DotA Mathematics
DotA Mathematics
This is a guide to show you the mathcraft of some commonly argued issues. Reading this will not instantly boost your DotA skills overnight, but will give you a rough idea on what to do and what not to do in more general situations. Having some forms of mathcraft in mind, you will make less logical mistakes in terms of selecting items and skills for heroes. The guide will be written in Q and A form. More important phrases and conclusions will be highlighted in ORANGE, and calculations to support the arguments will be separated so that those who trust me on the mathematics can skip those and read the conclusion. Enjoy!
Contents
1: Introduction to the concept of EHP (Effective Hit Points)
2: Introduction to the concept of Effective Damage
3: Introduction to the concept of DPS (Damage Per Second)
4: Application of EHP, Effective Damage, and DPS
5: The most argued topic: Buriza or Monkey King Bar?
6: How good is Hyperstone?
7: Armor reduction skills, how good/ bad are they?
8: How to optimize my DPS?
9: Maelstrom — n00b item or useful?
Topic 1: Introduction to the concept of EHP (Effective Hit Points)
Basic information regarding this question:
How do I calculate EHP?
Quoting directly from The Official Blizzard site:
Damage Reduction or Increases for Armor
For positive Armor, damage reduction =((armor)*0.06)/(1+0.06*(armor))
For negative Armor, it is damage increase = 2-0.94^(-armor) since you take more damage for negative armor scores.
Although the formula for armor may look intimidating, it actually works out to mean that one point of armor means +6% HP. So a unit with 20 armor basically has 120% extra hitpoints -- 100 would become effectively 220.
Important note 2: Fuck, Blizzard’s information is incomplete. There is another way to increase your EHP, which is to increase the chance of evading attacks. One of the most popular ways to increase evasion chance is to obtain a Butterfly. Since Butterfly gives you 25% to evade physical attacks, your real EHP will be A*(1+0.06B )/(1-25%). In general, if your evasion chance is C%, then the real EHP will be A*(1+0.06B )/(1-C%).
From now on, it is assumed that C is always 0 to avoid complications in calculations.
Examples of calculating EHP:
Consider a hero with 1000 HP, 25 armor. This hero’s EHP will be 1000 * (1+0.06*25) = 2500.
Consider a hero with 2000 HP, 4 armor. This hero’s EHP will be 2000* (1 + 0.06*4) = 2480.
From this example, we can see that the 1000 HP hero can actually withstand more physical attack than the hero with 2000 HP. Counter-intuitive?
If an item gives you X HP, and you have A HP, B armor, then you will have a 100*X/A % increase in EHP.
This can be easily verified. Without the item, your EHP is A*(1+0.06*B ). With the item, your EHP is (A+X)(1+0.06*B ), so the percentage difference is 100%*X(1+0.06*B )/A(1+0.06*B ) = 100*X/A
If an item gives you Y armor, and you have A HP, B armor, then you will have a 6*Y/(1+0.06*B ) % increase in EHP.
This can be easily verified. Without the item, your EHP is A*(1+0.06*B ). With the item, your EHP is A*(1+0.06*(B+Y)), so the percentage difference is 100%*A*0.06Y/A(1+0.06*B ) = 6*Y/(1+0.06*B )
If an item gives you X HP and Y armor, and you have A HP, B armor, then you will have a 100*X/A + 6*Y/(1+0.06*B ) + 6XY/A(1+0.06B ) % increase in EHP.
