Income and population mechanics
 

I am playing MA Man in CBM and follow the advice to maximize money.
I have Order 3 Growth 3 Sloth 1 Heat 1 Misfortune 1.
I try to have a Forrester patrol each province with a halfway decent income, and overtax them to 110%
Seems to work great. But how could I really maximize the gains? Where is the break even between killed population and more income?
Any experience?

Re: Income and population mechanics
 

Break even in what sense? Forgive me if I'm wrong, but hasn't it been established that patrol-killing is simply always worse overall, what it brings is only in short term.

Re: Income and population mechanics
 

From the wiki we know

Every 3% tax above 100% kills 0.1% of the population.

In CBM 1.92, each level of growth increases population by .3%. So growth-3 gives +.9% growth which is enough to negate 27% taxation. Since we can only tax in increments of 10%, if you run tax at 130% you'll lose .1% of your pop each turn.


However, this does nothing to mitigate the unrest which will build up over time. Specifically the 6 unrest/turn from 130% taxation:

Every 5% tax above 100% increases unrest by 1.

I can't find the source but I seem to recall you lose 10 population for every point of unrest you reduce via patrol. That means that every 10% taxation above 100 is going to generate 20 deaths/turn from patrolling, in addition to the roughly .3% pop-death from over-taxation. Since we're now dealing in absolute numbers and not percentages, the larger the province's population, the less the unrest/patrolling deaths are going to matter. In a capital with a population of 30,000, with a tax rate of 130%, you are killing 1% of the population from over-taxation plus .2% of the population (60 people) from patrolling to reduce the unrest. That's 1.2% lost and .9% gained at growth-3 in your capital, resulting in a net loss of .3% each turn. For every province smaller than that (i.e. all of them), the patrolling deaths will count for a larger percentage of the population killed, further reducing the efficacy of using growth+overtaxing for profit.

As such, you have two options:
1) Take Growth-3 and overtax at 120% each turn (for -.8333% death rate mitigated by your .9% growth rate for .07% overall growth... assuming capital-size populations)

or

2) Take Growth-3 and repeat the following pattern: run 130% tax for 3 turns (while patrolling) and then set the tax to 100% for one turn. That will keep your population roughly stable and give you an average tax rate of 122.5% which is > option-1's 120% tax rate. Of course, this will be a micro-management nightmare so I'd recommend against this option.


TLDR: with full patrolling, you can overtax at 120% with growth-3 and have a stable population. Anything more and you're population will be in decline. If this is ever "worth it" it would only work in provinces with lots of money multipliers (high-admin castle, high order scales, no money loss from temperature).

Re: Income and population mechanics
 

For the illiterate among us: The best you are aiming at above is stable population. Is it not the case that you would always be better (richer) in the long-run letting your population actually grow? I'm just trying to conform my understanding.

Re: Income and population mechanics
 

Money now is worth more than money later.

Re: Income and population mechanics
 

Omikron Warrior breaks down the income gain from population growth here. Granted it's from back when Growth got you +.2% pop-growth/scale instead of the .3% you get now. But if you pretend he says Growth-2 whenever he says Growth-3 then the math works out the same.

The reason I bring that up is that it allows you to do cost-benefit comparisons on the actual income brought in by the various scales. For example:

Order-2 gives you +12% income on turn 1, 2, 3, and so on. You will be averaging +12% income over all those turns. Growth-2 gives +4% income from turn 1 and an average of +12% income by turn 6 (+4% from scale, +8% from pop-growth). By turn 12 you have averaged +14% income, thus earning more money from an 80-point investment in Growth-2 over an 80-point investment in Order-2.

Of course, this all assumes you are allowing your population to grow. With overtaxing and Growth-2 you're are getting +24% income on turns 1, 2, 3, etc, for an average of +24% income each turn. That's as much as you would have gotten from roughly 42 turns of Growth-2 without overtaxing... and double what you would have gotten from just Order-2.

Since having a bigger income on turns 1 through 41 is usually more important than having a bigger income on turns 42+, there is definite merit in long-term overtaxing.

