Glacius' Glacial Downpour damage distribution

[edxs]

New graph:


http://i.imgur.com/6DWKx.png


Old stuff:

Point Target
http://i43.tinypic.com/263x1l0.png
http://i43.tinypic.com/s46lgi.png

Every 400ms for 4s one burst of 190 radius damage is spawned in each of 4 evenly sized sectors with maximum radius 635 and minimum radius 125.

It is possible that a hero may be hit by all 40 impacts or by none, though it is exceedingly unlikely and depends somewhat on location. I don't have any math for this other than mental estimation.

This was all done assuming the target being impacted was a point. I don't believe this is actually the case in HoN. I believe heroes have a 24 'radius' bounding box, and I don't know how they translate a radius into a square. If you assume it's 42x42 (matching areas) you can do some mental convolution. I did further plots for an assumed 24 radius circular hero target.


Approximate Hero-sized Target
http://i44.tinypic.com/2i6p7rk.png
http://i44.tinypic.com/n436e.png

For quick reference, the expected impact breakpoints on a hero target:
more than 6: 301 units away
more than 5: 375
more than 4: 451
more than 3: 519
more than 2: 595
more than 1: 687
more than 0: 850

[Llama]

Very nice. I tried doing this a while ago when they remade it, but gave up.

Good work

[ElementUser]

I certainly hope integration was involved in this probability density graph lol. Nicely done

Moved to Guides & Lists

[edxs]

I certainly hope integration was involved in this probability density graph lol. Nicely done

Moved to Guides & Lists

If someone wants to do the real math, they're welcome to. I don't have the patience to create a 6+ piece function with 2d integrals to calculate the precise expected value and variance. I just verified the uniform distribution of bursts in-game with 320000 impacts and then accumulated 10000 casts worth of trials overnight in MATLAB.

[gral]

hey not to be insulting but how long did this take you..?

[tanis1]

hey not to be insulting but how long did this take you..?

It shouldn't take very long if you know what you're doing. 15-20 minutes at most.

Running the full simulation, however... takes a full night, as he says.

[ElementUser]

If someone wants to do the real math, they're welcome to. I don't have the patience to create a 6+ piece function with 2d integrals to calculate the precise expected value and variance. I just verified the uniform distribution of bursts in-game with 320000 impacts and then accumulated 10000 casts worth of trials overnight in MATLAB.

I don't really expect anyone to, but since I'm learning integrals I would have liked to see more mathcraft in action.

Anyway that's fine, I like what you've come up with regardless :)

[edxs]

Just a heads up, I made another plot except for impacts vs. angle. There is a pronounced increase in impacts at 0,90,180, and 270 degrees. The affectors follow your hero's facing, so this is straight ahead, behind, left, and right. It's about 1.9 times as many impacts as at 45, 135, 225, 315. This is averaged over all distances, so it probably won't amount to nearly as much in practice. I'm not sure why it didn't show up in the heatmap.

(edit: Disregard the previous, it must be due to some sort of rounding error. I plotted curves for various angles and distances and couldn't verify this effect.)

I'll redo pre- and post-patch graphs with 100000 trials each after the next patch. My code got 8x faster and I can get that done in just under 5 hours now.

[Harmonium]

matlab ♥

[BlacRyu]

Glacius
- Reverted Ult to be around himQ_Q4

[Norroar]

I take no credit for most of the following information;

--- --- ---

How to find the probability that a given location will be hit by a frost nova:

Let p(x) be the function:

http://i17.photobucket.com/albums/b61/Virot2/FreezingFieldPD.jpg

An approximation for the probability P(x,y) that any one frost nova will hit the location (x,y) is given by the formula:

P(x,y) = 36100 * pi * p(x) * p(y)

Example: the probability that each explosion will hit a unit standing 300 units directly to the right of the Glacius is approximately:

P(300,0) = 36100 * pi * p(300) * p(0) = (36100)(3.14)(0.000862)(.00101) = 9.92%

so units standing 300 units directly to the right of the Glacius will be hit by approximately 9.92% of the explosions from Glacial Downpour.

--- --- ---

The formula P(x,y) = 36100 * pi * p(x) * p(y) is only an approximation, though it should get fairly close to the right probability in most cases.

The exact probability that the point (x,y) will be hit by a given nova is described by the formula:

http://i17.photobucket.com/albums/b61/Virot2/FreezingFieldExact.jpg

where the function p is defined in the same way as in my last post. However, this formula is unreasonable to calculate without math software, and it is much less accessible to most people than the simpler approximation I listed above (which anyone can use by simply entering numbers into a calculator, even if they don't understand the math).

