Hi Grubby. I've been following your channel for quite a while and have noticed something you mentioned in previous video regarding the Evasion and Armor. At first it may seems that Evasion and Armor have a diminishing return relationship. Which makes sense since if you have 25% Damage reduction and 25% Evasion, your total Damage reduction will be 0.75 * 0.75 = 0.5625 which means you only gain 0.75 - 0.5625 = 0.1875 or 18.75% Damage reduction from evasion instead of 25%. But what we really should look at is not the value of Damage Reduction but the value of EHP. If you reverse the Damage Reduction and calculate it as an increase in EHP (Effective HP) or how much total damage that unit can take, we'll see that Evasion and Armor help each other in a multiplicative way. In other words, more Armor is better for Evasion. Let's lay down some basic formula first and make some calculation so we can see clearer picture. 1 Armor increase EHP by 6% e.g. 10 Armor = 60% increase in EHP Armor damage reduction = 1 - (1 / (1 + (Armor * 0.06))) e.g. 10 Armor = 1 - (1 / (1 + 0.6)) = 1 - (1 / 1.6) = 1 - (0.625) = 0.375 or 37.5% damage reduction Evasion increase EHP by = 1 / (1 - Evasion Rate) e.g. 15% Evasion = 1 / (1 - 0.15) = 1 / 0.85 ≈ 1.1764 or 17.64% increase in EHP for 15% evasion Evasion damage reduction is pretty much the percentage of evasion. e.g. 15% evasion = 15% damage reduction Now for the example if your unit has 1000 HP with 10 armor. EHP = 1000 * 1.6 = 1600 Add 15% Evasion to this unit its EHP will become. EHP = 1000 * 1.6 * 1.1764 = 1882.24 EHP 15% Evasion will increase this unit EHP by 1882.24 - 1600 = 282.24 Now let's compare another unit with 1000 HP and 30 armor EHP = 1000 * 2.8 = 2800 Add 15% Evasion to this unit. EHP = 1000 * 2.8 * 1.1764 = 3293.92 15% Evasion will increase this unit EHP by 3293.92 - 2800 = 493.92 Now we can see clearly that evasion benefit from more armor. Next to the main question. Which item is better to get, Ring of Protection +5 or Talisman of Evasion? The answer is it depends on how much armor that unit currently has. What we have to find is the point where EHP you gain from 15% Evasion exceed the EHP you gain from Ring of Protection +5 The equation to find out how much EHP you gain from additional 5 armor is X = ( (1 + 0.06(Y + 5)) / (1 + 0.06Y) ) - 1 where X = EHP% and Y = Current armor e.g. if you have 10 armor then (1 + 0.9) / (1 + 0.6) - 1 = (1.9/1.6) - 1 = 18.75% EHP gain from Ring of Protection +5 now we have to find the amount of armor where EHP you gain is more than 17.64% by applying X = 17.64% which we get 0.1764 = ( (1 + 0.06(Y + 5)) / (1 + 0.06Y) ) - 1 after solving equation the answer is Y ≈ 11.67 or 11.67 armor What this means is that Ring of Protection +5 will be better than Talisman of Evasion until your base armor is more than 11.67 What about the cost of items? I would like to say that the cost is pretty much negligible since it's only 15 Gold different with limited inventory. But if you insist then lets do some calculation. Let find out the cost of EHP from talisman of evasion first. Talisman is 240 gold with 17.64% EHP gain. Which means 1% EHP cost about 13.6 gold at any armor. Ring of Protection +5 Cost 225 gold with 30% EHP gain. Which means 1% EHP cost about 7.5 gold at 0 armor. As your armor increase, the EHP you gain from this item will decrease. That means the cost of 1% EHP will increase along with your armor. What we have to do next is to find a point where cost for 1% EHP from Ring of Protection +5 exceed the cost of 1% EHP from evasion. Written as a formula it would be X = 225/13.6 X = 16.5441 or 16.5441% EHP is the point where the value gain from Talisman exceed Ring of Protection +5 Now we have to find out how much base armor will decrease EHP gain of 5 Armor from 30% to 16.5441% by apply X = 16.5441% to the first equation 16.5441% = ( (1 + 0.06(Y + 5)) / (1 + 0.06Y) ) - 1 After solving equation we get Y ≈ 13.5556 or about 13.56 armor What this means is that at 13.56 base armor the cost of EHP gain from Ring of Protection +5 will start to exceed the cost of EHP gain from Talisman. In other words, if you have more than 13.56 base armor the gold you spent on Talisman will worth more than Ring of Protection +5 Bonus question. What about buying another Talisman? That depends on how Evasion work which can be separate into 3 case. 1. It stack additively. 