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Math of the Storm: Scaling Part II
Hi there, ChaosOS again. Today's article is a continuation of Scaling Part I, focusing on NPC scaling this time. Generally invisible in the game, today's article was made possible by looking through XML files and via AhliObs

Today's spreadsheet can be found here: https://docs.google.com/spreadsheets/d/1Z0tTZR8GhzfqQPYyp1pQt0GikmWfh_YZ87ZflLNhNxA/edit?usp=sharing I highly suggest checking out this spreadsheet because it contains a lot of details about the exact values. Disclaimer: Not all values are totally filled in, as the XML files occasionally did not seem to match my experimental and observed data at all. Abilities used by NPCs seemed to be the most likely to be inaccurate.

EDIT: I'd like to thank BlizzNeyman for providing the missing information!

Terminology

Structure - The buildings that each team owns
Minions - Spawning every 30 seconds at each team's core, minions march down the lanes. Each minion wave consists of 3 high health low attack footmen, a low HP wizard that will drop a health globe on death, and a high damage archer.

Mercenary - Mercenaries come in two types. First, "Wild" mercenaries are neutral enemies that spawn in predefined locations on each map. A group of mercenaries is a camp, and killing all the mercenaries in a camp creates a capture beacon. Capturing this beacon usually then spawns the second type of "Captured" mercenaries, but a few camps instead give different rewards.

Boss - A special type of mercenary, Bosses are immune to more effects than normal mercenaries and are capable of ending games on their own in the late game.

Monster - Monsters are similar to wild mercenaries in that they are neutral enemies (Except for the BoE immortals, which have teams). However, unlike Mercenaries, Monsters do not spawn capture beacons when they die, instead giving some other reward (Such as seeds or coins). Furthermore, certain talents that work on mercenaries do not work on Monsters.

Vehicles - Vehicles are player controlled entities that have completely different abilities, and last until killed or their timer runs out. The only vehicles in the game right now are the Dragon Knight and Garden Terror. Vehicles count as heroes for almost all abilities, except Stukov's massive shove and Greymane's cursed bullet cannot hit them. EDIT: There's a few others I forgot such as Stitches' Gorge.

Structures

The general rule is that non-core structures do not scale, while the core's damage, HP, shields, and shield regeneration increase linearly every minute until 20 minutes into the game, when the scaling stops. Towers of Doom is an exception to the first rule, with the "towers upgrading" at 14:33. The towers of doom upgrade affects only the structures that respawn when a keep is captured, so the outer two towers + gate will not upgrade even if they are still standing at this point in the game. Damaged buildings keep their current % hp, so increasing their HP remaining by the same % the max HP increases. The upgrade increases the HP and damage of the affected structures from "fort level" to "keep level". 

A brief bit of trivia on the core's shields: The core's shields are worth half of the core's life when fully charged, or one third of the total amount of damage needed to kill a core from full. The shield regen delay is 8 seconds, which means that core shields will start to regenerate 8 seconds after the last time the core took damage. Once the core has started to regenerate shields it will take 70 seconds of uninterrupted regeneration to go back to full core HP.

Minions

Minions increase their statistics every minute, on the minute. Minutes 1-5 increase at 1x the scaling factor, 6-10 at 1.5x the scaling factor, 11-15 at 2x the scaling factor, 16-20 at 2.5x the scaling factor, and 21 onwards at 3.5x the scaling factor. Catapults are slightly different, scaling at 3x from minutes 21 to 25 and 3.5x from minute 26 onwards. This "Ramping Linear" style of scaling keeps gametimes more consistent relative to linear scaling. Minute 10 is equivalent to minute 12.5 in pure linear scaling, minute 15 is equivalent to minute 22.5 , and minute 20 is equivalent to minute 30. This helps keeps game times down relative to pure linear scaling, as if the base scaling factor was increased to keep a linear system the same strength 20:00 in it would make pushes during the first 10 minutes significantly stronger. Minion scaling is important because structures do not scale, so large, uncleared minion waves are more of a threat to structures as game time increases.


Mercenaries and Bosses

 Mercenaries also increase their statistics every minute, in a linear ramping fashion. See the spreadsheet for exact details on this scaling. "Wild" Mercenaries (The neutral ones) have different statistics from the captured ones. Captured mercenaries *usually* have more HP and Damage than the wild ones at the same time, however this is not always true. Also, captured mercenaries are flagged as minions for the purpose of spells and talents that affect minions but not mercenaries.

Wild mercenary statistics update every minute, but mercenary camp that has been "pulled" will not update its statistics mid-fight. Resetting aggro on a mercenary camp will update its statistics to the current minute. Captured mercenaries have snapshot their statistics when the capture beacon becomes available, so clearing a mercenary camp then waiting on capturing the beacon will not yield additional statistics.

