Math of the Storm: Block

Hi there, ChaosOS again. Today's topic, rather than analyzing a hero and their talents, is focused on a talent and the heroes that have it.



Going into this blog post, my goal is to analyze how good block is, given that we have seen an increase in high attack speed heroes released in the form of the various Overwatch heroes. Many members of the community have suggested that Block be reworked to be more like Dampen Magic, a level 1 talent on Stitches and Anub'arak that gives a spell shield effect at reduced duration. For reference, here is the description of the generic block talent:

"Every 5 seconds, gain up to 75 physical armor against the next enemy hero basic attack, reducing the damage taken by 75%. Stores up to 2 charges".

Today's spreadsheet of block value: https://docs.google.com/spreadsheets/d/1Apg3fmbWgdx5bDekHHj1TfYz58FBs7dtl_4AcgH3ZNY/edit?usp=sharing

Usual Disclaimer: All damage and health values below scale at 4% per level unless otherwise noted.

Who actually can gain block stacks?

Heroes who have block:
The Butcher
Kerrigan
Leoric
Muradin
Sonya
Surprisingly, generic block is hard to find now. As hero reworks happen Blizzard has increasingly moved away from generic talents and towards "Hero specific" versions, of which there are many. I've broken them down into what talent tier they are available as the expected strength of a block variant changes based on tier. Also, I'm defining a "block variant" as a talent that mitigates a certain number of basic attacks, rather than lasting for a set duration. This disqualifies Chen's "Elusive Brawler" and Kharazim's "Earth Ally".

Heroes who have block variants at level 1:
Artanis (Reactive Parry): Tied to Twin Strike, 4 instead of 5 second CD, only 50 armor.
Arthas (Rime): 3 stacks but only 60 armor
Brightwing (Pixie Dust): E ability on 10 second CD, can target ally
ETC (Block Party): Tied to spellcast, Affects allies but only 50 armor
Johanna (Reinforce): Tied to spellcast, only 50 armor
The Lost Vikings (Olaf the Stout): Regular Block for Olaf
Valeera (Combat Readiness): Tied to eviscerate, only 50 armor

A note on the ETC, Johanna, and Arthas Variants: Each of these heroes has a baseline way to gain armor, so with block stacks both Johanna hits the armor cap of 75 physical armor and Arthas goes up to 70 physical armor. ETC goes up to 70 physical armor for 2 seconds while his passive is active.

Heroes who have block variants at level 4:
Greymane (Thick Skin): Tied to Darkflight, only 50 armor
Jaina (Frost Armor): 1 charge, 10 second CD, applies Chill, only 50 armor
Lt. Morales (Automated Block): 3 charges, only 50 armor
Medivh (Mage Armor): Tied to going through portal, can affect allies, only 50 armor
Rexxar (Grizzled Fortitude): 7 second cooldown, individual stacks for Rexxar and Misha
Thrall (Feral Resilience): Tied to Feral Spirit hits, only 50 armor
Zarya (Defensive Shielding): Tied to Personal Shield/Shield Ally

A note on the Lt. Morales block: If she uses safeguard on herself and has block stacks she reaches the armor cap of 75 physical armor

Heroes who have block variants at level 7:
Genji (Dodge): 8 second CD, full evasion so no on-hit effects
Illidan (Reflexive Block): Tied to dive, so effective CD of 3 to 6 seconds

Heroes who have block variants at level 13:
Li Li (Elusive Feet): 10 second cooldown, 2 charges of block whenever her passive procs. This talent is about equivalent to Artanis' Reactive Parry, but is somehow at level 13. Please do not take this talent, there's good reason this has the lowest pick and win rate of her level 13 talents.

A brief explanation of how basic attacks work

On the character sheet there are three numbers related to basic attacks: Attack range, Attack damage (AD), and Attack Speed (AS). The typical melee hero has an attack range of 1.5, while a typical ranged hero has an attack range of 5.5 (Exceptions to both exist in either direction, for further info see the spreadsheet linked above). Attack speed is measured in attacks per second. To calculate a hero's damage per second, multiply attack speed by attack damage. A more interesting number though is a hero's attack period, or seconds per attack. To derive a hero's attack period calculate (1/AS). For 69 of the 71 heroes in the game right now the attack period is a much neater number than attack speed, for most heroes ranging from 0.9 to 1.1 but fully ranging from 0.125 (Tracer) to 1.3 (Leoric). The two heroes who do not have "neat" attack periods are Xul and Alarak, whose attack speed of 1.2 translates to an attack period of 0.833. 

