Hypothetical and Ridiculous HON Math, Your Questions Answered! - For Entertainment Only

[Padsoldier]

For the max dmg of puppet's ulti, won't you need to count additional damage auras and spells to it? Like Revenant's Q, or Andromeda's damage aura, Wolf Commander's damage aura, Empath's As One, Ophelia's Nature's Wrath, or additional damage from items like Abyssal Skull? It's armor reduced by Sol's Bulwark, Shieldbreaker, Daemonic Breastplate and capping -armor with other ways (Pestilence ulti).

Additional questions: max damage of Mana Rift? Maximal amount of life gained on a single autoattack?

[[FDJ]J3rk]

That would mean that max puppet dmg is (considering dmg is signed integer) and devourer can get so many charges:
2.147.483.647

[[LN]Vida]

I guess the damage is a unsigned short value not a normal 32bit integer value.

[[S2]MacroHard]

What is the intelligence pont where vindicator would recieve a higher dps from his natural passive than from harkons blade modifier?

94.9 Intelligence (when the enemy has 20 physical armor and 10.5 magic armor)

Added to first post.

[KARTlK]

what is mathematically the best item progression for a 60 minute game with drunken master with 300gpm CONSTANT throughout the game starting with 603 gold using STRICTLY damage (no dooms)?

i'd probably assume that drunken master attacks every single time his attack is off cooldown and calculate that total damage with different item progressions and tell me which results in best total damage (you can sell items and stuff nbd).

thanks brah.

[GregerMoek]

94.9 Intelligence (when the enemy has 20 physical armor and 10.5 magic armor)

Added to first post.

If you don't mind me "stealing" the thread to post my own "experiments", with the same question in mind (about Master's Incantation VS Harkon's), from about a week ago.

I noticed we're using kind of different equations so I wouldn't be surprised if I have missed something, beacause I got slightly different values using my method for 20armor/5.5magic armor (283) too. However it's sometimes hard to see my own errors.
Also I didn't plot anything which isn't as stylish

You're probably doing it the right way.

Anyways, here goes!

Variables and some assumptions

• PC=Physical Coefficient (from armor usually OR flat damage reducing abilities like SW's Dissipate or Armadon's Armordillo)
  
• PA=Physical armor
  
• x=int (including int from passive, items, etc)
  
• 50 = starting damage(average)
  
• 50+62 = starting damage + Harkon's damage
  
• Harkon's int = 35
• Harkon's Raw Damage = 27
  
• 21 = starting int
  
• MC=Magic coefficient (from magic armor usually OR flat damage reducing abilities SW's Dissipate or Armadon's Armordillo)
  
• MA=Magic armor
  
• D= damage from abilities or items (NOT FROM STATS)
  
• PC=(1-armor reduction value)
  
• MC=(1-magic armor reduction value)
  
• OR=(Other reductions (Armodillo etc...)
  
• B= Block value (average)

Limits:
Not taking immunities into consideration, if someone goes magic immune or physical immune I hope you can decide what's better for yourself.

Both sides of the equation has Harkon's equipped and possibly stat items with no + damage component (I'm thinking that switching modifier based on situation is what you do)

• PC= 1-((0.06*PA/(1+0.06*PA))*(OR)) if armor is positive
• PC= 1-(0.94^(-PA) -1) if armor is negative, unsure on how OR would affect negative armor.
  
• MC= 1-((0.06*MA/(1+0.06*MA))*(OR)) if magic armor is positive
• MC= 1-(0.94^(-MA) -1) if magic armor is negative, unsure on how OR would affect negative magic armor.

Equation used:

Equation (1)
PC(x+50+62+D-B) + 0.6(x+21+35) = MC(x+50+62+D)


Which basically are the formulas for Master's Incantation + Physical damage (left side)
Damage = PC(x+50+62+D-B) + 0.6(x+21+35)
along with Harkon's Blade damage formula (right side)
Damage = MC(x+50+62+D)


USING EQUATION (1) on the site http://www.wolframalpha.com will help you calculate the value x if you enter the MC, PC, B and D values.
Two lines will be plotted, one for Harkon's and one for Masters Incantation+auto attack. Where the lines intersect the required +int will be show where the attacks are equal.