2. It stack multiplicatively. 3. It doesn't stacks. The test can be done easily by buying 6 Talisman which provide a varied enough result to determine which case it is and then let the tower hit your hero to see how often it miss. case 1 Total evasion = 90% case 2 Total evasion = 62.28% case 3 Total evasion = 15% After testing done. I'm pretty certain that it doesn't stack which mean case 3. TL;DR - You gain more EHP from Armor +5 until you have more than 11.67 base armor then Evasion will give more EHP. In other words, if you have more than 11.67 base armor Talisman will be better than Ring of Protection +5. but if you took the value of gold into calculation then the armor change from 11.67 to 13.56 . TL;DR of TL;DR - have less than 11.67 armor? buy Ring+5 More than 11.67 armor? buy Talisman
“He still gets XP while in the cyclone.” I’m imagining Demon Hunter twirling around inside a tornado with a pen and pad of paper taking notes on the battle that’s happening underneath him.
Oh I think what happened to those confused druid was that the of the talon were not transforming back to human form because the AI still saw there were air units in range, which is their trigger for being transformed or not. However the tornado was messing with their targetability of the chimeras. So the druids both thought there were both air units and no units. Schrodinger's flying unit!
@@SCARaw Grubby ranked wyvern tier D in warcraft 3 frozen throne. And Spoiler......Lyn destroyed happy using wyvern in all games finishing him 3-0 in last tournament final they played. Can't even remember when Happy was even 3-0 ed
if you want to do a bypass at the beginning of the game make one unit in front and half /or 3 quarter high and the other unit full back and to the other side of the front unit
Grubby I have a challenge for you but I'm not sure if you read all comments.. can you win with each race only using 3 heros and no army?? Like Rambo mode but instead of only one hero using 3 for each race..
Once again Grubby is obsessed with expensive, low HP, low DPS siege with targeting issues. (long animation windup getting canceled by target switching) Look at his meat wagons and try to count how many attacks they get off.
Hi Grubby. I've been following your channel for quite a while and
have noticed something you mentioned in previous video regarding the Evasion and Armor.
At first it may seems that Evasion and Armor have a diminishing return relationship.
Which makes sense since if you have 25% Damage reduction and 25% Evasion,
your total Damage reduction will be 0.75 * 0.75 = 0.5625 which means
you only gain 0.75 - 0.5625 = 0.1875 or 18.75% Damage reduction from evasion instead of 25%.
But what we really should look at is not the value of Damage Reduction but the value of EHP.
If you reverse the Damage Reduction and calculate it as an increase in EHP (Effective HP) or how much total damage that unit can take,
we'll see that Evasion and Armor help each other in a multiplicative way.
In other words, more Armor is better for Evasion.
Let's lay down some basic formula first and make some calculation so we can see clearer picture.
1 Armor increase EHP by 6%
e.g. 10 Armor = 60% increase in EHP
Armor damage reduction = 1 - (1 / (1 + (Armor * 0.06)))
e.g. 10 Armor = 1 - (1 / (1 + 0.6))
= 1 - (1 / 1.6)
= 1 - (0.625)
= 0.375 or 37.5% damage reduction
Evasion increase EHP by = 1 / (1 - Evasion Rate)
e.g. 15% Evasion = 1 / (1 - 0.15)
= 1 / 0.85 ≈ 1.1764
or 17.64% increase in EHP for 15% evasion
Evasion damage reduction is pretty much the percentage of evasion.
e.g. 15% evasion = 15% damage reduction
Now for the example if your unit has 1000 HP with 10 armor.
