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Math of the Storm: Scaling Part I

Hi there, ChaosOS again. I'm back with a more informative than analytical article. Today's topic is Scaling, which is how the numbers in Heroes of the Storm grow over the duration of a game. Part I will focus on how Heroes scale, while Part II (coming next week) will cover Minions, Monsters, Mercenaries, and Map Objectives.

Today's spreadsheet can be found here: https://docs.google.com/spreadsheets/d/1igyk9SQHkA4JkjQPyV63ZNmP3leROK_ce_85CsCJGG8/edit?usp=sharing 

Credit for assistance with this article goes to reddit users Ahli, DizzyMongoose, and greythepirate


History and Background 

The current scaling system comes from the big “Scaling Patch” that came with Cho’Gall. These changes were talked about during the Blizzcon 2015 State of the Game Panel (Could not find an official VoD for this strangely).  

(Almost) Every other game that has a leveling system uses a linear progression of statistics with each level. This is to say that base stats can be represented in y=mx+b format, or (Stat) = (Scaling) * (Level) + (Base). I’ll use a fighter in 5th edition D&D as my example here. A level 1 fighter (with 10 con) has 10 HP, and gains 6 per level after 1st. So a 2nd level fighter with 16 HP is 60% more durable than a 1st level fighter, while a 19th level fighter with 118 HP is only 5.36% more durable than an 18th level fighter with 112 HP. This means early level ups feel significantly more powerful than later ones, barring some compensatory measure such as major abilities unlocking at each of those later levels. (Side note: I hypothesize this contributes to the preference towards lower level play that D&D and many other RPGs exhibit, because those early level gains have a greater feeling of significance.) 

Heroes of the Storm breaks this mold by using exponential scaling, (Stat) = (Base) * (1+Scaling)^(Level). This makes the % increase on the previous level completely flat (standardized to 4%, the exceptions to which we will investigate later in the article). This change also has the benefit of stabilizing ratios between damage and health. If an ability scales at the same rate as a hero’s health pool, it will always do the same percentage of their hit points. This normalizes the feeling of various character matchups, as you can count on attacks to retain the same effectiveness as a game goes on. 

As explained in the 2015 State of the Game panel, the primary benefit was addressing early level leads having a disproportionate impact on game outcome. The level 4 vs. level 3 fight not only was accompanied by a talent advantage but also a potential 20% stat advantage in both health and damage. Now the difference in each is only 4%, making early fights much more even and comebacks more possible.


Deviations from 4% 

The standard scaling in Heroes of the Storm is 4% per level, but the following numbers scale at some other percentage 

Cho 

  • Attack damage: 4.5% 
  • HP: 4.5% 
  • Hammer of Twilight (Active): 4.5% 

Gall 

  • Shadowflame: 5% 
  • Dread Orb: 
  • Twisting Nether: 5% 

Likely reasoning: Cho’gall has high scaling because the downside of a single body becomes more relevant as counterpick talents become available 

Falstad 

  • Hinterland Blast: 4.75% 

Likely reasoning: Intended to promote flashy late game plays and clips of teams getting deleted by Hinterland Blast 

Greymane 

  • HP: 4.5% 

Reasoning (Dev confirmed): Greymane’s hp scaling is to help him “survive team fights later in the game” (without increasing his strong early game). 

Gul'Dan 

  • Fel Flame: 4.5% 
  • Corruption: 4.5% 

Likely reasoning: Gul’dans range becomes more of a liability as the game goes on, this helps keep him relevant 

Kael'thas 

  • Pyroblast: 5% 

Likely reasoning: Similar to Hinterland Blast, Pyroblast has high scaling to promote flashy late game “Did you SEE how much damage that Pyroblast did?!?” 

Li Ming  

  • Magic Missiles: 3% 
  • Arcane Orb: 3% 
  • Calamity: 3% 
  • Disintegrate: 5% 
  • Wave of Force: 5% 

Likely reasoning: Shifts her power budget into her ultimates late game? Also, Li Ming’s talents are major damage upgrades, so lower scaling gives more power budget to her talents, increasing the distinction between builds. Overall seems more targeted at the “feel” of the character than a specific balance motive. 

Lunara  

  • Nature's Toxin: 5% 

Likely reasoning: DoTs like Nature’s Toxin are inherently stronger in the early laning phase when poking with basic attacks is much less risky compared to the late game. 

Murky 

  • Pufferfish HP: 5.5% 

Likely reasoning: This is an attempt to allow Pufferfish to survive late game teamfights without being impossible to kill in lane. 

