High BE Strat

[Ethan]

Peasants create more NW than Moving buildings from Homes to Banks, while increasing military numbers/draft to maintain same off/def from the loss of BE.

Lower Draft is never an economic/military advantage now, the only benefit is you are better at growing through exploration while maintaining the same draft.

Perfectly backwards. I point at your "increasing military numbers" - at between 4 and 6.5 NW per unit, how is this *NOT* increasing your NW more than the 1 NW pes? And then, you end up with the same military strength, because you lower BE and thus your TG/Fort effect. And then you take from some building you needed... in effect, stealing from more possible TG/Fort to get banks to get your income back up.

I can't say for certainty that lower draft will produce better MPNW (OPNW + DPNW, assuming constant O/D split). I *CAN* say that BE sci is worth it if your TG/Forts are not already MAXED! As in, you have room for 20% TG, 20% forts? Then BE after sci should be .5=X*.8*.2, so BE = 312.5%. Now
of course if BE gets to 150%, you will free up space so you run a higher % of TG/Fort, so noone ever needs 300% BE - but if they did, it'd still be worth it to eat the sci NW!

There's a simple way to see what is happening (the following DOES assume 1.076 ME form pay, but NOT the 1.05 from MP). If you assume land takes up at least 1/4 your NW (it's usually much more for sci) and you keep a 50/50 split on off/def, you CAN'T have better than .448 OPNW and .448 DPNW. And that assumed 100% draft! Now, lets assume Pes take the same NW as the military we replace, and drop to 80% draft. But we get max TG and max fort in exchange... Now we have .493 OPNW and DPNW. *IF* you could magicly run your prov at 100% draft rate, don't your think 80% draft rate would let you max TG and rax?

It gets even better if we realize that our NW/A will go down because pes are lower NW than the troops they replace. I already assumed the best O/NW (1.25) and D/NW (1) units - specs. (elites are better because they reduce the land%. But I just assumed a very low land % to start with.) Now I have to note the land % will go up - but it's total NW added is fixed, the % goes up only because the other part is decreasing. Accounting for this, we find that decreasing the NW gives .528 OPNW and DPNW.

In fact, that 20% draft reduction only requires a 16.67% from your TG/Forts to produce the same military as the 100% draft strat. Shouldn't be that hard to find the space with a huge BE jump and much less need for banks.

The point is, you simple can't get above .448 if you don't use TG/Fort. But there's no reason you can't get above that... in fact, I know high sci human strats that get up to .45/.45. .5/.5 in theory, but no-one ever gets enough sci to pull those off, even with the old human sage combo. And we made some ridiculous assumptions when we found a "max" of .448 - you clearly can't run 100% draft in the game, but we assumed we could. Yet real strats go higher! So clearly the 100% draft strat was missing something - and that was the BE needed to run high TG/Forts.

Think Different

[Ezzerland]

For the sake of argument, here is some test results of different draft rates:

Basic Prov Setup
A prov with 0 sci
1k acres
0 homes
spec only army, counting 1 raw tpa/wpa, rest 50/50 split off/def specs counting at 5 point specs for test purposes.
max stables
only offensive/defensive modifiers are TG's and Forts (no MP, etc)
Modified OPA/DPA is rounded to nearest hundredth


65% Draft Rate results:
73% Building Efficiency
51.07 MOPA (1 gen)
43.45 MDPA


55% Draft Rate results:
81% Building Efficiency
43.19 MOPA (1 gen)
36.81 MDPA

Running 55% draft, a 30% increase in TG's would bring the OPA (under the above test circumstances) to 47.83 MOPA (1 gen)


My guess is, If you can maintain a stable economy, go with the higher draft :p

[Ishandra]

Perfectly backwards. I point at your "increasing military numbers" - at between 4 and 6.5 NW per unit, how is this *NOT* increasing your NW more than the 1 NW pes? And then, you end up with the same military strength, because you lower BE and thus your TG/Fort effect. And then you take from some building you needed... in effect, stealing from more possible TG/Fort to get banks to get your income back up.

Because, dear Ethan, the rise in BE from 1 more peasant per acre is NO WHERE NEAR the rise in Offence from 1 elite per acre, certainly not 1/6.5th of it!

The abundance of peasants needed to raise BE to make up for an extra military unit, even when running 20% TG with 16 offensive units per acre, carries more NW than just having 1 extra military uni.

My point was, you will never reach the point where BE raises offence more than Draft, because the point is so far above the wage limitations to be impossible to reach. You would need most of the KD funneling GC into you while stealing for your wages every hour, which is not going to happen. As soon as you took a bottomfeeding hit it would take you days to rebuild the lost troops.

The rest of your post is really irrelevant im afraid, other than

I can't say for certainty that lower draft will produce better MPNW (OPNW + DPNW, assuming constant O/D split).

Surely you've run the numbers to show that it isnt true? I certainly have.