This can be easily verified. Without the item, your EHP is A*(1+0.06*B ). With the item, your EHP is (A+X)*(1+0.06*(B+Y)), so the percentage difference is 100*(A*0.06Y+X(1+0.06B )+0.06XY) /A(1+0.06*B ) = 100*X/A + 6*Y/(1+0.06*B ) + 6XY/A(1+0.06B )
Examples to calculate percentage difference in EHP:
Consider a level 10 Pudge, with no HP/ Strength item equipped. He has 1157 HP, 2.8 armor. His current EHP is 1157 * (1+0.06*2.8) = 1351.4
Now if he buys a platemail, his new EHP is 1157* (1+0.06*12.8) = 2045.6, % gain in EHP is 0.6/(1+0.06*2.8) = 51.4%
If he buys a Messerschmidt Reaver, his new EHP is 1632 * (1+0.06*2.8) = 1906.2, % gain in EHP is 475/1157 = 41.1%
Clearly, in terms of survivability, an early game Platemail is much better than a Reaver (considering that Platemail is much cheaper too).
Topic 2: Introduction to the concept of Effective Damage
Damage type? What is it?
All kinds of actions in DotA that deal damage have a certain damage type. They can be simplified to 3 types. Normal physical attack and certain spells belong to physical damage type. Most spells e.g. nukes belong to magical attack type. A very small number of spells belong to exact damage type.
Each damage type acts on a unit differently. Physical damage type can be reduced by armor; magical damage type ignores armor, but can be reduced by magic resistance, and completely negated by magic immunity. Exact damage ignores both armor and magic resistance, but can be negated by magic immunity.
For detailed information on the categorization of hero spells, please consult The Triggered Damage Guide.
Since different damage types work on a unit differently, it is clear that 1 point of physical damage is different from 1 point of magical/ exact damage. Moreover, in most DotA games we usually care about physical damage, therefore it is helpful to find a way to standardize all damage types. One way of seeing different damage types is to see them as different units e.g. kilograms, pounds, catty. It is very confusing to say “this item weighs 1 kilogram and 3 pounds plus half a catty”. Instead, we would want to say “this item weighs 2457 grams”.
How to convert all damage types into one single standard?
By convention, I will use physical damage type as the basis of conversion i.e. using the vocabularies in the example of weighing, I mean “I’m converting all weights into grams”. Therefore 1 point of physical damage equals 1 point of effective damage.
Since exact damage completely ignores armor, 1 point of exact damage of course is worth more than 1 point of effective damage as long as the unit has positive armor. Specifically, assuming the target has A armor, 1 point of HP means 1 + 0.06*A EHP, so 1 point of exact damage is equal to 1 + 0.06*A effective damage.
The difference between exact damage and magical damage is that the latter can be reduced by magic resistance. Assuming the target has A armor and B% magic resistance, 1 point of magical attack will be (1-B%) as effective as 1 point of exact damage. Therefore 1 point of magical damage equals (1+ 0.06*A)(1-B%) effective damage.
Sample calculation on how to convert different damage types
Suppose an Obsidian Destroyer has 100 base damage, level 4 Arcane Orb (deals 9% damage of current mana pool), 2000 mana, and level 1 Sanity’s Eclipse. It shoots a hero with 1500 HP, 15 armor, and 51.75% magic resistance (this is the magic resistance when the target has Aegis of the Immortal). Moreover. Assume that Obsidian Destroyer has 40 more intelligence than the target hero.
The target hero’s EHP will be 1500 (1+0.06*15) = 2850.
Now the Obsidian Destroyer hits the target with Arcane Orb, then use Sanity’s Eclipse. It will deal 100 (effective damage from physical attack) + 2000*0.09*(1+0.06*15) (effective damage from Arcane OrB ) + 40*10*(1+0.06*15)*(1-51.75%) (effective damage from Sanity’s Eclipse) = 808.7 effective damage.
Topic 3: Introduction to the concept of DPS (Damage Per Second)
Basic information regarding this question:
How do I calculate DPS?
When considering items that are good for dealing damage, you should only consider the percentage increase in DPS. The higher the better;
In order to calculate DPS, you need the following information:
Once you have all these numbers. This is how we calculate:
Assume your average damage is A;
Agility is B;
Bonus attack speed from items and skills is C;
Base Attack Speed is 1.7;
Your DPS will be (A)*(100+B+C)/170.
