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Increased Draft Size: 5/11/2021 18:43:46


Z 
Level 62
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I have searched through the forums and only found vague finger waving and guessing at exactly how Drafts work.

Has anyone figured out specifically how they are calculated and how Increased Draft Size (IDS) affects them? (ie a formula?)

I have seen people think there is a limited "Draft pool" that you draw from and IDS either increases the max or increases the the amount you get each time while the max stays the same. I have seen some formulae that do not seem to match with what I see in game (though that may be before an update). And various other thoughts.

The general consensus is "it's good," but I am curious to know "how good?"

Things that increase drafts by my observations:
Gaining troops (or conquering territories)
Time (could be a byproduct of gaining troops)
Other mystic nonsense
- downvoted post by Hodop
Increased Draft Size: 5/11/2021 22:21:17


Master Jz 
Level 62
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The most you can draft at once is the following:

3690 * Army Income * (1 + Modifiers)

I've done the calculation on a few levels. I suspect that the formula for drafts is based on armies per second, total armies earned, and total drafts so far. Then, it multiplies that result by (1 + Draft Boost artifact + Tech Boost + Increased Draft Sizes).

Edited 5/11/2021 22:32:36
Increased Draft Size: 5/11/2021 22:48:03

Fizzer 
Level 62

Warzone Creator
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The number of armies you gain from drafting is the sum of two separate formulas: The fixed draft portion and the sliding draft portion.

The fixed portion is calculated based on your armies/sec number every time you draft. Therefore, the total armies gained from the fixed portion scales linearly with the number of times you draft as well as modifiers that increase your draft sizes.

The sliding portion is calculated based on both your armies/sec number as well as how many armies you've drafted in the past. The total armies gained from the sliding portion will approach but not exceed a percentage of the total armies gained in that level.
Increased Draft Size: 5/12/2021 11:40:14


Z 
Level 62
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Interesting. Thanks for the info.

So, if I am understanding it correctly, Increased Draft Size (IDS) will increase your minimum (fixed) draft size, but will do little to change your maximum income from drafts as that is fixed by the limit on the sliding portion.

Increased Draft Size is useful to help you hit the Draft limit faster. If you actively pick up Drafts, you will have consistent minimum drafts and constantly be near the limit. If you occasionally Draft (or after big Caches/Mercs), they will be barely affected by IDS since the bulk will be from the sliding scale.

I had figured that IDS would increase the maximum amount that I would get from Drafting, but that looks like it is more impacted by your Army Camp production. IDS only affects the speed at which you hit the cap.

Not sure if I will continue investing in Increased Draft Size for now. I see other more useful upgrades on which I can spend my AP.
Increased Draft Size: 5/13/2021 17:13:29


Master Jz 
Level 62
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Do drafts obtained from the fixed portion affect the sliding scale calculation?
Increased Draft Size: 5/13/2021 17:19:12

Fizzer 
Level 62

Warzone Creator
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Do drafts obtained from the fixed portion affect the sliding scale calculation?

Nope.
Increased Draft Size: 5/13/2021 17:48:47


krinid 
Level 60
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Do drafts obtained from the fixed portion affect the sliding scale calculation?

Nope.


This confuses me ... can we pls reword the question?

What we want to actually identify is: will investing in IDS will actually get us xx% (whatever % we upgrade IDS to) more armies compared to the exact same drafts without any IDS investment? (ie: total armies gained from drafting = draft size * xx%, where draft size=result of formula dealing with fixed draft portion & sliding portion)

I think Z just took away from this conversation that investing in IDS gets you bigger drafts each time, but over the course of an entire map, it doesn't actually get you more armies, and thus investing in IDS is not efficient. But I don't think this is right, I think it will get more armies overall. If not, I will be very sad for having invested so much in it already.

Edited 5/13/2021 17:51:10
Increased Draft Size: 5/13/2021 18:06:19

Fizzer 
Level 62

Warzone Creator
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but over the course of an entire map, it doesn't actually get you more armies

That is incorrect. The draft modifiers affect both portions, the fixed and the sliding.

