The content of the article

## Intro

Just as a refresher, let's go over how Block currently works: once the talent is selected, your Hero starts gaining charges of Block. Each charge gets added after a cooldown (around 5-6 seconds), and charges will continue to accumulate up to a maximum number (typically 2 or 3). If your hero has at least one stack of Block, then the next Basic Attack from an enemy Hero has its damage reduced by a certain percentage (50-75%), one charge of Block is consumed, and the cooldown starts to get it back. Generic Block can have a max of 2 charges of 75 Physical Armor, gaining one stack every 5 seconds.

Some examples of Heroes of who have Block or one of its Hero-specific variants:

• Artanis
• Arthas
• E.T.C.
• Greymane
• Illidan
• Mal'Ganis
• Rexxar & Misha
• Sonya
• The Butcher
• Thrall
• Valeera
• Zarya

I will show mathematically that Block reduces Basic Attack DPS by so little that it does not provide enough value to be worth taking.

## Assumptions

To derive the formula for Block's effectiveness ad infinitum, I made several assumptions:

• There is one enemy Hero who is Basic Attacking your Hero constantly
• Your Hero has as much health as a Training Dummy in Try Mode so that the fight can be treated as a continuous function instead of a 5-15 second burst
• Your Hero is not moving out of the enemy Hero's Basic Attack range
• Your Hero starts with zero charges of Block
• Your Hero is gaining new Block charges as quickly as possible

## Variables used

• Basic Attack speed of the enemy Hero ("AtkSpd")
• Basic Attack damage of the enemy Hero ("AtkDmg")
• Phyiscal Armor of the Block charge ("Armor")
• Cooldown before gaining another Block charge ("CD")

## Setting up the equations for the derivation

1. In a vacuum, the enemy Hero's Basic Attack DPS against you is equal to their Attack Speed times their Attack Damage

AtkSpd * AtkDmg

2. The DPS of the enemy Hero when reduced by Block can be modeled continuously by calculating their total damage over the duration of a Block charge cooldown, subtracting the decimal Armor value of a Block charge times one Basic Attack's Damage to account for the attack that was "blocked" during the period, and then dividing the reduced damage by the Block charge cooldown.

(AtkSpd * AtkDmg * CD – AtkDmg * Armor) / CD

3. The effectiveness of Block can be expressed by dividing the reduced DPS by the vacuum DPS, and then subtracting that quotient from 1

1 – (Reduced DPS / Vacuum DPS)

## Derivation of the formula

1 – (Reduced DPS / Vacuum DPS)

Substitute the other two equations

1 – (((AtkSpd * AtkDmg * CD – AtkDmg * Armor) / CD) / (AtkSpd * AtkDmg))

Because the numerator is being divided by two different quantities, we can simplify the denominator

1 – ((AtkSpd * AtkDmg * CD – AtkDmg * Armor) / (CD * AtkSpd * AtkDmg))

Separate the fraction at the minus sign into two fractions

1 – ((AtkSpd * AtkDmg * CD) / (CD * AtkSpd * AtkDmg) – (AtkDmg * Armor) / (CD * AtkSpd * AtkDmg))

The fraction in the middle is equal to 1, since its numerator and denominator are the same value.

1 – (1 – (AtkDmg * Armor) / (CD * AtkSpd * AtkDmg))

Simplify the 1 – (1 – X) = X

(AtkDmg * Armor) / (CD * AtkSpd * AtkDmg)

Since the numerator and denominator share a common factor, AtkDmg, it can be canceled out. This leaves the final formula for Block's effectiveness as:

Block Phyiscal Armor / (Block Charge Cooldown * Attack Speed)

## The Argument

Using the generic Block, we can substitute 75 for the Physical Armor, and 5 seconds for the Cooldown. We are left with a x-1 style equation:

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75 / (5 * AtkSpd) = 15 / Attack Speed

So, if the enemy Hero has an Attack Speed of 1.0 Attacks/Second (many Heroes do), then Block is effectively reducing 15% of their Basic Attack DPS. However, if they have an Attack Speed of 2.5 (low-health Zuljin), now Block is only reducing 6% of their DPS. Scale this up to Tychus/Zarya and we're talking less than 4% DPS reduction. Conversely, Heroes with slower attack speed like Yrel or Stukov will lose more DPS to Block (19.48% and 22.39% respectively). Thus, generic Block reduces DPS from one Hero by anywhere from 4-22%, depending on the attack speed of that Hero.

Now the real issue comes to light: what happens when you're attacked by more than one Hero? Ganks while laning and teamfights around objectives group the teams together, and Basic Attacks go flying every which way. Regardless of how this gets modeled, it must mean that the Attack Speed in the denominator gets increased since there will be more than one Hero attacking you during the cooldown of the Block charge. Even just adding 1.0 to the Attack Speed in the denominator reduces the best case scenario of Stukov from 22.39% to 8.98%, whereas Tychus goes from 3.75% to 3%. By only adding one Hero attacking, the range of effectiveness has been reduced from 4-22% to 3-9%.

In my opinion, a < 9% reduction of incoming damage is not worth taking when other talents at the same tier can provide more value to your Hero such as increased damage, utility, or survivability.

## Caveats

The formula does not account for the initial mitigation of the multiple stacks of Block as the fight starts because it treats the Basic Attack damage as a continuous period of time while a Block charge is on cooldown. Thus, in quick fights where all charges are used at the start and only one or two charges need to be built up during the fight, the effectiveness of Block will be greater than the values listed above.

Additionally, there are some Hero-specific variants of Block that can have much shorter charge cooldowns which make them worth taking. Specifically:

• Illidan's <> combined with his trait, <>, can bring the charge cooldown down to a minimum of 1.3 seconds
• ETC's <> combined with <> and <> leads to a charge cooldown of slightly more than 2 seconds for both ETC and his allies

## What can be done to improve Block?

These are just some ideas to spark discussion; odds are none of these are a balanced long-term solution.

1. Decrease the cooldown of Block charges (might make it too strong vs Hanzo, Leoric, Yrel, and other slow Attack Speed Heroes?)
2. Change Block to store charges that are specific to each enemy Hero unit (think of Zuljin's <> talent at level 1), which would increase its effectiveness during teamfights up to the effectiveness of 1v1s
3. Change Block to give Phyiscal Armor for a duration once activated, like Johanna's <> or Yrel's <>
4. Change Block to reduce the Attack Speed of the enemy Hero that triggers the Block charge by a certain percentage for a second to equalize its effectiveness across all Attack Speeds.

## Conclusion

In its current state, Block and most of its Hero-specific variants provide less than 9% Basic Attack DPS reduction during long teamfights. Other talents at the same tier for every Hero will probably provide better value, and as such Block isn't worth taking. While the formula used is limited by the number of assumptions it makes, it provides a concrete way to evaluate Block's effectiveness and shows that Blocking one Basic Attack every few seconds is just not enough during teamfights, and is barely good vs certain Heroes in 1v1s.

I hope that this provides a new perspective on Block, and that it will spark a constructive discussion on what changes could be made to give it more consistent value throughout each game.

EDIT: Fixed some formatting issues