Sample calculations from real situations:
Level 25 Razor, with Power Treads, Sange and Yasha, Lothar’s Edge, and Radiance, and turn on Frenzy:
Average damage = (37 + 39)/ 2 + 2.5*24 (Agility gain per level) + 2*10 (Attribute Bonus) + 32 (Sange and Yasha) + 31 (Lothar’s Edge) + 70 (Radiance) = 251
Agility = 22 + 2.5*24 + 2*10 + 16 (Sange and Yasha) + 10 (Lothar) = 128
Bonus attack speed = 10 (Sange and Yasha) + 30 (from Treads) + 100 (from Frenzy) = 130
DPS = 251*(100 + 128 + 130)/ 170 = 528.6 damage per second.
If an item just gives you X damage, and your average damage is A, then you will gain X/A % in DPS.
This can be easily verified. Recall that DPS is A*(100 + B+ C) / 170. Your new DPS will be (X+A) * (100 + B + C)/ 170, so the percentage difference will be X/A%
If an item just gives you Y% increase in attack speed, and you have agility B, and items/ skills that give you C% bonus attack speed, then you will gain Y/(100 + B+ C) % in DPS.
This can be easily verified. Recall that DPS is A*(100 + B+ C) / 170. Your new DPS will be A * (100 + Y + B + C)/ 170, so the percentage difference will be Y/(100 + B + C)%
If an item just gives you X damage and Y% increase in attack speed, the percentage difference in DPS will be X/A + Y/( 100 + B + C) + X*Y/ A*(100 + B + C).
Recall that original DPS is A* (100 + B + C) / 170, and new DPS will be (A + X) * (100 + Y + B + C)/ 170. The percentage difference will be X/A + Y/(100 + B + C) + X*Y/ A*(100 + B + C).
Sample calculations:
Suppose a Stealth Assassin has a Yasha at level 8 (Ignore Backstab for the time being). His original base damage is (48 + 52) /2 + 2.9*7 = 70.3
His original attack speed is 24 + 2.9*7 = 44.3
DPS = 70.3* (100 + 44.3) / 170 = 59.7
Now with Yasha, the percentage gain in DPS will be 16/ 70 + 21/ (100 + 44.3) + 16*21/ (144.3*70.3) = 40.6%
Topic 4: Application of EHP, Effective Damage, and DPS
Many of you will wonder why I bother to bring up many topics with seemingly no connection to the game. The reason is that with this concept, you can theoretically calculate how much damage you will deal in a battle. Of course, it is impossible to predict whether you will kill/ die in every single battle, but when planning item builds for killers, you certainly want to make a build that can deal as much damage as possible. That’s why all these concepts can help you.
Example: You are Rhasta, and you have decided that your killing combo would be Mass Serpent Wards + Shackle + Forked Lightning. How effective is that? Here is the calculation:
Assume that you hold the units for 4.75 seconds (duration of Shackle). From the Basic Information of All Units FAQ, on average each level 1 Serpent Wards deal 41 piercing damage every 1.5 seconds.
So here are the calculations:
Assume the target hero has 25% magic resistance and 10 armor.
Effective Damage from Shackle: 40*4.75*(1+0.06*10)*(1-25%) = 228
Effective Damage from Forked Lightning: 300*(1+0.06*10)*(1-25%) = 360
Effective Damage from Serpent Wards, assuming that each ward hits the hero 4 times: 41*8*4*50% (piercing damage reduction) = 656.
In this case, if the target hero has less than 1244 EHP, then he’ll die. Given he has 10 armor, 1244 EHP means 777.5 HP.
Topic 5: The most argued topic: Buriza or Monkey King Bar?
Basic information regarding this question:
Who are the concerned heroes for this topic?
Generally speaking, all heroes that deal damage mainly by physical attack and do not rely on images are relevant in this topic.
Which hero killers MUST NOT get Monkey King Bar/ Buriza?