All that said, I'm not actually sure how all the money bonuses combine when determining your income. If I had those numbers I could math-hammer this problem and figure out the sweet spots. Does anyone know how Order-3's +18% + Production-3's +12% + Growth-3's +6% + Castle Administration + Overtaxation actually combine?

Re: Income and population mechanics
 

I'll do some tests in a spreadsheet this evening. Perhaps I can show up with some graphs.

Re: Income and population mechanics
 

Obviously, over an infinitely long game you would do best to tax at 100%.

However, in practice income during the first 30 turns is worth A LOT more than income during turns 31-60 (for example). This means it's hard to give a mathematically meaningful answer as to what the best approach is. Plotting some graphs and/or just playing with different strategies should give you some idea of what strategy you want to take.

Playing as Man you have powerful troops but weak magic. I think it might make a lot of sense to overtax at the beginning and create large armies in order to get a lot of territory early on. Hopefully you'll have enough gems and forts (for research mages) by the midgame that you'll be able to remain strong when magic becomes dominant.

Re: Income and population mechanics
 

I cannot reproduce the income in my provinces.
I am always somewhat higher than the game, regardless if I just add up all scale effects (Order 2 + Growth 2 = 12%+4%=16%) , add up one scale and multiply sequentially (Order 2 + Growth 2 = 1,12*1,04=1,165) or multiply even within one scale (Order 2 + Growth 2 = 1,06*1,06*1,02*1,02=1,169).
Has CBM changed more than just scale effects (basic income)?
Its even for provinces with no unrest and no admin.
Or any Idea how it is really done?

Example: Pop 5260, Basic Income 52,6 Scales: Order 3 Growth 3 Heat 1 Sloth 1, 100% tax no unrest.
Ingame Income: 57

1st case: 18%+6%-4%-5%=15%; 52,6*1,15=60,49
2nd case: 1,18*1,06*0,96*0,95=1,141; 52,6*1,141=60,01
3rd case: 1,06³*1,02³*0,96*0,95=1,153; 52,6*1,153=60,63

Nothing near 57. I am puzzled.

We are more in the region of a scale Effect of 8%: 57/52,6=1,084
I also tried rounding to full digits, doesn't do the trick either.

Another province with the same scales has 9080 pop, basic income 90,8, actual income 101.
So actual scale effect for this province is roughly 11% (101/90,8=1,112).
Am I missing something?

Re: Income and population mechanics
 

I agree, it's puzzling. The only formula I've gotten to work so far was
1) Round income down to nearest 10: 52.6 becomes 50
2) Sequentially multiply by negative modifiers first: ((50 * .95) * .96) = 45.6
3) Sequentially multiply by positive modifiers: ((45.6 * 1.06) * 1.18) = 57.03648
4) Round result down: 57

And that's just me throwing those numbers into the formula-blender and taking whatever output looks right. I'll need more data points to test this or any other formula before I can be confident we've reverse-engineered the solution.

Also, are you sure the base income for that province is population/100? I ask because if the base number weren't 52.6 than it'd explain the difficulty we're having.

Re: Income and population mechanics
 

Thats what the manual says. Don't know if CBM changes that.

Re: Income and population mechanics
 

Loaded an old SP game of mine to check how its without CBM.
Turns out I had chosen zero scales for that.
Without any scale effects income is Pop/100 rounded down.
For one scale effect it seems like ((Pop/100 rounded down)*scale modifier) rounded down.
I check now on multiple scale effects.