For the most NW efficient army, draft should be taken as high as you can a) afford to go and b) feel comfortable with the risk of being peasant dropped

[Ethan]

Ok, lets work though it Ezzerland's way (it's a little less abstract than my last post, for those that get scared away by abstract reasoning). 65% draft vs. 55% draft, no sci or homes. But look at MPNW instead of MPA, and look at our build.

First, we'll assume a worst case setup where only our TG/Forts are DBE, and that our dungeons+stables+banks(fixed bonus)+homes = 30%. So BE only works on 70% of our prov, and only linearly. And we won't trade banks into TG/Forts. And we'll assume we start at 20% TG, 20% fort, so the DBE will hurt the tradeoff. And there is no BE sci. So again, a worst case setup for lowering draft.

I will NOT mount my troops for these calcs. I do have space for them, but the NW counting gets annoying, and adds nothing conceptually. Thus my OPA=DPA and OPNW = DPNW, and only one will be listed. I also will NOT simulate WPA/TPA, for the same reasons.

65% draft:
25 ppa total
25*.35 = 8.75 pes/acre
76.25% BE
25*.65 = 16.25 military/acre
8.125 off units/acre
20% TG effect:
.2*.8*1.5*.7625 = +18.3% OME
8.125*5*1.183 = 48.06 OPA
NW/A calc:
55 (land) + 8.75*1 (pes) + 8.125*4 (off) + 8.125*5 (def) = 136.875 NW/A
48.06/136.875 = .3511 OPNW

55% draft:
25 ppa total
25*.45 = 11.25 pes/acre
83.75% BE
25*.55 = 13.75 military/acre
6.875 off units/acre
*Saved Land Calc*: 30% land is effected by BE, but isn't TG/Forts. Since the BE is higher, we only need New BE*X=Old BE*30%, X=27.32% land needed. This gives 1.34% more land for TG (and the same for Forts).
21.34% TG effect:
.2134*(1-.2134)*1.5*.8375 = +21.1% OME
6.875*5*1.211 = 41.63 OPA
NW/A calc:
55 (land) + 11.25*1 (pes) + 6.875*4 (off) + 6.875*5 (def) = 128.125 NW/A
41.63/128.125 = .3249 OPNW

So, in the 65% vs. 55%, under just about the worst assumptions I could make for my point, we find
65% = .3511 OPNW
55% = .3249 OPNW

Now, lets assume that your DBE rax and hospitals offset the homes and stables, so that on average your 60% land not in TG/Forts is effected linearly by your BE. Let us also assume that your 28.57% higher income due to pes allows you to remove 10% banks (at the higher BE rate... but that is almost 30% more base income! I think it's a reasonable approximation).

So the 65% case is identical, but the "land saved" from the 55% case changes, and thus the OME will go up. Our new land used from BE is:
(New BE)*X = (Old BE)*.6
X = .6*.7625/.8375
X = .5462
So we save .6 - .5462 +.1 (banks savings) = 15.38%
Half of this goes to TGs, so we have 27.69% land as TGs.

(above here same as first 55% example)
27.69% TG effect:
.2769*(1-.2769)*1.5*.8375 = +25.1% OME
6.875*5*1.251 = 43.00 OPA
NW/A calc:
55 (land) + 11.25*1 (pes) + 6.875*4 (off) + 6.875*5 (def) = 128.125 NW/A
43.00/128.125 = .3356 OPNW


65% = .3511 OPNW
55% = .3356 OPNW

So for a 10% drop in draft rate (and a 18% drop in military size), we are losing only 4.6% military strength as measured via OPNW.

And if you think that's it, remember we were assuming NO science, NO BE bonuses, and that the prov is using enough non BE buildings to offset the more than linear effect of it's DBE buildings. Plus I was still probably conservative with only 10% banks shaved from the build.

And if you think it doesn't matter - just look at pop sci. The % drop in military isn't effected by pop sci. The % gain in income isn't either. But the increase in BE *IS* effected, because it is comparing against that fixed 16.66 jobs per acre value.

Also, any non art dwarf should be avoiding stables, and other fixed effect buildings. And should use DBE buildings over BE buildings when possible, since their 30% BE is *after* the DBE effect (and the DBE are usually better at low levels of DBE). So the land saved calc should have been very conservative for a good Dwarf strat, again helping the low draft strat.

So, *IF* your strat is set up for it, lowering your draft WILL INCREASE YOUR OPNW! Look at how close it got to doing so under unfavorable assumptions, then just try telling me it doesn't work if we pick a setup that favors high BE.


Think Different

[Ishandra]

Ethan, your assuming 20% TG/Forts already, the point where BE will have biggest impact and STILL showed draft raised OPNW more than BE.

Pop sci is irrelvant, as draft is a %. BE will raise by itself with pop sci, so shoving more population into BE will actually help you less. Military numbers are affected because acre's arent, thus raising OPNW, income, BE without anything else even changing.

BE science however, assuming multiplicative (pretty sure its proven) does lend to a higher BE strat, but even then isnt enough to bring optimal draft down below wage limitations.