Some heroes have skills that will interfere/ be interfered by the bonus damage from Monkey King Bar and Buriza. Get other weapons for these heroes.
Are there hero killers that should get Monkey King Bar over Buriza all the time?
Yes, and for these heroes, there is no need to consider this topic at all. The heroes are:
These heroes have innate critical strike, which will be overridden by the critical strike from Buriza if both are triggered at the same hit. In particular, these heroes are all melee heroes, so it’s almost always better to buy Monkey King Bar instead of Buriza.
Spirit Breaker’s Empowering Haste damage bonus is not amplified by critical attack.
Slardar’s Amplified Damage does not amplify Monkey King Bar’s bonus damage.
Are there hero killers that should get Buriza over Monkey King Bar all the time?
These heroes have splash attack (Dragon Knight in red and blue dragon form do 100% and 50% splash respectively), but the bonus damage from Monkey King Bar will not be splashed. Therefore Buriza is always better than Monkey King Bar for these units.
Sniper has an innate mini-stun passive, and this stun will be overridden the Monkey King Bar mini-stun when both are triggered at the same time.
Mathematics section:
How do you come up with the number 102 in calculating the DPS of ranged hero with Monkey King Bar?
There is 30% chance to trigger Monkey King Bar’s 90 bonus damage, meaning on average you increase your damage by 27 just because of the mini-stun. Overall you gain 75 + 27 = 102 damage.
How do you come up with the number 24 when calculating the DPS increase in Buriza?
Buriza gives 20% chance to deal 2.2 times critical strike, which mean on average for every 5 hits, you will do the equivalent damage of 6.2 hits, representing a (6.2-5)/5 = 24% increase in DPS.
How do you come up with the number Z (30 – 40) in calculating the DPS of melee hero with Monkey King Bar?
As explained above, on average the bonus damage from Monkey King Bar increases your damage by 27. However, for melee hero, this damage is of MAGIC TYPE, and can only be reduced by magic resistance. Therefore, on the condition that heroes do not have magic resistance items, magic damage is better than physical damage, especially when heroes have high armor. For example, for a hero with 50% armor reduction, every 90 physical damage will cause the target to lose 45 HP, but every 90 magic damage will cause the target to lose 67.5 HP. In this case magic damage is 1.5 as effective as physical damage. In my calculation, I assume that Z is around 30 – 40, meaning magic damage is around 1.11 (=30/27) to 1.48 (40/27) times more effective than physical damage. In other words, I’m assuming that the heroes have around 8 – 16 armor, which is a reasonable assumption. However, it should be noted that magic immunity can negate melee heroes’ mini-stun damage. If the enemies are getting multiple Black King Bars, Buriza will be much more effective.
What if the enemies have Aegis of Immortality? Would Monkey King Bar be a worse item then?
Due to magic resistance, enemies will receive less damage from Monkey King Bar bonus damage. In particular, the hero’s armor reduction should be roughly the same as its magic resistance reduction, so you can use the ranged hero’s table to compare when Buriza is better than Monkey King Bar.
How do you come up with the number Y (6 – 8%) in calculating the DPS of Monkey King Bar?
From the attack speed FAQ, we know that a 15% increase in attack speed means a 15*100% /(100 + agility + items and skills that increase attack speed) increase in DPS. By choosing the number 6 – 8, I’m assuming that the hero’s agility + items and skills that increase attack speed is around 87.5 – 150, which is a reasonable guess.
Can you give me a reference on how much I gain from Monkey King Bar/ Buriza in terms of DPS at various levels?
Check the attached table. In this calculation, since the hero’s bonus attack speed does affect the calculation, I have set the bonus attack speed to be 80, 110, 140, and 220 respectively. Read the first row for example. It says that when a hero originally has 100 damage and 80 bonus attack speed (e.g. Power Treads + 50 agility), getting a Monkey King Bar will boost his DPS by 118.8% if he is a ranged hero, 127.5% if he is a melee hero. Getting a Burzia will boost his DPS by 99.9%.
