Armor vs damage block

Because i have too much time on hands, i'm doing some calculation. I'm kind of interested on comparing Ring of Protection and its upgrades against Stout Shield and its upgrades to determine which ones give the most benefit for the hero.

Some disclaimer first:
1. Calculation assumes perfect standard RNG distribution. If it's written 60%, then it happens exactly 60% of the time. No Pseudo-RNG.
2. Calculation assumes the hero is fighting another hero (important for PMS 100% chance).
3. Calculation assumes no damage bonus from main attribute (important for Aquila attributes giving damage bonus)
4. Calculation assumes all numbers are rounded down to the second decimal. 7.896 is rounded to 7.89, not 7.90. Most of the time, it's ignorable anyway.
5. Calculation assumes the objective of buying the items are for the damage reduction. Mana regen from basilius, stats from Aquila (except Agility which grants armor), HP regen from Vanguard are ignored but will be partially discussed in comparing.
6. DR = Damage Reduction (exclusive from armor), DB = Damage Block (flat, applied before armor)

Let's compare the six items.

Ring of Protection, 2 armor (10.71% DR), slightly cheaper and comparable with Stout Shield, 12/6 DB (60% of 20/10).
Ring of Basilius, 3 armor (15.25% DR), still slightly cheaper and comparable with Poor Man's Shield, 0.84 armor (4.79% DR, all from AGI) and 20/10 DB.
Ring of Aquila, 3.84 armor (18.72% DR, partially from AGI) has no real counterpart because its cost is too different to be compared with PMS or Vanguard.
Vanguard, 28/14 DR (70% from 40/20).

To compare the items, there is one formula i use to calculate a threshold between the two compared items. The threshold shows the damage needed (taken) to be reduced further by DB (the shields) before it's more effective to use DR (the rings).

1. Subtract the DR% from armor by the DR% from block.
2. Suppose the damage blocked is also the damage reduced by the armor. DB = DR%.
3. Divide the DB by DR% to get 1% of the damage blocked. DB/DR% = 1%.
4. Multiply by 100 to get the damage threshold. (DB/DR% * 100) = 100%.
5. If the damage taken is lower, then DB is better at reducing damage. If higher, then DR is better.

Example: Ring of Protection vs Stout Shield (melee)
1. This step is skipped because Stout Shield doesn't grant any DR.
2. 12 DB = 10.71% DR
3. 12/10.71 = 1.1204
4. 1.1204*100 = 112.04
5. Stout Shield is better than RoP on melee heroes if the damage taken < 112.04. Otherwise, RoP is better.

Example 2: Ring of Basilius vs Poor Man's Shield (ranged)
1. 15.25% - 4.79% = 10.46%
2. 10 DB = 10.46% DR
3. 10/10.46 = 0.9560
4. 0.960*100 = 95.60
5. PMS is better than RoB on ranged heroes if the damage taken < 95.60. Otherwise, RoB is better.

Using those formula, i managed to gain these numbers. Bolded are the important/makes sense to compare:

RoP vs Stout: 112.04 (melee), 56.02 (ranged)
RoB vs Stout: 78.68 (melee), 39.34 (ranged)
RoA vs Stout: 64.10 (melee), 32.05 (ranged)

RoP vs PMS: 337.83 (melee), 168.91 (ranged)
RoB vs PMS: 191.20 (melee), 95.60 (ranged)
RoA vs PMS: 143.57 (melee), 71.78 (ranged)

RoP vs Vang: 261.43 (melee), 130.71 (ranged)
RoB vs Vang: 183.60 (melee), 91.80 (ranged)
RoA vs Vang: 149.57 (melee), 74.78 (ranged)

Conclusion:
Damage range in early game is usually 50-70 (rough estimation, need confirmation) so in most cases ranged heroes simply benefit more from RoP.
In late game, these numbers can be ignored because most likely the hero has enough gold to buy armor (probably Plate Mail, build into AC or Shiva) and they can deal up to 150 damage, where even Vanguard lose its effectiveness compared to plain armor. This is also why Vanguard is best rushed.
Upgrading Basilius to Aquila grants only little DR (3.47%), but the most benefit comes from the stats it gives from an entire Wraith Band.
Vanguard actually offers only little more than PMS in terms of damage reduction. Its expensive cost goes mostly into HP an HP regen, which makes it negligible if the hero using it is not very squishy so that it needs HP and HP regen so badly, or needs to be very tanky.
Compare the PMS comparation against the Vanguard comparation. There is an anomaly wher PMS is better in blocking more damage compared to Vanguard (except when the two are against Aquila) simply because it has 4.79% DR from AGI and its 100% chance compared to Vanguard's 70%. In fact, Vanguard is only better at blocking up to 167.01 damage (melee, ranged is half that) before PMS' armor kicks in and blocks more. Of course, 167 damage is mid-late game, so if rushed Vanguard is still better overall.

Any thoughts for these?

TL;DR, or actually my opinion.


Armor more valuable late game than early, damage block more valuable early than late.Damage block does not scale late game, but armor gives more EHP.


Case of point.I suck at math.

Yeah, damage block > armour EARLY game
Armour >>> Damage Block mid-late

Also, DR/armour depends on how much armour you already have, a few points are worth more when you have less. E.g. 0 -> 2 = +10.7%, 5 -> 7 = 6.5%, 15 -> 17 = 3.1%

TLDR - items like RoP are much better on heroes with low starting armour.

I'm aware it's more or less common sense that damage block is better early, what i wanted to find out was how early is "early".

Well, "from the beginning"; is "early" too.

Used to build Vanguard on Viper, then i decided to switch to PMS to hasten core. Now i'm switching to Aquila after this calculation.

This might seem insane, build Mekansm on Viper.I started building Mekansm on Axe, did not regret it.And Viper is not so mana intensive, so he can use it rather freely. Axe needs arcane boots.

Not insane at all, saw Purge video playing him and he mentioned it being better than Vanguard because armor. Then i saw some more source recommending it on some more tanky ranged.

Then i ran the calculation which says at 60 damage it's already better than Vanguard (ranged with active skill not used yet).

This was really interesting to read. I knew already that armor is better mid/late but the exact calculations are always better. :)

Thankyou - i wanted to ask this question but i wasn't sure how to ask it properly.
You're a champ!!

Adding to this thread, I suggest this video
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