision at the margins. An observer ward lasts for 360 seconds (6 minutes). It takes 150 seconds (2 and a half minutes) for a ward to replentish in stock. So essentially the question is, can your off lane survive for the first three minutes of the game without a ward (assuming about thirty seconds for courier use)? I think they should be able to. Here's the general location I'd suggest you ward in the off lane:
Like everything else in Dota, these suggestions are just that - suggestions. If you have a solo off laner who is up against a tri-lane, give that buckaroo a ward (perhaps even at the expense of your mid). In subsequent posts we'll cover what to do when the options are more expanded and wards begin to come off cool down. Till then, stand tall.
What are all these small numbers next to my hero portrait? Why are they in the way of Terrorblade's intimidating features? Why is my hero so dang squishy to right-clicks, especially in the late game (or, if you're feeding like me, for the entire game)? Trigger warning: This post will contain math. As our good friend Cheeks would say, Dota is just one giant math equation, so buckle up buckaroos.
Pictured below is a wonderful Terrorblade, prancing about in a practice match. The two red arrows point us towards his armor. What does armor do? Armor decreases the amount of damage you take from physical attacks (enemy right clicks, as well as lots of abilities like Anchor Smash, Quill Spray, Shadow Wave, Slithereen Crush, etc).
The number in grey is his main armor. Main armor is defined as a hero's base armor plus armor gained by agility. Base armor is different for each hero - Terrorblade starts with 7. Don't worry too much about base armor - IceFrog assigns each hero their base armor and there's nothing you can do to change it. But to understand main armor, you need this component. So once you take into consideration Terrorbale's armor gain from agility, and you wind up with 10.14, which gets rounded up to 11. Here's a fun math equation for all of you keeping score at home:
main armor = base armor + (agility * (1 / 7)).
10.14 = 7 + (22 * (1/7))
Again, that 10.14 gets rounded up to 11, and represents Terrorblade's main armor, which you see in grey. Each point in agility gets you a whopping 1/7th of a unit of armor. Is it super important that you remember that 7 points in agility equals 1 unit of armor? Probably not, but we're doing a deep dive into armor, so this is what you get.
The green number is the amount of armor gained from items. The armor bonus received from items does not transfer to illusions. So here's the best way to think about armor - it makes your hit point pool bigger. This idea is called Effective HP - as you increase armor, it takes more physical damage to bring you down. So here's another fun math equation:
Once you get over the shock of high school algebra, that handy-dandy equation allows you to understand that armor stacks linearly. Check out the table below. Assume you have a hero who has 1000 hit points. If my squishy, make believe hero has 0 armor, his Effective HP is also 1000. Now let's say we get a gift-card for 1400 gold coins and buy ourselves a platemail. Our platemail gives 10 armor, so Effective HP jumps up to 1600. In this example, our 10 armor gave us 600 additional hit points. Now say there was a 2 for 1 special going on at the Secret Shop, so we have two platemails in our inventory. Now our armor is 20. Our fine hero now has an effective HP of 2,200! On the margins, we gained another 600 hit points. That's what we mean when we say armor stacks linearly.
The key take-away from all this - armor will help you from getting right clicked down, but not from getting nuked. Armor will help you tank up against physical attacks, even if you already have an armor item in your inventory. I find myself doing this frequently when I'm playing Undying. I'll buy a Blade Mail in the early mid-game, and then pat myself on the back and never consider another armor item. The earlier acquisition of Blade Mail shouldn't affect my decision later in the game - if I'm against a physical-heavy lineup, I should definitely consider a Plate Mail to build into a Lotus Orb or a Shiva's Guard. So - buy armor! It'll help. I promise.