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In this table, I’ve assumed that every 27 magic damage is equal to 35 physical damage.
If Monkey King Bar is so good according to your calculations, why is Buriza more expensive?
First, it is harder to farm for a Monkey King Bar. The two major components cost 2600 and 1650 respectively, whereas the components of Buriza are cheaper. If you farm for Monkey King Bar there is a higher risk that you will be killed and lose gold before you have enough gold to buy a major item. Second, most people first build up Crystalis before they get Buriza. Once you have Broadsword/ Claws of Attack, you can do last hit creeping much easier, and this will speed up your farming ability. Of course if you’re omfgbbqimba last hit gosu creeper, then this advantage doesn’t apply on you.
In short, if you’re confident on your basic DotA skills relative to your opponents, it is always better to get Monkey King Bar as the first major damage weapon.
Topic 6: How good is Hyperstone?
Basic information regarding this question:
Read the table below for detailed information.
I have divided the table into 3 sections. The yellow section is usually applicable to most intelligence and strength heroes (with around 15 – 20 initial agility, around 1.8 agility gain / level). The orange section is applicable to most agility heroes with no skill that boosts attack speed (with around 25 agility, 2.8 agility gain / level). The teal section is applicable to most agility heroes with skills that boosts attack speed.
The table reads like this: if your agility and bonus attack speed is 100 (e.g. Power Treads + 70 agility), then getting a Hyperstone will increase your DPS by 27.5%. With this number, you can easily compare the effectiveness between Hyperstone and other damage items.
For example, for a hero with 100 average damage and 100 bonus attack speed, getting a Demonedge will increase his/ her DPS by 36%, Hyperstone 27.5%. In this situation, it’s better to get a Demonedge first.
Topic 7: Armor reduction skills, how good/ bad are they?
Basic information regarding this question:
A review of all armor reduction skills:
Here is a complete list of all skills that reduce armor:
Reducing enemy’s armor is the same increasing your DPS towards that particular enemy
Using the concept of DPS, it is very easy to explain what exactly armor reduction skills work. For example, before the armor reduction skill is applied, the enemy a certain amount of HP per second. After the armor reduction skill is applied, the enemy loses more HP per second. We can then say that the armor reduction skill increases your DPS by a percentage, which will be further discussed below.
Note: I have avoided using the concept of EHP to explain armor reduction, since the formula for EHP does not hold at negative armor values. For details please check topic 1.
The effectiveness of armor reduction is determined by the skills that you apply, and the target’s armor before the skill is applied
Suppose your DPS is X, and the target has armor B. Now you have an armor reduction skill that reduces N armor. By the Blizzard formula quoted in topic 1, before the armor reduction skill is applied, the target will lose X/(1+0.06B ) HP per second. Now it loses X/( 1+0.06(B-N)) HP per second if B is larger than or equal to N, X(2-0.94^(N-B )) HP per second otherwise, i.e. when the resulting armor is a negative number.
After some simplifications, it can be shown that:
If the resulting armor value is non-negative, the percentage increase in DPS will be 6N%/(1+0.06(B-N));
If the resulting armor value is negative, the percentage increase in DPS will be (1+0.06B )(2-0.94^(N-B ))-1
Since both equations only consist of N, B, and some constants, it is obvious that only the skill and the target’s original armor decide how effective the skill is. Our next step is to find out how to achieve the most effective result, that is, to reach the highest percentage reduction in EHP.
Mathematics Section: Warning! It is assumed that you have some basic college level math to understand this part. If you are confused, simply read the conclusion of the section!
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Conclusion: For an armor reduction spell that reduces N armor, it is most effective when the target has around 0.7 N – 0.3 armor before the spell is applied.
OK, so how effective are my armor reduction spells?
The following table summarizes the percentage increase in DPS of most commonly seen armor reduction combos.
