Dota 2 Counter-picking

The problem with them is that you can counter-pick all you want, but strategies can mitigate weaknesses. As long as the other team can force you into a situation where your counter doesn't work, then it won't matter.

Like, let's say you pick up Razor to go against Outworld Devourer, typically favorable for Razor. However, they put Outworld Devourer safe lane solo and now your Razor is not able to counter him because you selected Clockwerk to offlane early on and he cannot rotate mid to face off against Queen of Pain since he will get dominated.
Throwing together a list could be a useful thing, but it is only useful when used correctly. The problem is that most people see "counter" and just pick it blindly. There are still a lot of caveats to counter-picking.

The best thing is to just build up "Dota common sense" and understand concepts.

For instance:

Ticking damage is good against skills with charges (e.g. Templar Assassin Refraction, Treant Living Armor)

therefore, Viper, Venomancer, etc. CAN be good against those heroes

Spells that go through Black King Bar are good against BKB heroes

e.g. Treant Protector Overgrowth, Bane Fiend's Grip, etc. are good for locking down mobile Black King Bar heroes

Illusions inherit stats & base damage, mana burn, etc. so they are good on heroes that build lots of stats, diffusal blade, etc.

i.e. consider building Manta Style
On a side note: Manta Style dispells many debuffs, so it is good for getting rid of things like Silence

Physical Damage immunity good against physical damage

i.e. consider picking up Ghost Scepter on heroes that do not need to attack, provided the other team does not have high magical burst (or you are a high priority target for magic damage spells)
e.g. get it on a support that is getting rocked by Phantom Assassin so she is forced to wait 4 seconds or change targets while your spells come off cooldown

Being able to move over barriers or just quickly away is good against heroes that want to lock you in place

e.g. get Force Staff on support/utility/INT carries against Clockwerk Power Cogs, Nature's Prophet Sprout, or kitable heroes like Lifestealer

Being able to see and slow an invisible hero is good when you already know where they are

e.g. buy dust when you gank a hero like Riki that is farming in plain sight for an extended period of time
e.g. buy Dust when you're against Bounty Hunter or Clinkz in lane

It is outline heroes in ways like:

Strengths/Weaknesses

Game Phase where they peak
Disables
Farm/XP dependency
Magical/Physical DPS

Role

DPS/Support/Utility
Can offlane
Can jungle
Potential Mek carrier
Initiator
Push

Synergies

e.g. Phantom Lancer + Keeper of the Light
e.g. Ancient Apparition synergizing with pretty much any ranged hero to some extent, as well as Faceless Void for making early game Chronosphere more useful

Counters/Weaknesses

e.g. Templar Assassin sucks against Viper
e.g. Bloodseeker is decent against Weaver and Slark for fucking with their ults and mobility

Ideally, this would help you see strengths and weaknesses of your draft and theirs. This would hopefully lead to smarter picks and bans.

The problem would still be that:

They can do unconventional things

e.g. EG ran offlane Faceless Void --> an app might tell you to run an aggro trilane to shut down Faceless Void, but in reality you may be giving him a favorable 1v1 matchup, or doing exactly what the other team wanted from the start

Their strategy may come together in a way you did not anticipate (i.e. you can only quantify DotA so much)

The way a hero is built (items and skills) can determine a lot

e.g. heavy silence can be good against Puck, but if Puck builds a Eul's Scepter, then it can still initiate and survive, despite not being able to use Phase Shift.

So at the end of the day, the information would be there to help you, but not tell you what to pick -- similar to how a basic calculator can help you solve Calculus problems, but not actually do them for you.

Here is a list of very obvious counters:

Force staff and Eul's

Both are great to kite the opponents right clickers. This is especially true to Ursa, Riki, Troll Warlord, Drow Ranger, Templar Assassin and so on. You can also tornado Faceless Void in his Chronosphere, or Bloodseeker when he tries to eat you while you tp out to safety.

Maelstrom/Mjöllnir/Battlefury

Lots of minions/illusions on the enemy team and they are pushing like mad? Consider these items and you will have a better chance to stop a deathpush from Lycan and his friends.