Probius 

  • Pylon HP: 5% 
  • Disruption Pulse: 5% 
  • Warp Rift Detonation: 5% 

Likely reasoning: Probius’ kit is inherently stronger in the laning phase than in late-game teamfights, so this helps even out his power curve. 

Sgt. Hammer 

  • Blunt Force Gun: 3% 

Likely reasoning: Orbital BFG is such a large upgrade to the ability that a lower scaling (but higher base) helps even out its power curve 

Tracer  

  • Pulse Bomb: 5.5% 

Likely reasoning: Pulse bomb is an ultimate ability available from level 1, so a low base and high scaling helps keep it reasonable early while still feeling like an ultimate later in the game. 

Varian 

  • HP: 3% 
  • Attack damage: 3.5% 
  • Heroic Strike: 3.5% 

Likely reasoning: Varian’s level 10 is such a large power spike and provides so much additional stats that high base and low scaling helps keep him relevant early game while still affording power budget to level 10. 

Zagara 

  • Creep Tumor HP: 3% 
  • Hydralisk HP: 3.5% 
  • Infested Drop Impact Damage: 3% 
  • Infested Drop Roachling Damage: 3% 
  • Infested Drop Roachling HP: 3% 
  • Nydus HP: 3% 

Likely reasoning: Zagara has been designated as a lane bully and as such has very high base stats but low scaling. This accentuates her kits natural power curve, unlike similar heroes (such as Probius) whose scaling is intended to smooth out their power curve 


Quantifying the difference in scaling 

TL;DR Each half percent change in scaling from 4% is ~10% gain/loss at level 20 

Trying to understand the impact of what deviations from 4% scaling means can be a bit tricky, so I’ve provided some tables to help. 

Increase relative to base stats 

Level 

3% 

3.5% 

4% 

4.5% 

5% 

5.5% 

15.9% 

18.8% 

21.7% 

24.6% 

27.6% 

30.7% 

10 

41.1% 

41.1% 

48.0% 

55.3% 

62.9% 

70.8% 

15 

55.8% 

67.5% 

80.1% 

93.5% 

107.9% 

123.2% 

20 

80.6% 

99% 

119.1% 

141.2% 

165.3% 

191.8% 

Difference from 4% scaling 

Level 

3% 

3.5% 

4% 

4.5% 

5% 

5.5%

-4.72% 

-2.38% 

0.00% 

2.43% 

4.90% 

7.42% 

10 

-9.21% 

-4.71% 

0.00% 

4.91% 

10.04% 

15.40% 

15 

-13.49% 

-6.97% 

0.00% 

7.46% 

15.44% 

23.96% 

20 

-17.57% 

-9.19% 

0.00% 

10.07% 

21.09% 

33.16% 


Things that don’t scale 

There are some numbers in HOTS that don’t scale. The general rule is that quest talent rewards do not scale, while non-quest damage and healing bonuses do. Anything that provides a % change acts as another multiplier on the end of the scaling equation. Furthermore, talents that modifies numbers that are not health or damage related do not scale (Eg mana talents do not scale unless they provide % mana return). Here is the list of talents that provide a damage or healing bonus and do not scale with levels. 

  • Seasoned Marksmen (And its variants) 
  • Regeneration Master (And its variants) 
  • Alarak’s Chaos Reigns 
  • Arthas’ Eternal Hunger 
  • Auriel’s Increasing Clarity, Repeated Offense, Reservoir of Hope 
  • Azmodan’s Taste for Blood and Sieging Wrath 
  • Butcher’s Meat quest passive 
  • Cassia’s Thunderstroke and Plate of the Whale
  • Chen’s Keg Toss 
  • Gall’s Bombs Away 
  • Chromie’s Compounding Aether, Deep Breathing 
  • ETC’s Prog Rock bonus healing on E (The AOE healing quest reward does scale) 
  • Falstad’s Gathering Power 
  • Genji’s Shuriken Mastery 
  • Greymane’s Incendiary Elixir 
  • Kaelthas’ Convection 
  • Malfurion’s Vengeful Roots (Treant HP scales, but damage is only from quest reward) 
  • Medivh’s The Master’s Touch 
  • Muradin’s Perfect Storm 
  • Murky’s Slime Time 
  • Nazeebo’s Voodoo Ritual bonus HP/Mana 
  • Probius’ Warp Resonance and Gather Minerals (HP bonus) 
  • Ragnaros’ Sulfuras Hungers 
  • Samuro’s Way of Illusion 
  • Thrall’s Crash Lightning and Maelstrom Weapon 
  • Valla’s Puncturing Arrow 
  • Varian’s Lion’s Maw, High King’s Quest 
  • Zagara’s Serrated Spines 
  • Zarya’s Give Me Twenty 

Mana Scaling 

Mana in Heroes of the Storm scales linearly and is uniform across all mana users (EDIT: Except for Probius, who has a flat 600 mana and regenerates 100 mana per second while in his power field). The max mana pool for heroes is equal to 490+10*level, while mana regeneration is equal to 2.9024+0.0976 per level. 

