Note: I realized too late that physical defense and magic defense are the terms used in game. I apologize for the possible confusion. The terms used are listed below so the readers can be more familiar with them.
Armor/Physical defense: Attribute that reduces physical damage
Magic defense/ Magic resistance/Magic resist: Attribute that reduces magic damage
Physical penetration: Attribute that ignores some armor
Magic penetration: Attribute that ignores some magic resistance
Passive skill: It is the ability of a hero that activates automatically. All heroes have one passive that may include more than one effect.
Skills: These are the buttons we click in game. Most heroes have 3 skills
Innate: Built in, already part of. I used this to refer to base armor/magic resistance added to the growth of each hero.
Unique passive: Similar to the passive skill, unique passive is an ability that activates automatically. However I’ll exclusively use this term to refer to item passive effects.
Physical and Magical Damage are Reduced by a Percentage Depending on the Value of Armor and Magic Resistance
Damage after considering armor value = Initial damage*[100/(100+(armor*0.84))]
Note that 0.84 isn’t the exact number, the formula only gives a very close approximate. Both armor and magic resistance uses the same formula. Furthermore, the formula only considers armor/magic resist value
Both Armor and Magic Resistance have Diminishing Returns
The more armor a hero has, the less effective each subsequent armor will be. Because of this, it is a good idea to get a mix of both armor/magic resistance and hp especially for tanks.
30 armor = ~80% damage received
60 armor = ~66% damage received
120 armor = ~50% damage received
180 armor = ~40% damage received
240 armor = ~33% damage received
Physical and Magic Penetration Can Ignore Some Armor and Magic Resistance
There are two kinds of penetration[pen.] values, flat and percentage. Flat pen. is simply subtracted from armor/magic resistance before the formula is used, while percentage pen. is multiplied to the armor/magic resistance and then subtracted.
20 physical pen. against 100 armor -> 100-20 -> Armor used is 80
40% physical pen. against 100 armor -> 100-(100*0.40) -> Armor used is 60
When there are both flat and percentage pen., the flat pen. is first applied before the percentage pen. 
One tip: Flat penetration is very effective in the early game. Heroes will have low starting armor (20+) and magic resistance (10+) so it’s possible to deal the full damage without any reductions. Here’s an example to show its significance.
A fighter with 20 armor will reduce about 15% of any physical damage, whether it is basic attack or from skills. An assassin emblem’s maximum physical pen. is 19.5 (but I’ll use 20 for convenience’s sake). With the 15% physical damage reduction gone, 100% of the damage from a skill’s base damage and (+total physical attack) will affect that fighter.
At lv 15, that fighter will now have around 60 armor that reduces ~33% of physical damage. With the same 20 physical pen., the damage reduction becomes ~25%. That is a small 8% difference compared to the first example’s 15%. With a single warrior boots, the damage increase caused by the flat physical pen. becomes even smaller.
There are Some Skills or Items That Can Reduce Armor/Magic Resistance
Unlike physical/magic pen., armor or magic resistance reduction reduces these values (temporarily). This is helpful not just for your hero, but also for your allies. Some examples are Saber and Silvanna’s passive, Genius wand, and Kaja’s ultimate.
Some Heroes have Skills or Passive Abilities That Increases Their Armor/Magic Resistance
This is quite obvious, but this information is relevant in this post. As discussed above, armor and magic resistance have diminishing returns. This means that skills or passive abilities that give such bonuses should be considered before buying defensive equipments. However, what the overall best item to buy always depends on the circumstances. When buying defensive equipments, their passive abilities should also be considered and not just the hp and armor attributes.