First off, it depends on how often you draft.

If you're a very active player who drafts very often, then the sliding portion will always be capped by its percentage. In this case, draft modifiers are still beneficial to you since they increase the fixed portion of the draft.

If you draft only a couple times per day, then the fixed portion won't amount to much. But the draft modifiers are still useful for helping you reach the sliding percentage faster.
Increased Draft Size: 5/13/2021 18:29:01


Z 
Level 62
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Ok, thank you for clarifying. This helps greatly. It seems to help players differently based on their playstyle.

A few key points that I have learned:
Draft is broken into two components: Fixed Draft and Sliding Draft
Sliding Draft is capped at the Draft Cap, but Fixed Draft is not
Draft Cap is not affected by Fixed Draft or Increased Draft Sized (IDS)

Active Players:
Drafting constantly will continuously give you the Fixed Draft which is boosted by IDS.
Sliding Draft will, for the most part, be at the the Draft Cap for the level and barely affected by IDS.

Inactive Players:
Not Drafting constantly will diminish the effects of IDS on Fixed Drafts as fewer Drafts are gotten.
Sliding Draft will be boosted greatly as it will not be at Draft Cap, and IDS will help bring it to Draft Cap.


Overall though, inactive players will not see more Drafts per level with IDS as they will get fewer Fixed Drafts, and Sliding Drafts are capped regardless. Active players are the ones who benefit the most. They will hit the Draft Cap with ease and their Fixed Drafts will be much bigger.

I think what caused my confusion is how the two different Draft types are lumped together. I was expecting to see a huge jump in my Total Draft percentage, but it stayed more or less the same with +90% IDS. Though I did notice my minimum Drafts get larger. Confirming what was said above.

Thanks

(The real takeaway is: Draft constantly to maximize Drafting.)

Edited 5/13/2021 18:30:56
Increased Draft Size: 5/14/2021 03:26:29


krinid 
Level 60
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Thanks Fizzer, great to have confirmation!
Increased Draft Size: 5/14/2021 22:52:33

megaol
Level 50
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Is the sliding draft cap (fixed draft cap) just a fixed number? like, say 10%? Or is this affected by army camp income/other factors?
Increased Draft Size: 5/15/2021 02:18:14


krinid 
Level 60
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See bolded part.

The number of armies you gain from drafting is the sum of two separate formulas: The fixed draft portion and the sliding draft portion.

The fixed portion is calculated based on your armies/sec number every time you draft. Therefore, the total armies gained from the fixed portion scales linearly with the number of times you draft as well as modifiers that increase your draft sizes.

The sliding portion is calculated based on both your armies/sec number as well as how many armies you've drafted in the past. The total armies gained from the sliding portion will approach but not exceed a percentage of the total armies gained in that level.
Increased Draft Size: 5/15/2021 04:52:43

Parsifal
Level 62
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...."but not exceed a percentage of the total armies"......

I guess that's also my question. what is this percentage?

some kind of a formula would help
Increased Draft Size: 5/15/2021 09:41:12

Phoenix
Level 22
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If Fizzer wanted us to know these details, I guess he would have told us in the first place. So - if I understood this whole concept right - the only thing you can try is drafting as often as possible over some time (perhaps an hour or two or even a day) with nothing else changing, write down your numbers, and do the math.
Increased Draft Size: 5/15/2021 12:38:31

Parsifal
Level 62
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@Phoenix

That is exactly the point of these threads: posing questions. Some players share thought, some even find the calculations.
Thanks for your great tip though!
Increased Draft Size: 5/15/2021 13:23:47

Phoenix
Level 22
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okay, you're right, I was a but too quick with writing this. But I thought you were (mainly) addressing Fizzer. And I realized something else. You don't just want to draft as often as possible, but you want to draft as often as possible while writing down all the individual drafts. As soon as the drafts stabilize, you want to calculate the percentage. Because while the numbers still change (decrease), it means that the whatever percentage isn't reached yet, and as soon as the drafts stabilized, you might actually draft too much (in regards to the percentage). The exact moment of convergence is important.
Increased Draft Size: 5/15/2021 13:49:11