This next bit isn't directly applicable to block stacks, but in short, basic attacks work more like spells and abilities than might otherwise be expected. The attack period on basic attacks is functionally the "cooldown" on the basic attack. Basic attack resets, such as Butcher's hamstring, work by resetting this basic attack cooldown. Some abilities, such as Malthael's Wraith Strike put the basic attack on cooldown, while others pause the cooldown timer. The "Cast time" on basic attacks is the forward swing animation. This is the amount of time a hero must stand still before they can start moving. Then, there is a back swing animation that is cancellable without penalty but helps make the attack animation look smooth while standing still and attacking. "Orb-walking" or "Stutter-stepping" is using the time after the forward swing animation and before the basic attack cooldown is finished to move, maximizing both damage and movement. Stutter stepping slows movement by (forward swing animation time/attack period)%. As a general trend forward swing time does not decrease proportionally with attack period, meaning slower attacks are more optimal for stutter stepping. This effect is why "Attacking while moving" on Tracer, Lucio, and D.Va is so powerful, while Tassadar, Tychus, and Pilot D.Va are severely hindered by their fast attack speeds that leave no room for stutter stepping without losing damage. A note on genji here: He is not able to attack while moving, but instead has a very short forward swing animation and a backward swing animation that continues to play even while he moves (but is canceled by using an ability)

How good is a stack of block?

The effectiveness of a stack of block is directly proportional to an enemy's attack damage, gaining .5 or .75 points of mitigation per point of attack damage increase on the opponent. Block's effective duration is inversely proportional to the opponent's attack speed, with the effective duration of 2 stacks of block being equal to the attacker's attack period. The first stack of block is consumed at 0.0 seconds, while the second stack is consumed after the attacker's attack period. Following intuition, block is stronger the more damage each basic attack does and the slower they come.

From the spreadsheet, the median base damage is 85 damage while the median attack speed is 1.11 attacks per second, leaving an attack period of 0.9 seconds per attack. Thus, the typical duration of block is 0.9 seconds and will block 127.5 damage. Longer fights may result in additional mitigation, as the cooldown on base block stacks is 5 seconds. The median will be a better measure of what a "typical" hero looks like than the mean, as the median grabs an actual hero's statistics while the mean is pulled heavily by the cluster of heroes with very high attack speeds. 

Just looking at the median values is not enough though. The talent system allows us to adjust our builds based on the enemy composition, thus we ought to see how good block in optimal scenarios. Ergo, the 10 best heroes to pick block against by damage blocked, from greatest to least:
1. Ragnaros
2. Thrall
3. Leoric
4. Alarak
5. The Butcher
6. Greymane
7. Cho'Gall
8. Sgt. Hammer
9. Zeratul
10. Cassia

What you may notice about these heroes is that most of these are traditional "solo laners". This mostly confirms the community consensus that block is a powerful tool in the solo lane. Conversely, block can lose value in 4v4s as it can end up absorbing the weak attacks from mages or supports instead of the powerful swings of a Thrall or Ragnaros. Furthermore, most ranged, basic attack based, heroes have higher attack speeds than their melee counterparts.Heroes who break these trends include Samuro and Illidan as melee heroes with high attack speeds, and Greymane and Sgt. Hammer as slow attacking ranged heroes. (If you are curious about where a particular hero sits in terms of how much value block gets, check out the spreadsheet linked at the top of the post.)

As an example, let's use Sonya vs. Thrall. At level 1 Sonya has the option to go War Paint (30% lifesteal) or Block. War Paint has uses outside of lane, for example it is an important part of her boss-soloing build, but let's compare them inside of lane. Sonya's base AD is 88, so each attack regains (88*0.3)=26.4 life. Per the spreadsheet block's two charges will mitigate 247.5 damage, so to regain the life she would have mitigated she needs to auto attack (247.5/26.4)=9.375 times. With sonya's base AS of 1.25, she has an attack period of 0.8, so 9 basic attacks would take (9*.8)=7.2 seconds. One charge of block would have half the value, so it would take (9.375/2)=4.685 attacks to equal one charge of block. (4.685*.8)=3.75 seconds. What that says is it doesn't take much trading in lane between Sonya and Thrall for block to be the better talent. 

What is not included in the above data is how auto attack enhancers move certain heroes up the list. Characters with access to Follow Through,Seasoned Marksman, or Focused Attack (and their variants) can gain significant amounts of basic attack damage that make Block an effective mitigating tool. As an example, against a Nova who picked One in the Chamber, each charge of block prevents (106*1.8*.75)=143.1 damage. Given that snipe has a base damage of 310, two charges of block is almost equivalent to dodging the snipe.

Conclusion

Block, as it exists, is a powerful talent that can mitigate a significant quantity of damage in solo lane matchups. Strong against heroes with slow, powerful attacks it can swing lanes against hard-hitting heroes. While evaluating the question of "Should Block give physical armor for a set duration", I would not recommend any changes. Not only is block an effective talent as-is, but it would make block a burst mitigation tool by potentially blocking many attacks from multiple heroes. The rise of heroes who attack quickly does make block less effective, but they pay for it with a lack of mobility (In the case of Tychus, Tassadar, Zarya, and D.Va) or fragility (In the case of Tracer and Lucio). As an early game talent that is most powerful in the early laning phase, block fills a unique niche in Heroes of the Storm that I would not change, and functions as a nice contrast to the prominence of late game power spikes with early quest talents.

EDITS: Added some clarification and a few corrections.
Tags: Block, Math
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yay (5) kappa (0)
Good writeup! Thanks
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