EHP = 1000 * 1.6 = 1600
Add 15% Evasion to this unit its EHP will become.
EHP = 1000 * 1.6 * 1.1764 = 1882.24 EHP
15% Evasion will increase this unit EHP by 1882.24 - 1600 = 282.24
Now let's compare another unit with 1000 HP and 30 armor
EHP = 1000 * 2.8 = 2800
Add 15% Evasion to this unit.
EHP = 1000 * 2.8 * 1.1764 = 3293.92
15% Evasion will increase this unit EHP by 3293.92 - 2800 = 493.92
Now we can see clearly that evasion benefit from more armor.
Next to the main question.
Which item is better to get, Ring of Protection +5 or Talisman of Evasion?
The answer is it depends on how much armor that unit currently has.
What we have to find is the point where EHP you gain from 15% Evasion exceed the EHP you gain from Ring of Protection +5
The equation to find out how much EHP you gain from additional 5 armor is
X = ( (1 + 0.06(Y + 5)) / (1 + 0.06Y) ) - 1
where X = EHP% and Y = Current armor
e.g. if you have 10 armor then (1 + 0.9) / (1 + 0.6) - 1 = (1.9/1.6) - 1 = 18.75% EHP gain from Ring of Protection +5
now we have to find the amount of armor where EHP you gain is more than 17.64%
by applying X = 17.64%
which we get 0.1764 = ( (1 + 0.06(Y + 5)) / (1 + 0.06Y) ) - 1
after solving equation the answer is Y ≈ 11.67 or 11.67 armor
What this means is that
Ring of Protection +5 will be better than Talisman of Evasion
until your base armor is more than 11.67
What about the cost of items?
I would like to say that the cost is pretty much negligible since
it's only 15 Gold different with limited inventory.
But if you insist then lets do some calculation.
Let find out the cost of EHP from talisman of evasion first.
Talisman is 240 gold with 17.64% EHP gain.
Which means 1% EHP cost about 13.6 gold at any armor.
Ring of Protection +5 Cost 225 gold with 30% EHP gain.
Which means 1% EHP cost about 7.5 gold at 0 armor.
As your armor increase, the EHP you gain from this item will decrease.
That means the cost of 1% EHP will increase along with your armor.
What we have to do next is to find a point where cost for 1% EHP from Ring of Protection +5 exceed the cost of 1% EHP from evasion.
Written as a formula it would be X = 225/13.6
X = 16.5441 or 16.5441% EHP is the point where the value gain from Talisman exceed Ring of Protection +5
Now we have to find out how much base armor will decrease EHP gain of 5 Armor from 30% to 16.5441% by
apply X = 16.5441% to the first equation
16.5441% = ( (1 + 0.06(Y + 5)) / (1 + 0.06Y) ) - 1
After solving equation we get Y ≈ 13.5556 or about 13.56 armor
What this means is that at 13.56 base armor the cost of EHP gain from Ring of Protection +5 will start to exceed the cost of EHP gain from Talisman.
In other words, if you have more than 13.56 base armor the gold you spent on Talisman will worth more than Ring of Protection +5
Bonus question.
What about buying another Talisman?
That depends on how Evasion work which can be separate into 3 case.
1. It stack additively.
2. It stack multiplicatively.
3. It doesn't stacks.
The test can be done easily by buying 6 Talisman which provide a varied enough result to determine which case it is and then let the tower hit your hero
to see how often it miss.
case 1 Total evasion = 90%
case 2 Total evasion = 62.28%
case 3 Total evasion = 15%
After testing done. I'm pretty certain that it doesn't stack which mean case 3.
TL;DR - You gain more EHP from Armor +5 until you have more than 11.67 base armor then Evasion will give more EHP.