Blade mail

Good against glass cannons like Tinker, Mirana, Riki, Bounty Hunter, Puck, mass Dagons and lots of other things.

Tank items like Skadi, Heart, SnY, Satanic

You need these if you really have to live trough some damage in a fight and you have some ways to contribute or recover after you are focused. The raw HP you get from these can counter Doom pretty well.

Hex

If the game is going late and they have bullshit heroes like Weaver, Tinker, Phantom Lancer, Naga Siren whatever else you need one of these. Also to be considered against Bristleback since it disables his passive.

Basher/Abyssal blade

You need to lock down those pesky heroes that were smart enough to buy a Black King Bar? Do not hesitate buying one of these. Black King Bar + Abyssal Blade + PA + RNG = 4v5.

Ghost scepter

When the enemy team is really hard to kite, but they don't have many stuns this item can save many lives. Blocks all the physical damage but amplifies magical damage. Mandatory for fountain camping.

Linken's Sphere

Batrider, Doom, Vengeful Spirit, Legion Commander hate this item. Then they realize they can just ask for someone to pop it with a Force Staff/Eul's Scepter/Rod of Atos of Aui_2000. Very good on splitpush heroes like Weaver. Core on Morphling. Alliance really likes to stack them on Loda when he plays Slark.

Black King Bar

Do you have anything really important to do in fights? Do you feel like that there are too many spells casted in your general direction? Then this is your item. Ask EternaLEnVy when it's good and when it's bad. Eye of Skadi is a good alternative if you are facing a Doom and you are the only one that he wants to doom.

AC, Shiva's, Vlad's

Is your useless team dying to rightclicks every single fight? Some armor and maybe even some AOE attack speed slow can help you out.

Now a bit about heroes:

Bloodseeker

Counters anyone who really wants to cast spells and run around. Perfect example: Weaver, Slark, Tinker .

Timbersaw

He eats strength heroes for breakfast. Pure damage destroys heroes like Phantom Assassin, Morphling, Huskar, Viper etc. He can't be kited. Black King Bar makes him pretty useless.

Templar Assassin

Destroys most mid match-ups. If you have no DoT she will be pretty much unkillable with a Black King Bar. Huge physical burst damage with armor reduction. He melts down non agility heroes in a few hits, makes your supports disappear in a fight. Hard to kite thanks to her traps. Can become a strong DPS hero later on. She can rosh really fast.

Batrider

Nightmare of splitpushing carries or single core teams. Really strong in mid, good offlaner, fast jungler. Counters most Black King Bar heroes. Linken's Sphere counters him, so does Nyx Assassin (then he gets Black King Bar).

Elder titan

He is the biggest enemy of agility carries. Natural order makes them drop like flies. Also makes all the magical damage from your team to be Pure.

Weaver

Counters any team with no disables or silences. Orchid Malevolence, Scythe of Vyse, Ghost Scepter is needed to deal with him. Gives no fucks about slows or DoT spells. Storm Spirit, Skywrath Mage can be decent against him (in the other hand skywrath has 0 armor making him a flying sack of gold in Weaver's eyes.)

Disruptor

Good against high mobility targets who rely on spells (Weaver). Excellent counter initiator. Really good when you five man early and the opposing team is not organised enough to do the same. Glimpse is a really-really good skill.

Pugna

Enemy team likes to casts spells. If they actually do that they get ZAPPED. Pushes towers down in seconds. Free eblade for team. Very good 5 man hero.

Clockwerk

Are there many heroes on the enemy team who can't handle a brief conversation between you, Power Cogs and some Battery Assault? Then Clockwerk is a good counter to those heroes. Hook goes trough Black King Bar. Battery Assault does a billion damage IF you are "up close and arsenal" with the victim. Power Cogs are really good to control teamfights. Counters heroes that have really long cast animations.

Silencer

Counters Phoenix and other stupid Wombination-combination line ups. He can pump out pretty decent amount of DPS making him an okay rightclicker. Black King Bar must be used to remove Global Silence. If you Black King Bar before Global you will be silenced.

Doom

Counters every hero and every item in the game. He can be countered by giving him too many targets to Doom .