Some notable examples:
Atlas’ passive. +60 armor and magic resistance after casting a skill
Barats’ passive. +125 armor and magic resistance at max stacks
Faramis’ 1st skill. +100 armor and magic resistance during duration of skill
Gatot’s passive. +200 armor as he loses hp
Grock’s passive. +135 armor and magic resistance near walls
Lapu Lapu’s ultimate. +70 armor and magic resistance during heavy sword state
Leomord’s ultimate. +60 armor and magic resistance during mounted state
Roger’s ultimate. +50 armor and magic resistance during wolf form
Ruby’s passive. +135 armor and magic resistance at 3 stacks
These armor and magic resistance valuesare just the bonuses from their skills or passives at level 15. Most tank heroes also have a relatively higher innate armor and magic resistance compared to non tanks.
How does True Damage Relate to Armor and Magic Resistance
Well it doesn’t (except for one weird case). True damage is special because of its ability to ignore any armor and magic resistance values. Furthermore, true damage also ignores any form of % damage reduction such as WotAQ unique passive, Vengeance, and Odette’s ultimate. The most effective ways to counter true damage is building more hp or relying on shields.
The weird case I mentioned is Lord’s true damage attacks. It is affected by armor, but it has the true damage property of ignoring % damage reductions.
When does % Based Damage Reduction Come Into Play
Because the % based damage reduction is just a multiplication, the order of which comes first doesn’t matter. Here’s an example:
100 damage against 120 armor (50% damage modifier) and 30% damage reduction from Wings of Apo queen. 2. (100 * .50) * .70 = 35 3. which is the same as 100 * .70 * 0.30 = 35
In summary, this is how the final damage is calculated:
Check if there is a shield on the target, if there is then reduce the shield by the damage value
Compute the damage modifier caused by armor/magic resistance. Must include pen. values.
Compute the damage modifier caused by % based damage reduction
Multiply the damage and the 2 modifiers.
Relating To Items
As I have already mentioned, everything about an item should be considered when analysing its effectiveness in a particular circumstance. This means that both the attribute increase and unique passive may potentially be important. In each of the item below, I will discuss my thoughts about it and how the concept of armor and magic resistance may apply.
Blade armor [1660 gold, 90 armor]. Gives the highest armor among all items in the game, and is also one of the cheapest final items.It’s current unique passive is probably one of the worst in the game. Because it only returns 25% of the attackers physical attack attribute, it will rarely deal any significant damage against most heroes. The main reason this item is built is to get the quick significant buff to physical defense.When considering the diminishing return concept I have mentioned, this item is very ineffective unless you are using Johnson. Consider whether the unique passive is useable in the particular match you have.
Thunder belt [2290 gold, 40 armor, 800 hp]. The main reason you should buy this item is if you want the cooldown reduction, mana regen, and/or slow effect. It gives a good amount of defense and hp, but there are better items that improves overall defense.
Antique Cuirass [2170 gold, 54 armor, 920 hp]. Imo this is the best physical defense item for tanks that is effective in almost any circumstance. This item has slightly better attribute bonuses, and also a great unique passive that weakens enemies’ physical attack. Even after considering the diminishing concept, this item is a great choice for tanks and fighters because of the increased survivability caused by the unique passive.
Immortality [2120 gold, 40 armor, 800 hp]. The main reason this item should be bought is for the ressurection unique passive. The item does give decent attributes, so it is still a decent defense item while the unique passive is on cooldown.
Dominance ice [2010 gold, 70 armor]. Similar to blade armor, this item gives a large value of armo and doesn’t have any hp bonus. Similar to the blade armor again, this item isn’t effective when considering only the diminishing concept. The cooldown reduction, mana, and unique passive must be necessary in a particular match for this item to be worth its price.
Brute force breastplate [1870 gold, 45 armor, 770 hp]. This is an overall good item because of its low price and all around unique passive. In the classic games I have been playing, I have learned that movement speed has become a very important attribute. This item gives movement speed on top of the high armor and hp it gives. When thinking about buying this item, consider whether the movement speed bonus will be useful.
Guardian Helmet [2200 gold, 1550 hp]. When considering the diminishing concept, this item seems ideal for all tanks at lategame. However, it is important to consider whether the other item’s unique passive are more useful than 1.5k hp. For non tanks, this item is quite terrible imo.
Do share your thoughts or criticisms, thank you for reading.