One notable exception is the Goblin Sapper explosion, which is a flat 1875 damage to the affected structure. This is 50% an outer turret, 16.7% of fort, 40% of an inner turret, and 13% of a keep. Remember that at 14:33 on Towers of Doom the forts upgrade to keeps for HP and damage purposes.

Monsters

Similar to everything else, monsters scale with minutes elapsed. The scaling patterns vary significantly more, with some monsters linearly scaling in the standard constant fashion, while others scale in the linear ramping style like mercenaries. For more details see the spreadsheet linked above.

Map Specific Notes

Haunted Mines
Summoned Golem: Ahli's Spreadsheet does the detail work, but there are some details I would like to highlight. First, golem scaling is marked at 60 skulls in total acquired, so taking 99 skulls and waiting will not increase the golems power. Next, HP and damage are individually linear scaling with the number of skulls acquired, but because more HP means the golem can get more swings in, skull collection overall has a quadratic effect on how powerful the golem is.

Minor skeletons: The only difference between the ranged skeletons and melee skeletons is that the melee skeletons have 150 less base HP.

Dragon Shire
Dragon Knight: The Dragon Knight scales similar to mercenary camps with time, except for the Fire Breath and punt abilities. Those two both scale linearly with game time, meaning they early minutes are a much larger power up than the later ones, relative to the AA and HP scaling.

Blackheart's Bay:
The coins for each turn in, per team, increase by 2 per turn in.
Turn in  Coins required (current) Coins required (total)
1 10 10
2 12 22
3 14 36
4 16 52
5 18 70
6 20 90
7 22 112
8 24 136

I could not find data on how much damage each cannon does, but a common trick is to damage the front towers of the middle fort a bit so that way a turn in full kills the fort rather than waste a bunch of damage on towers with a sliver of health.

Gardens of Terror
Garden Terror: The garden terror vehicle snapshots its power when the channel to enter the vehicle is finished, while Overgrowth plants base their HP on when the spell is cast.

Tomb of the Spider Queen
The gems for each turn in, per team, increase by 5 per turn in.
Turn in  Gems required (current) Gems required (total)
1 50 50
2 55 105
3 60 165
4 65 230
5 70 300
6 75 375
7 80 455
8 85 540

Infernal Shrines
The strength of the punisher appears to be based on when one team acquires 20 skeletal defender kills, although this may not be exactly accurate as this is based on experimental data from replays and not looking at the game triggers (which I do not have access to). 

Towers of Doom 
The Towers of Doom objective does not scale, shrines are worth a constant 1+(Forts owned) shots on the enemy core, sappers are 1 damage each, and the horseman is 4 damage.

Braxis Holdout 
Zerg units take 50% more damage from structures and do 50% less damage to heroes.

Warhead Junction 
Nuke damage is determined on cast, and deals 70% more damage in the center of the nuke. See the spreadsheet for exact details on the thresholds for "At what minute does a nuke kill which structure", but a quick and easy table with relevant breakpoints
 
Structure Breakpoint
Fort Gate Dies to inner radius 7:00 in
Fort Turret Always dies to inner radius, dies to outer radius 21:00 in
Fort Moonwell Always dies
Fort Dies to 2 inner radius 15:00
Keep Gate Dies to inner 14:00 in
Keep Turret Dies to inner 7:00 in
Keep Moonwell Always dies
Keep Dies to 2x inner 28:00 in

As for the core, nukes do about 29% of the core's maximum HP all game, so accounting for shields 5 nukes will leave the core with just a sliver of health (Or fully kill 23:00 into a game).

Actual applications in games tend not to shoot for exact breakpoints like this however because heroes are capable of cleaning up structures left at a sliver of HP, but this information may be relevant against an Abathur with Mule and well-defended structures that will be healed back to full.

Some Summons Analysis

Having these numbers, while nice, is only good if there's a use for them. Fortunately there is an easy analysis we can do that also leverages what we learned in Scaling Part I: How many shots does it take to get to the center of a hydralisk pop? Check out the "Summons Analysis" page of the spreadsheet for a full visual representation, but as an example I'll use the Xul Skeleton nerf from 300 to 270 base HP a few weeks ago. Base xul skeletons take 3 shots from a fort turret to kill (Forts do 1.5x the damage of their turrets, so that's 2 fort shots). Before, when Xul reached level 6, his Skeletons took 4 shots to kill (Realistically level 7 due to the degeneration). Now, Xul Skeletons don't tank the additional shot until level 9 (Realistically level 10). This is a measurable nerf to his ability to split push uncontested in the soak race to level 10 and probably contributes to a good chunk of his win rate loss after that nerf.

Closing Thoughts

Today's article was much more informational than analytical, but I wanted to make all of these numbers available to the community. I will likely reference many of these numbers in any future analysis of wave clear or push power brought by various heroes, even though it is unlikely we will get more summon based heroes like our current roster of specialists.
Tags: Math, Scaling
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Perhaps include that Vehicles are able to be cancelled by the occupant as well.