MC values and PC values and detailes presented in the spoiler below.

(only for armor now, NOT abilities even if they are part of the real MC value)

PC
MIN=0.25=(1-0.75)
MAX=1.95=(1+0.95)
PC= 1-((0.06*PA/(1+0.06*PA))*(OR)) if armor is positive
PC= 1-(0.94^(-PA) -1) if armor is negative, unsure on how OR would affect negative armor.

MC

MC is more limited because of the limited supply of magic armor manipulating items and abilities

Max magic armor reduction is 4+4+4+6+5+5.5=28.5
(++++:HarkonsBlade:+ :VoidTalisman: (on the target ofc))

Meaning minimum temporary magic armor is 5.5-28.5 = -23 magic armor
Max magic armor is 5.5+10+37
Arachna using Carapace while Magebane used blink nearby grants 32+5=37 magic armor, never happens, but gotta take that into consideration I guess.

MIN=1-0.689=0.311
Min "permanent" ~ 1-0.48 = 0.52 (15.5 magic armor, no magebane nearby)
MAX=1.759
Max "permanent" = 1 (spellshards+Harkon's without help from hero with -MA)
Harkon's only means roughly a MC of 0.975 or so. Almost true damage that is if the target is not wearing any vestments or similar.

MC= 1-((0.06*MA/(1+0.06*MA))*(OR)) if armor is positive
MC= 1-(0.94^(-MA) -1) if magic armor is negative, unsure on how OR would affect negative magic armor.


As one realize, -armor debuffs favours Masters Incantation (PC is increased)
+damage items highly favours Harkon's in most "real" cases.

Some item experiments including +stat items, Savage Mace and Riftshards rank 4

IF
D=0 (no damage items except Harkon's, just stat items)
MA = 5.5 MC will be ~0.975
PA = 17 means PC will be ~0.5
0.5(x+112) + 0.6(x+56) = 0.975(x+112) (equation (1))
x=156 (INCLUDING STATS FROM ITEMS)


D=88 (ADDING SAVAGE MACE)
Remember the 35+damage from the proc is reduced by physical armor hence why it's not added to the equation as it contributes equally on both sides.

0.5(x+112+88) + 0.6(x+56) = 0.975(x+112+88)
x= 491

Seriously this made me terrified, please correct any math fails I might have done. Apparently just one raw damage item screws things up for Masters Incantation big time.

Riftshards rank 4 (no savage mace) damage multiplier 1.48=(1+(0.2*2.4))
x=-950

LOL, basically Master's incantation can't beat Riftshards + Harkon's unless agic immunity happens.

Changing the PC in favour of Master's Incantation

PC= 0.6 (they have rougly 11 armor)

Only stat items:
0.6(x+112) + 0.6(x+56) = 0.975(x+112)
x= 37

Savage Mace:
0.6(x+112+88) + 0.6(x+56) = 0.975(x+112+88)
x=184

Riftshards rank 4

0.6(x+112+75)*1.48 + 0.6(x+56) = 0.975(x+112+75)*1.48
x=1559

Again, allow me to LOL at Riftshards+Harkon's power.

Let's say we have pesti on our team!

PC= 0.8 (rougly 4 armor)

Stat items =
0.8(x+112) + 0.6(x+56) = 0.975(x+112)

x=-33. Master's incantation wins in every scenario with these MC/PC conditions

Savage Mace
0.8(x+112+88) + 0.6(x+56) = 0.975(x+112+88)
x=3

Master's Incantation wins if 3 int. lal

Riftshards rank 4
0.8(x+112+75)*1.48 + 0.6(x+56) = 0.975(x+112+75)*1.48
x= 43

Phew!