I understand you like high BE builds and your right if you set up to use them they work well. I'm just showing (well, you've just shown) that raising BE is inferior to raising draft to gain better OPNW and DPNW values. Higher BE however does lend itself to:
Better growth
Better recovery
Better T/M defences
Better income for AID/Science
So its still important, even for those trying to push their draft to its limits.

[FaeryRediculous]

Ishandra is right, I had a Dwarf/Shepard last age and the first half of the age I ran a 52% draft rate with very high BE. Near halfway I changed to 68% draft with still fairly good BE, and there was a very large difference in my military strenth. BE doesn't make as much of an impact as Draft Rate.

However, it is important to build up your BE still, I'm just saying that you should keep your draft high also. Lower draft earlier in the age might be good if you want to continue building your sciences anyways.

[Ethan]

Short note summarizing long post. I'm wrong, your right - I'll even make small changes to my play style because of it. But I am close, and in rare circumstances might be technically correct. So I'm almost right as well...
________________________________________________________

I appear good at proving your point. Lets run this though with 1 more set of assumptions. It shows, at the end, about the same as before, but with an even less pronounced drop. (So the build + the sci did weaken the draft-OPNW correlation, but didn't make it go negative like I expected.)

Assume 1 WPA, 1 TPA (attacker build). Assume no sci or pop bonus. Again assume specs for simplicity, the point holds for elites as well.
So, lets say we have 400 BPA pop sci, 196 BPA tools sci, and another 600 bpa in the other fields (we don't care where, just +13 NW/A total sci). Lets use the following build:
10% homes
5% farms
10% Hospitals
10% Rax
10% GS
15% TG
15% Forts
5% Guilds
5% Towers
15% Banks

Pop sci is 13%, Tools sci is 14%.

65% draft case:
(25+8*.1)*1.13 = 29.154 PPA
1 WPA
28.154*.35 = 9.8539 Pes/Acre
15 Jobs/acre
(1+9.8539/15)/2+.14 = 96.84% BE
Income, Base: 9.85*2.25+25*.15 = 25.92 gc/acre/hour
15% Banks @ 96.84% BE:
.15*(1-.15)*1.25*.9684 = +15.43%
Income, Total: 25.92*1.1543 = 29.92 gc/acre/hour
28.154*.65 = 18.3001 MPA
1 TPA
17.3/2 = 8.65 Ospec/Acre (same # dspec)
20% TG @ 96.84% BE:
.15*(1-.15)*1.5*.9684 = +18.52%
8.65*5*1.1852 = 51.26 OPA
NW:
55 (land) + 13 (sci) + 4 (WPA) + 4 (TPA) + 9.85 (pes) + 8.65*4 (off) + 8.65*5 (def)
= 163.70 NW/A
Thus:
51.26/163.7 = .3131 OPNW

Now, we do the first part again, at 55% draft:
(25+8*.1)*1.13 = 29.154 PPA
1 WPA
28.154*.45 = 12.6693 Pes/Acre
15 Jobs/acre
(1+ 12.6693/15)/2+.14 = 106.23% BE
28.154*.55 = 15.4847 MPA
1 TPA
14.4847/2 = 7.24235 Ospec/Acre (same # dspec)
NW:
55 (land) + 13 (sci) + 4 (WPA) + 4 (TPA) + 12.6693 (pes) + 7.24235*9 (off+def)
= 153.85 NW/A

Now an interlude to recalc the build strat in light of the new BE of 106.23% (from 96.84% BE). Banks pose a special case, dealt with last.
10% homes -> 10% (no BE effect we care about)
5% farms -> 4.5580%
10% Hospitals -> 9.0176% (DBE)
10% Rax -> 9.0176%
10% GS -> 9.0176%
15% TG -> 23.5095% (via totaling others)
15% Forts -> 23.5095%
5% Guilds -> 4.5580%
5% Towers -> 4.5580%
15% Banks -> 2.2543% (below)

We see we need 29.92 mod gc/a/h income. Our total with x% banks is:
(2.25*12.6693+25*x)*(1+x*(1-x)*1.25*1.0623) = 29.92
Approximating for x gives x=.022543.

Now, finally, with our new BE and new TG%, we can calc offense.
28.0183% TG @ 106.23% BE:
.235095*(1-. 235095)*1.5*1.0623 = +28.65% OME
7.24235*5*1.2865 = 46.59 OPA
153.85 NW/A (from above)
46.59/153.85 = .3028 OPNW

So, in the end, we find
65% = .3131 OPNW
55% = .3028 OPNW
So 10% draft drop gives 3.4% reduction in military. I'll take that trade of power for intangibles like: 20h bonus, faster to rebuild to, better PK resist. And my particular strat late age might be one of the special cases were it is an even smaller trade off. *But*, I'm also going to start overdrafting more in prep for war, and not worry as much about my BE falling, because I'm technically getting a little stronger by doing so, and more importantly, it gives me more room to grow into my draft.

Think Different

[FaeryRediculous]

I think your calculations are a little bit off... the difference should be higher then even that..

[Ishandra]

No they are right, the example just uses a build to maximise the use of BE through good sciences.