 downvoted post by Hodop
Increased Draft Size: 5/11/2021 22:48:03 
Fizzer
Level 62
Warzone Creator
Report

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: 5/13/2021 17:19:12 
Fizzer
Level 62
Warzone Creator
Report

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
Report

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
Report

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: 5/14/2021 22:52:33 
megaol
Level 49
Report

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 04:52:43 
Parsifal
Level 61
Report

...."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 19
Report

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 61
Report

@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 19
Report

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 61
Report

@Phoenix
I remember (some 45 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 9B11B  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 19:17:46 
asdfgh
Level 17
Report

Here you go Master Jz
I draft often
AfroEurasia 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 58
Report

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 2627%. By maxing it out (300% upgrades + 64% legendary artifact), the drafts increase by 9598%, 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 22:06:46 
Parsifal
Level 61
Report

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: ~4565M
so what now?

Increased Draft Size: 5/15/2021 22:24:48 
Phoenix
Level 19
Report

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
Report

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
Report

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 15:48:57 
Toadee
Level 28
Report

This is great work. Thank you to everyone contributing.

Increased Draft Size: 5/21/2021 17:20:01 
krinid
Level 60
Report

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 47T, so 15% of that would be 600900B, 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) 26B, which assuming I was 5075% finished the map (# of armies) at that point would make the value <1%.

Post a reply to this thread
Before posting, please proofread to ensure your post uses proper grammar and is free of spelling mistakes or typos.