Parsifal
Level 62
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@Phoenix

I remember (some 4-5 months ago), while playing the Netherlands level, that at the very end (I had some 15 territories to go) my drafts dropped from 1B+ to about 100M - Draft Cap reached - that was quite unfortunate because at this point I was out of mercenaries and it took ages (2 more days) to finish the level.
So my first estimation (based on a blur memory): sliding portion is about 10 times bigger than the fixed portion....

At the end phase of my play through Europe Huge, my drafts were 9B-11B - I never reached the draft cap because it never dropped from that number. It was a surprise to me - I was drafting frequently
Increased Draft Size: 5/15/2021 13:51:20


Master Jz 
Level 62
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Fizzer said in the past that drafts were meant to be 17% to 21% of your total armies earned. I haven't pinned down the exact number, but they appear to converge around 17% for me. I have seen the number go higher when I've unlocked the draft tech early and drafted consistently every few minutes. I haven't put any AP into increasing draft sizes. I would love to see the numbers from someone who has increased their draft sizes (by 100% or more).
Increased Draft Size: 5/15/2021 19:17:46


asdfgh
Level 20
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Here you go Master Jz


I draft often

Afro-Eurasia Gargantuan stats Draft Sizes 120%, Draft Boost rare 16%

Army Camp ~247.7 B
Mercenary ~567.9 B
Cache ~352.6 B
Drafting ~269.3 B
Drafting% ~23.05%

Orbis Veteribus Notus stats Draft Sizes 150%, Draft Boost rare 16%

Army Camp ~27.6 B
Mercenary ~60.5 B
Cache ~28.1 B
Drafting ~28.4 B
Drafting% ~24.4%
Increased Draft Size: 5/15/2021 20:06:59

Dj Storm
Level 59
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Thanks, Master Jz and asdfgh, for posting values.
I'm missing the values from someone with 0% Draft Sizes. (Master Jz?)
I upgraded draft sizes, and noticed I don't gain from drafting what I expected. There were some changes in the formula through the updates (for example, in the past drafting was affected by all armies gained since the previous draft - army camps, mercenaries, caches/arenas and also drafted armies; now armies drafted during the previous draft don't seem to influence current draft).
However, even once the drafting formula stabilised, the increase is not that high.
In the examples above, Afro Eurasia Gargantuan provided 1168.2B armies from camps/mercenaries/caches. If unupgraded drafting accounts for 17% as Master Jz said, it comes out to 198.6B. Upgraded drafting increased it to 269.3B, or +35.6%, about a quarter (26.2%) of the expected 136%.
In Orbis Veteribus Notus, 17% unupgraded drafting would amount to 19.75B. Upgrading drafting to +166% effectively added 43.8% (26.4%).
This suggests me that the Draft Sizes upgrade affects only the 26%-27% portion of drafting, leaving the remaining 73%-74% unaffected.
So, by raising Draft Sizes from 0 to 100% (upgrades plus artifacts), the drafted armies increase by 26-27%.
By maxing it out (300% upgrades + 64% legendary artifact), the drafts increase by 95-98%, close to doubling in size.
We need more data points in order to pin down these values. Unfortunately "turning off" Draft Sizes is costly, we have to rely on different players with different playing styles, causing uncertainities in our evaluation.

Players who think about investing AP in Draft Sizes should consider that the effective increase is little more than a quarter of the expected increase.
Increased Draft Size: 5/15/2021 20:10:27


krinid 
Level 60
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Here's my stats for Europe Huge.

Army counts in Billions.