Let's say everyone gets vestments on the other team when they discover you've got your fancy Harkon's Blade

MC from ~0.975 to ~0.745
PC is normal at 17 armor which is around 0.5

Stat items
0.5(x+112) + 0.6(x+56) = 0.745(x+112)

x=-17 in favour of Master's INcantation

Savage Mace

x=43

Riftshards rank 4

x=144

MIN and MAX PC/MC values just for lolz
MIN PC and MC

0.311 = MC
0.25 = PC

You're choosing between attacking Arachna with Carapace and Magebane buff ready, or attacking a fully leveled pebbles with DS ulti, Daemonic Breastplate, and Four frostfield plates and for some reason is extremely lucky with Helm of the Black Legion

Stats only
0.25(x+50+62-40) + 0.6(x+21+35) = 0.311(x+50+62)
x-31 int. Master's INcantation better

Savage Mace (no block this time)
0.25(x+112+88) + 0.6(x+56) = 0.311(x+112+88)
x= -32int

Riftshards (no block)
0.25(x+112+75-)*1.48 + 0.6(x+56) = 0.311(x+112+75)*1.48
x=-39int

If both MC and PC are reduced drastically Master's INcantation wins, but that's pretty obvious.

As Max(PC) > Max(MC) same thing goes with the extreme max values of MC and PC

The most extreme case of int needed

Min(PC) vs Max (MC) and high d + crit.

MC=MAX=1.759
MC=MIN =0.25

Stats only
0.25(x+50+62) + 0.6(x+21+35) = 1.759(x+50+62)

x=-148 meaning you'd need -148int in order to not heal (I guess?) your opponent as much as you would otherwise. But this is impossible.

Summary
Well, the MC and PC values mostly determine which orb is best in terms of damage.

• High PC (Low Armor) AND/OR Low MC (Moderate to high Magic Armor) favours Master's Incantation
  
• High MC and low PC => Favours Harkon's Blade.
  
• Abilities such as SW's passive which reduces both MC and PC values generally favours Master's Incantation because the true damage part ignores reductions.
  
• If MC = PC Master's Incantation is always best.
  
• +Damage items highly favours Harkon's Blade in most "real" situations.
  
• Crit favours Harkon's Blade in most cases because the +damage from Master's Incantation can't crit. Only time it favours Master's Incantation is when PC > MC
  
• Immunities means MC or PC gets to 0 (depending on immunity)

Again, please correct any wrongs I might have done. I know there must be some flaw somewhere I just can't find it.

Just thought it would be fun :P Apologies if it's considered OffTopic or whatever.

[[S2]MacroHard]

^your analysis is fine.

The difference is that my "X" for int is the total displayed int, not additional int from items and the passive. This is why my base damage is 29 btw.

Damage items only really mess up Master's Incantation because you were using 5.5 magic armor. Once Harkon's is applied it reduces that to 0.5... which is almost true damage. Applying true damage to all pre-existing damage is better than adding 60% of int only true damage. Armor and EHP ftw.

I also did not include any other damage sources. You went into far more detail (impressive). My intent for this thread is specific hypothetical situations. That way I can be quick with novelty responses.

Nice work.

[[S2]MacroHard]

what is mathematically the best item progression for a 60 minute game with drunken master with 300gpm CONSTANT throughout the game starting with 603 gold using STRICTLY damage (no dooms)?

i'd probably assume that drunken master attacks every single time his attack is off cooldown and calculate that total damage with different item progressions and tell me which results in best total damage (you can sell items and stuff nbd).

thanks brah.

This is somewhat overwhelming. The permutations are almost endless. I am going to take a pass on this.

[GregerMoek]

^your analysis is fine.

The difference is that my "X" for int is the total displayed int, not additional int from items and the passive. This is why my base damage is 29 btw.

Damage items only really mess up Master's Incantation because you were using 5.5 magic armor. Once Harkon's is applied it reduces that to 0.5... which is almost true damage. Applying true damage to all pre-existing damage is better than adding 60% of int only true damage. Armor and EHP ftw.