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Column A has numbers from 1 – 30. These are the armor values of the target before any spell is applied. In rows 1 and 2, there are names of spells that can reduce armor. In row 3, some numbers e.g. N= 4 are listed. This is the armor value that is reduced by that spell. For example PDL (Presence of the Dark Lord) corresponds to N = 4.
This table shows you the % increase in DPS of the armor reduction spells at different armor values. The yellow slots are the maximum % increase of DPS for any particular spell. For example, cell H11 is 80.4%, which means if the enemy has 8 armor (cell A11), Howl and the corruption effect of Desolator means a 80.4% increase in DPS. This is the best percentage increase you can have for this combo.
In the last row (Row 29), I have listed the maximum percentage increase in DPS assuming the target has 0.7 N – 0.3 armor. Comparing the purple numbers and yellow numbers, and you can confirm that the approximation used above is valid.
Now you can confidently tell your friends how useful armor reduction spells are. For example, The corruption effect of Desolator can at most increase one’s DPS by 38.4%. This occurs when the enemy’s armor is around 4.
“The corruption effect of Desolator is shit because I can negate it with Netherezim Buckler”
Many people use this as a reason to argue that Desolator is shit. How true is this statement?
If you have a good understanding of EHP, and DPS, you will realize that this argument is completely bullshit. Why? Netherezim Buckler gives you +5 armor. Assume you have A HP and B armor, your original EHP is A*(1+0.06B ), your new EHP is A*(1+0.06(B+5)). The percentage gain in EHP is 30%/ (1 + 0.06B ). Note that this increase in EHP works against higher physical attack, critical attack, faster attack speed, and armor reduction bonus. In other words, with better armor, you will lose less HP per second even if the enemies have higher damage/ critical attack/ Hyperstone/ armor reduction spell. A Buriza basically increases your DPS by 24%. If a Buckler can increase your EHP by 30%/(1 + 0.06B ), then you can completely negate the effect of Buriza. Does this conclude that critical attack is shit?
In short, be fair to Desolator. Just because it is easier to observe the effect of armor reduction spells versus armor items, doesn’t mean that armor reduction spells are shitty.
Topic 8: How to optimize my DPS?
Basic information regarding this question:
This topic is almost self explanatory if you understand the previous topics. The main idea is that, ultimately only DPS matters, because this is the single factor that determines how fast you can kill your targets. Most players are only concerned on pumping damage, and critical attack, because of the psychological thrill of seeing big red numbers popping up on the target’s heads. This is unfortunately not entirely correct. In this section I will point out some common myths/ misconceptions, and correct them using the concepts I have introduced.
One note though: while mathcraft can tell you how to optimize your DPS, it doesn’t say anything about the difficulty to obtain the items. Apparently Divine Rapier can optimize your DPS, but nobody will get it first. Read the mathcraft, evaluate your ability in getting good items, and then design the best item build for yourself. This is why your own gaming experience matters.
Common mistakes in boosting DPS.
Myth 1: Since Shadow Fiend can naturally reduce enemy’s armor, I should further amplify this advantage by pumping his damage.
Correction: This statement is wrong for two reasons.
First, Shadow Fiend has a passive that increases his damage to a maximum of 60. Any pure damage weapon is not that useful to him, because the percentage gain in DPS is determined by Y/X, where Y is the damage of the new weapon, and X is Fiend’s average damage.
Second, Shadow Fiend’s Presence of the Dark Lord is very bad against heroes. However, combined with Desolator, the percentage increase in DPS will be significantly increased. If DPS is all that matters, you should seriously consider getting Desolator for Shadow Fiend.
Myth 2: I think it is good to buy 5 Aghanim Scepter for Obsidian Destroyer, since it will then deal 700 + damage per hit…
Correction: this is again wrong. Every Scepter gives around 100 damage. When you can only do 100 damage per hit, getting an additional 100 damage means a 100% increase in DPS. However, when you already can do 500 damage per hit, an additional Scepter merely increases your DPS by 20%. On the other hand, Hyperstone can increase the DPS by 25% - 30%.