To give you an idea of the difference between the approximation and the actual number: using the approximation at the point (0,300) we got a probability of 9.97%. The actual probability is 11.5%.

Note that this is the probability that a given point will be hit. To find the probability that a hero standing at (x,y) will be hit, apply the same formula but replace the 190 by 214 in the outermost integral.

--- --- ---

http://img.photobucket.com/albums/v398/bobthemilkman/ff7.jpg

http://img.photobucket.com/albums/v398/bobthemilkman/ff8.jpg

These show how many times, ON AVERAGE that a hero will get hit who is standing still at a given location during a single Glacial Downpour. Note that it is possible to be hit by as many as 30, or as few as 0, regardless of your location (unless you're in a zero region of the graph, in which case you have a 0% chance to be hit, always).

--- --- ---

resources0.s2z \ heroes \ frosty \ ability_04 \ state.entity



<state
name="State_Frosty_Ability4"



icon="icon.tga"
passiveeffect="state.effect"

movespeedslow="0.3"
attackspeed="-0.2"
>

</state>

Glacius' ultimate slows movement speed by 30%, and attack speed by 20%.

[ElementUser]

^

You should know that in DotA, Freezing Field's quadrants were square; in HoN, it's circular, so those diagrams are slightly off than the one edsx made.

Also, since the introduction of a Frost Nova hitting in the 4 quadrants (each one is separated by 90 degrees), the probability is distributed more evenly in a smaller time interval (ie, the 4 seconds of channeling rather than a full night of simulations). While it is still possible to get hit with all 40 Frost Novas, you'd have to be standing in the right place & you must have terrible luck.

You could've stated where you got the info from as well: http://forums.dota-allstars.com/index.php?showtopic=73652

[Norroar]

Except, I got it from multiple sources.

I should have posted all the sources, though.


I realize that most of the information is from DotA, hence it could be incorrect - like the graphs. It's easy to notice, that they differ. I basically just wanted to post the information and the formula.

In HoN, it seems like you are only capable of being hit by 10 shards, though. If you look at the .entity file, it spawns a shard every 400 ms (as stated), and it does this for 4000 ms.
Is this because it spawns multiple shards, at once?

[ElementUser]

In HoN, it seems like you are only capable of being hit by 10 shards, though. If you look at the .entity file, it spawns a shard every 400 ms (as stated), and it does this for 4000 ms.
Is this because it spawns multiple shards, at once?

Glacius' ultimate has 4 affectors that determine where a Frost Nova is going to land.

Each 1 of them has an impactinterval of 400ms. However, there is an offset of 100ms between each of the affectors.

affector_1 has no impactdelay, affector_2 has impactdelay="100", affector_3 has impactdelay="200" and affector_4 has impactdelay="300"

And yes it seems I was a bit inaccurate, it should be 40 Frost Novas and not 30 because they also changed the spell duration from 3s to 4s a long time ago in DotA.

[Norroar]

Oh yeah. That's right.

I was uncertain of how these extra affector entities worked out. Thanks for clarifying :)


Edit: Just a quick question. I can't test it right now, so can you confirm whether Glacial Downpour freezes in the area, or around the shards?

[ElementUser]

Edit: Just a quick question. I can't test it right now, so can you confirm whether Glacial Downpour freezes in the area, or around the shards?

All units around Glacius that are within 635 radius:


<state
name="State_Frosty_Ability4_Self"


ishidden="true"
icon="icon.tga"
>

<aura state="State_Frosty_Ability4" radius="635" targetscheme="enemy_units" duration="1000" />
</state>

[edxs]

Updated first post.

[edxs]

http://i.imgur.com/6DWKx.png

[ElementUser]

Welcome back! <3

They also increased the inner radius offset from 125 to 350:


radius="635"
innerradiusoffset="350"

I am assuming you covered for that though, seeing as how the damage distribution at ~0 distance are really low. Also it looks a lot more like a normal curve after the change! :)

[Demonwing]

Nice job. Hats off.

[MacroHard]

Wait, so ideally you should be 300 to 400 distance away from your target? No wonder I have been doing so little damage with this. I used to always PK directly on top of my intended target!

[ElementUser]

Wait, so ideally you should be 300 to 400 distance away from your target? No wonder I have been doing so little damage with this. I used to always PK directly on top of my intended target!

Come on, you should know this graph master!

<3