I also did not include any other damage sources. You went into far more detail (impressive). My intent for this thread is specific hypothetical situations. That way I can be quick with novelty responses.

Nice work.

I like this thread a lot. Fun facts + math + you're quite fast
And your point about the magic armor is what makes the item so effective, together with the fact that one can only wear one +magic armor item effectively which makes the damage reduction of Harkon's limited. Nowadays most heroes will pick up a pair of vestments unless they are a support with low income.

Sure there is magic immunity but that only lasts for so long. Harkon's is probably one of the more underrated items along with Charged Hammer.

What program/software are you using if I might ask?

[[S2]MacroHard]

Pencil and paper for equations.
MS Excel 2010 for number crunching, tables, and graphs.
Wolfram Mathematica for integration (for other threads, not this one yet)

[[AxL]xVirgil]

Epic thread,keep on going bro!

[LegoPirate]

largest crit possible, 5 man team only (so you cant stack up like 20 damage boosing abilities)

oh, and no doombringer

and show the item/skill combos you used.

and one slot to boots (of your choice)

you can put supportive aura damage boosting items on allied heroes as well (vlads specifically)

[LowtierLogan]

What is the worst combination of jungle creep spawns (Gold wise or XP wise) and what are the chances of that combination spawning.

What is the maximum amount of damage behe ult can do taking into account its radius and model radii? Assume 10 heroes with unitwalking, unlimited creeps none with unit walking.

If all you do is last hit every lane creep in one lane what GPM do you get?

At what hp and regen values will health pots regen you to 100% faster than the fountain. ( I dont really know the mechanics behind the fountain but early game it seems like health pots heal faster than the fountain)

[LegoPirate]

If all you do is last hit every lane creep in one lane what GPM do you get?

roughly 300 early game. this goes up to 350ish when you get 5 creeps per wave, and then about 600 when the wave doubles at 45 mins

[[S2]MacroHard]

Please keep huge permutation questions at bay. I really dont feel like setting up programs and running scenarios for a gagillion different item/spell/hero combinations.

Keep questions to one scenerio/set up. See first post for examples.

[LegoPirate]

Please keep huge permutation questions at bay. I really dont feel like setting up programs and running scenarios for a gagillion different item/spell/hero combinations.

Keep questions to one scenerio/set up. See first post for examples.

but the thread title has the word ridiculous in it

[Xenp]

Burges from Burge who are burged by other Burges from Burge, themselves, burge other Burges from Burge

Buffalo.


John had had had had


Given two ranged heroes fighting in a lane. If I Deny every creep of every wave (assuming four melee, one ranged) what experience will I have / my enemy have at 1,2,3,4,5,6,7,8,9,10 minutes mark?

Please format the answer with total xp for each hero at each time interval as well as their appropriate level.

=)

[Zwai]

5029 magic damage.

Added to first post.

Devourer can gain arbitrarily high attack damage if the game goes on long enough.

[[Poni]Octavia]

How much total damage does Blacksmith's Flaming Hammer do? Give answer as a function of the enemy's initial magic armour (if possible).

For reference, max rank is 40 damage per second and -4 magic armor over 7.5 seconds, with the magic armour reduction tapering back to 0 over the duration.

[[S2]MacroHard]

Buffalo.


John had had had had


Given two ranged heroes fighting in a lane. If I Deny every creep of every wave (assuming four melee, one ranged) what experience will I have / my enemy have at 1,2,3,4,5,6,7,8,9,10 minutes mark?

Please format the answer with total xp for each hero at each time interval as well as their appropriate level.

=)

How much total damage does Blacksmith's Flaming Hammer do? Give answer as a function of the enemy's initial magic armour (if possible).

For reference, max rank is 40 damage per second and -4 magic armor over 7.5 seconds, with the magic armour reduction tapering back to 0 over the duration.

I'll get both of these tomorrow. Reserving post slot.