Myth 3: I think getting Buriza for Phantom Assassin/ Juggernaut etc. is good. Although critical strikes don’t stack, more chances of triggering critical strike never hurts…
Correction: While more chances of triggering critical strike never hurts, there are better ways to increase your DPS. If you get Buriza for these heroes, when both Buriza and the heroes’ innate critical strikes are triggered in the same hit, Buriza will override the innate critical strikes. Therefore the critical attack from Buriza gives you less than 24% increase in DPS. Are there other items that can boost your DPS better? What about Hyperstone? What about Desolator? Have you considered all possible options?
Topic 9: Maelstrom —— n00b item or useful?
Many people have claimed that Maelstrom is a completely shit item.
“It’s just a farming tool.”
“It doesn’t help you in team games.”
“The lightning is unreliable.”
At the same time, many other players have claimed that Maelstrom is useful, and said things like:
“The lightning is triggered 3 times in a team battle!”
To what extent are these claims true? With the concept of DPS, we are now able to unravel this myth.
Maelstrom gives 3 bonuses: 24 physical damage, 6 agility, and 20% chance to send a lightning that deals 150 magical damage to 3 units.
On average, the lightning gives the hero 30 bonus magical damage over 3 units per attack. As I have explained before, 1 magical damage is worth (1+ 0.06A)(1-B%) physical damage, where A is the target’s armor, B is magic resistance. Unless the target has Aegis of Immortal, usually 1 magical damage is worth more than 1 physical damage. Using the assumptions in the calculations of Monkey King Bar (Check Topic 5), we can assume that 30 bonus magical damage is roughly the same as 36 physical damage over 3 units. Therefore, we can say that Maelstrom gives the user around 60 physical damage and 6 agility at a cost of 3360.
From Topic 3, we have found out the formula for calculating percentage difference in DPS for items that gives X damage and Y attack speed is:
If an item gives you X damage and Y% attack speed, the percentage increase in DPS is X/A + Y/( 100 + B + C) + X*Y/ A(100+B+C).
Since most people who dislike Maelstrom argue that Maelstrom is shit in dealing damage, I shall just focus on the benefits of getting Maelstrom on attacking 1 unit, which means I’m ignoring the fact that the lightning can hit 3 units. It is an unfair comparison against Maelstrom, but let’s look at the result first:
In this formula, A is your average damage, B is your agility, C is bonus attack speed from items and skills. In this equation, X is 66 (assuming you’re an agility hero), Y is 6. Now let’s say you rush Maelstrom first (which is a reasonable assumption), and by the time you have completed Maelstrom, you have around 80 base damage, and around 50 agility, 30 bonus attack speed (from Power Treads). Putting these numbers into the formula, the percentage increase in DPS is 66/ 80 + 6/180 + 66*6/80(180) = 88.6%. Bad? I think not.
But… But… Maelstrom is unreliable, it only has a 20% trigger chance!
Again, this is an unfound biased argument against Maelstrom. The fact is, critical attack from Buriza has a 20% trigger chance; bonus damage from Monkey King Bar 30%, Cranium Basher 15%, Sange and Yasha 10%. Do you think it is fair to isolate Maelstrom from the other items and bash it for its “unreliability”? As long as you deal more than 5 hits on average in team battles, you should, on average, be able to throw a lightning. Then the argument that Maelstrom is unreliable will be complete nonsense.
If you claim that Maelstrom is THAT good, why not get Maelstrom for most heroes?
The major drawback for getting Maelstrom is that the lightning is an orb effect. By getting Maelstrom, you may not be able to use other orb effects that are more strategically useful, e.g. Frost Arrow, Impetus, Mana Break etc. For heroes with these skills, the Maelstrom recipe is completely wasted, and therefore they are not advised to get Maelstrom.
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