Level 

Pool size 

Regeneration (mana per second) 

Time to recover full pool (seconds) 

500 

3.00 

166.67 

540 

3.39 

159.27 

10 

590 

3.89  

152.12 

15 

640 

4.37  

146.57 

20 

690 

4.85  

142.14 

What this means is by level 20 mana users have a mana pool that is almost 40% larger and have over 60% more mana regeneration. Mana costs are constant, so as the game progresses mana becomes less and less of an issue. 

There is a significant difference between how Heroes of the Storm and other MOBA’s handle mana, and that is because of items. In other MOBAs, (almost all) items that help with mana give a constant amount of max mana pool and or mana regeneration. Thus, mana costs and pools are balanced around how effective mana itemization should be at alleviating mana problems. DOTA 2’s Earthshaker has abysmal base mana and moderately high mana costs, but due to his long cooldowns choosing to itemize into mana can significantly alleviate his mana issues. Building for mana comes with the opportunity cost of not purchasing other items. By contrast, Skywrath Mage has much higher base mana, but his mana costs are also very high. Itemizing for mana regeneration on Skywrath Mage is still important, but gets him a less added casting time than it would Earthshaker. This makes comparing mana users much more difficult in other MOBAs, as the base stats do not tell the whole story. A mage and a tank may have the same base percentage consumption, but because a mage’s pool and costs are higher picking up a mana item will do less for them than it would a tank. This also plays into why flat mana burn is more effective on tanks than it is on mages, as it generally burns through a larger % of their mana pool than it does mages.

Heroes of the Storm, by contrast, makes it much easier to compare mana users. The only outside way to influence a hero’s mana pool is Malfurion’s Innervate, but the standardization of mana pools means that Innervate has a relatively standardized impact. EDIT: It has been pointed out that I forgot a few talents that affect mana. Probius at 13 has a talent "Power Overflowing" which grants 2 MPS to each ally in the field,  Medivh's Arcane Brilliance is an activateable talent that provides 200 mana, and Malfurion's Serenity upgrade to Tranquility provides 5 MPS to each ally.


A Minor Exception: Mule and Healing Ward

One exception to all of this talk about level-based scaling is two talents: Mule, and Healing Ward. Each of these talents' HP scales with game time rather than the user's level, with mule having 140+43*(minutes elapsed) HP and Healing Ward having 50+15*(minutes elapsed) HP


Minions, Monsters, and Mercenaries 

Non-heros (Minions, monsters, mercenaries, vehicles) scale strictly with game time. Some other MOBAs adjust jungle stats based on the levels of the heroes in the game, but that is not true for HOTS. Expect a full article on this topic next week. In the meanwhile, enjoy some work that has already been done by the community.

Haunted Mines Golem by Ahli: https://docs.google.com/spreadsheets/d/1uplOxnawBkKTuAi8tGUN5bXrOAptpwQPp_cU5LvYQgM/edit#gid=0 

Experience by Ahli: https://www.dropbox.com/s/hh02bgzzpx8d6sg/Experience%20of%20the%20Storm.pdf?dl=0 


Closing Thoughts

One of the best ways to create dynamic and interesting gameplay is by having different scaling. Card games know this by the difference between "Aggro" and "Control", whereby one deck is "on a clock" to finish out the game before the long term investments made by the other player pay off. Scaling, along with quests, can allow players to trade off early strength for power later in the game, an excellent way to ensure both players are incentivized to interact with each other. However, never forget that the base # scaling does not tell the full story. Many heroes have compensatory scaling, where they naturally are powerful in one stage of the game so the scaling differences are solely intended to balance that out. Varian may look like an early bully from his base stats, but his kit is too anemic pre-10 to actually exhibit any early dominance. Furthermore, talent-based power spikes play a role, where heroes such as Nazeebo don't have any particular high scaling factor but instead have extremely powerful 16 and 20 talents that make them late game beasts.

Tagged in: Scaling, Math
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i didnt know cassia was 4.5% on her Q (spear throw) until today