In other words, if you have more than 11.67 base armor Talisman will be better than Ring of Protection +5.
but if you took the value of gold into calculation then the armor change from 11.67 to 13.56 .
TL;DR of TL;DR - have less than 11.67 armor? buy Ring+5
More than 11.67 armor? buy Talisman
TL;DR this needs more upvotes
Can confirm all of this.
This is awesome a straight up thesis haha
Bro gonna have his uni degree thesis on wc3 mechanics
“He still gets XP while in the cyclone.”
I’m imagining Demon Hunter twirling around inside a tornado with a pen and pad of paper taking notes on the battle that’s happening underneath him.
Love the meta progression from "Shade OP" 2 days ago to "Shade sucks" today
tbf shade won this game for him lol
the whole Orc music made the whole game feel more epic
Oh I think what happened to those confused druid was that the of the talon were not transforming back to human form because the AI still saw there were air units in range, which is their trigger for being transformed or not. However the tornado was messing with their targetability of the chimeras. So the druids both thought there were both air units and no units. Schrodinger's flying unit!
it always one more game before it turns 4:00 am
I saw one of your Direct Strike Videos on Monday. I have poured so much time into this mode. I've done over 50 games just this week xD
I think it would be really funny if they added the hydralisk to this
Grubby's Undead skins are the best he has purchased.
doesn't hurt to be 3rd, seems all I do these days is wait for DS uploads lol
I like in games like this go meme strategy, going full one type army, or heroes only. Like who knows, maybe they can work : D
I see you got a Hero on the mountain Grubby!
Keep going on the ds! Love the content. The bit at the and was great
After last Happy Vs Lyn slaughter in finals I must say Happy is definately tier E
I dont get it
@@SCARaw Grubby ranked wyvern tier D in warcraft 3 frozen throne. And Spoiler......Lyn destroyed happy using wyvern in all games finishing him 3-0 in last tournament final they played. Can't even remember when Happy was even 3-0 ed
yeah surely we need our monthly happy vs lyn cast from grabby
Why spoil bruh
WE GOT THEM CROCKS MY GUY SPOOOOOKS
Direct Strike is amazingly fun. I m also addicted to watch*.
Legion TD when? that'd be awesome to watch the great grubby climb the ranks, it'd motivate me to play it more.
those mg skins look really sick
Love you grubby
I hope Grubby branches out to more custom competitive maps, Legion TD is another enjoyable one to watch :>
pls don’t skip the draft progress, that’s the best part of DS!
this seems fun i gota watch it when i wake up
Gotta up those numbers my man, 3-5 DS videos a day sounds good 👍
if you want to do a bypass at the beginning of the game make one unit in front and half /or 3 quarter high and the other unit full back and to the other side of the front unit
lol grubby so addicted to DS 😂
grubby what have you done to me I've played this all day every day for like 3 days now
Grubby I have a challenge for you but I'm not sure if you read all comments.. can you win with each race only using 3 heros and no army?? Like Rambo mode but instead of only one hero using 3 for each race..
after watching one the next one is up the best
BNet has more players and modes. W3Champions has a ladder. Both are separate leveling and point systems (skins don’t transfer between the 2)
Gru by I love watching your videos, but can you focue more on battles instead of spaming spawn repositioning xd
13:52 "every map is belong to us" guess why hahaha
its dota hahaha
One last one!
OOOOOOOH YEAH!
I miss playing so much. But mac use can't play anymorem
Once again Grubby is obsessed with expensive, low HP, low DPS siege with targeting issues. (long animation windup getting canceled by target switching)
Look at his meat wagons and try to count how many attacks they get off.
Someone is 100% making a full fledged game out of this mode, like it was with Dota 😅
y only one statue
This thumbnail face looks like you just farted, but it was not a fart after all....
reforged graphics direct strike when?
War3Champions currently doesn't allow Reforged graphics. They might fix it at some point in the future.
So much Ds 😭 no 1v1
oh cool i am first, have a great day grubster my friend
I am once again requesting grubby to play Warcraft strike in reforged graphics for one game!
1