Army camps 586.4233 7.9%
Mercs 1778.8 23.9%
Drafts 607.8218 8.2%
Caches 927.6203 12.4%
Joint strike 1256.7 16.9%
Hospitals 2299.2 30.8%
TOTAL 7456.5654

Or if you prefer to count w/o JS and hospitals like many seem to:
(but this is weird counting, b/c then your total army counts will be significantly less than the total actually present on the level)

Army camps 586.4233 15.0%
Mercs 1778.8 45.6%
Drafts 607.8218 15.6%
Caches 927.6203 23.8%
TOTAL 3900.6654

And based on the info from Fizzer here, this means that with my +250% draft Adv, these values would be approx 243B down from 607.8218B.

Edited 5/15/2021 20:13:29
Increased Draft Size: 5/15/2021 22:06:46

Parsifal
Level 62
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sorry, those numbers still don't explain how to calculate the two different components of one draft.
Here are my numbers from Scandinavia:
armies per sec: 172K
armies earned : 72B
armies from camps: 38B
armies drafted so far: 12B
drafting modifier: +186%

armies per one draft: ~45-65M

so what now?
Increased Draft Size: 5/15/2021 22:24:48

Phoenix
Level 22
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To determine the fixed portion:
For a while, don't buy mercenaries and don't claim Army Caches, and draft as often as possible. At some point the armies per individual draft should converge towards a (relatively low) value, meaning the varying portion should be almost zero. Put this value in contrast to your draft boosts and your army camp production and you have the fixed portion.
To determine the percentage of drafts that the varying portion converges towards:
After you have the formula for the fixed portion (and you have drafted regularly), look at the ratio of "total armies earned" and "drafted armies". This should apparently be around 20%.
To determine the varying portion:
Calculate the expected fixed portion based on army camp production and boosts, check the ratio of total armies and drafted armies, then draft and note down this value together with the observed ratio. Then try to interpolate several data points to find the formula for the varying portion. Ideally without any boosts first because the boost affects the varying portion.

The posted total stats won't help much, I'd assume. I will log out soon, so I can't try this today.
Increased Draft Size: 5/16/2021 00:46:40


krinid 
Level 60
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Well presumably the formula is something like:

- d = total draft size
- dm = drafting modifier
- fixed draft portion
- fdp% = fixed portion %
- sliding draft portion
- sdp% = sliding portion %
- aps = armies per second
- tagol = total armies gained on level
- tagol% = ratio, b/c we know "The total armies gained from the sliding portion will approach but not exceed a percentage of the total armies gained in that level."
- z = some alpha factor that we don't know about but is related to "how many armies you've drafted in the past", so this is some part of the formula that increases the sdp when you have acquired lots of armies from caches, drafts, mercs, and decreases as you draw down on them -- essentially this is the "pool" that everyone talks about

d = dm * (fdp + sdp)

fdp = fdp% * aps

sdp = min (sdp% * aps * z, tagol * tagol%)

There are too many variables to deal with, and the sdp is the tricky part. WZI rounding will likely not permit you to get a solid figure, but we could likely reasonably estimate fdp% by continuously drafting until you get to a stable #, which likely (but not definitely) means you've exhausted all or most of the sdp, and the resultant d value is largely coming from the fdp or the tagol*tagol% MIN clause of the sdp formula.

At that point you know d, dm, aps, assume sdp=0, and thus can estimate fdp & thus fdp%.

Maybe someone with better math skills could use the resultant estimated fdp% to figure out sdp%, z, tagol%. tagol is always known if you have the stats, or at least known well enough. I'm not sure armies saved from active artifacts like Field Hospital, Triple Strike, Quad Strike, Damage Territory are accounted for in the stats shown or if they factor into the tagol summation.
Increased Draft Size: 5/16/2021 14:50:47


Master Jz 
Level 62
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I drafted several times in a row on Europe Huge until the draft size stopped going down. I had no draft modifiers. My income was 219,244.30 and my smallest draft size was 38.4 Million. Taking the smallest draft size and dividing by income gives me the number 175. Part of that is the sliding portion. It's possible I could have seen a slightly lower number if I kept drafting. The formula for the maximum you can obtain from fixed drafts (by drafting exactly every 6 minutes) is:

Maximum Fixed Drafts (for constant drafting) = Total Armies From Camps x (Fixed Drafts Multiplier / 360 seconds) x (1 + Modifiers)

The multiplier for fixed drafts is less than 175.

In my previous post, I used the following to calculate my draft percentage:
Total armies drafted / Total armies earned (from army camps, mercenary camps, caches, and drafts).

Edit: Here are some additional numbers for the smallest drafts sizes I've seen (as a multiple of army income).

0% Boost: ~170.1
8% Boost: ~177.4 (Dividing by 1.08 gives 164.3)
40% Boost: ~212.4 (Dividing by 1.4 gives 151.7)
48% Boost: ~220.5 (Dividing by 1.48 gives 149.0)

Linear Regression Equation: y = 106.3462*x + 169.5769
(x is the boost to drafts, and y is the value you multiply your income by to get the draft amount)

If we round and reformat the equation, we get:
y = 106 * (1 + x) + 63

If the numbers are accurate and the relationship is linear, the contribution from the fixed portion is 106 times your income and the contribution from the sliding portion is 63 times your income. If you take 63 / 360 , you get 17.5% for the sliding portion. The sliding portion may be boosted by the sliding portion from the previous draft, and the fixed portion may be boosted due to the sliding portion obtained from the fixed draft. If so, this would put the sliding portion at around 15% of total armies earned and the fixed portion at around 90 times current income.

Edited 5/21/2021 14:33:28
Increased Draft Size: 5/21/2021 14:45:50


Master Jz 
Level 62
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I believe that the fixed portion is 90 * Armies Per Second and the Sliding portion maxes out at 15% of your total armies earned. I also believe that drafting increases the sliding draft pool.

Solving these equations in the opposite direction of my previous post:

Fixed Portion = 90 * (1 + sliding draft portion that results from past fixed drafts) * (1 + Modifiers)
Minimum Sliding Portion = 360 seconds * Armies Per Second * 15% * (1 + sliding draft portion due to past sliding drafts)
Sliding Draft From Past Drafts = 15% + 15%^2 + 15%^3 + ... + 15% ^ n = 15/85 = ~17.65%

Maximum Draft = 3690 * Armies Per Second * (1 + Modifiers)
Minimum Draft = Fixed Portion + Minimum Sliding Portion
Minimum Draft = 105.88 * Armies Per Second * (1 + Modifiers) + 63.53 * Armies Per Second

Moving around terms gives:
Minimum Draft = Armies Per Second * (105.88 * Modifiers + 169.41)
Minimum Draft (as a product of Armies Per Second) = (105.88 * Modifiers + 169.41)

I could probably figure out the draft sizes for non-minimum and non-maximum drafts from this information, but these are the values that really matter.
Increased Draft Size: 5/21/2021 15:48:57

Toadee
Level 53
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This is great work. Thank you to everyone contributing.
Increased Draft Size: 5/21/2021 17:20:01


krinid 
Level 60
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I also believe that drafting increases the sliding draft pool.


It should. As Fizz stated that the sliding portion is some % of total armies earned, and Drafting grants armies which increase the total # of armies earned, it follows logically that this increases the sliding portion.

That said, where did the 15% value for max sliding draft portion come from? Don't see the value calculation in your post.

15% seems too high. I see regular MAX draft values after rapidly expanding it after claiming caches or lots of mercs, etc, but I've never seen a draft in the range of 15% of the total armies earned.

Some of the final maps have total armies of 4-7T, so 15% of that would be 600-900B, but I've never seen anything that high. After buying even as high as 350B mercs, the drafts following are in the range of (going from memory) 2-6B, which assuming I was 50-75% finished the map (# of armies) at that point would make the value <1%.
Increased Draft Size: 5/21/2021 17:31:11


Master Jz 
Level 62
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15% is the max total of all sliding drafts. For my minimum draft size equation, the 15% are the new armies from the army camps over the 6 minutes between drafts. I'm able to do this because the drafts have leveled out to all be roughly equal.
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