Re: Income and population mechanics
 

You're remark about rounding to full digits got me thinking and, after a little trial-and-error, I think I've found a pattern that matches both examples: A) base income of 52.6 and B) base income of 90.8

1) Reduce base income to a whole number
a) 52.6 => 52
b) 90.8 => 90

2) Multiply the first positive scale (order's +18%) and reduce to whole number
a) floor(52 * 1.18) = floor(61.36) = 61
b) floor(90 * 1.18) = floor(106.2) = 106

3) Multiply the next positive scale (growth's +6%) and reduce to whole number
a) floor(61 * 1.06) = floor(64.66) = 64
b) floor(106 * 1.06) = floor(112.36) = 112

4) Multiply by the first negative scale (heat's -5%) and reduce to whole number
a) floor(64 * 0.95) = floor(60.8) = 60
b) floor(112 * 0.95) = floor(106.4) = 106

5) Multiply by the second negative scale (sloth's -4%) and reduce to whole number. Since there are no other income modifiers, this is the final income for the province for this turn.
a) floor(60 * 0.96) = floor(57.6) = 57
b) floor(106 * 0.96) = floor(101.76) = 101

That "reduce to whole number" and sequential multiplication really reduces the efficacy of positive scales and heightens the effects of negative scales!

Re: Income and population mechanics
 

Do you have a fort or unrest in the province? If so it would increase or decrease the gold income from the province.

As for overtaxing, keep in mind that you can invest the money you get from overtaxing in order to reap further dividends down the line. Using the money to build a fortified city in a province with 20k pop and neutral scales will net you 50g/turn for every turn after its completion. This in addition to whatever other utility you can get from the fort. And if thats not your fancy, how about investing the money in troops for taking lands from your enemies? Who cares that your capitol is worn down, you can just use the money to take some other poor schmucks capitol.

Re: Income and population mechanics
 

Who had the idea of doing it that way? It's ugly!
It even depends on the sequence you apply your boni. So one now has to check what the correct sequence is by examining lots of provinces and searching for the combination that works everywhere.
Perhaps I will do that another day.......

Re: Income and population mechanics
 

Are you currently (or were you previously) involved in running one of the world's major economies? ;)

Re: Income and population mechanics
 

I ran a few more numbers to determine the effects of administration from forts as well as over/under-taxing

As stated in the manual, forts offer an (admin/2)% boost to income. This boost appears to happen before any scales are factored in. Over/Under-taxing happens at the end as is a straight multiplier of the final income amount (rounded down). The scales are applied in the following order: order, production, temperature, growth. Therefore the income formula goes like this

1) floor(Population/100) = base income
2) floor(base income * (admin/2))% = F income
3) floor(F income * (order)%) = FO income
4) floor(FO income * (production)%) = FOP income
5) floor(FOP income * (temp)%) = FOPT income
6) floor(FOPT income * (growth)%) = FOPTG income
7) floor(FOPTG income * (tax rate)%) = final income

Examples:
Pop(29770), Admin(30), O/P/T/G(0,0,0,0), Tax(100%) = 341
Pop(29770), Admin(30), O/P/T/G(0,0,0,0), Tax(150%) = 511
Pop(30450), Admin(60), O/P/T/G(18,12,-15,-2), Tax(100%) = 433
Pop(30280), Admin(50), O/P/T/G(-18,12,-15,6), Tax(100%) = 311
Pop(30480), Admin(60), O/P/T/G(18,-12,-15,6), Tax(100%) = 368

Re: Income and population mechanics
 

income modifiers are definitely multiplicative.

-12% is actually multiply by .88, etc...

Multiplication is communicative and distributive, so there's no need to multiply by some first and then others as Elmokki does.

(x*.95*.95)*1.05*1.05 = x*.95*.95*1.05*1.05

So long as given modifiers multiply without flooring occuring inbetween, you can do all the multiplication operations at once.

Re: Income and population mechanics
 

=P

Its a basic fact of economics. Or to phrase it another way: Would you rather have $10 now or $10 next week?

Re: Income and population mechanics
 

So as to your original question, based on shatner's work.

So for the capital of man, you actually get around:

300 * 1.25 -> 375 * 1.18 -> 442 * 1.06 -> 468 * .95 -> 444 * .96 -> 426 base * 1.2 -> 511 from 20% overtax

For an extra 85 gp a turn, although in order to minimise failed patrols I'd probably use 2 Foresters.

That costs you two capital hires, 40 gp and 3 gp per turn in upkeep (As I understand it upkeep rounds up.

Assuming you don't overtax, on just turn twenty your capital will be worth:

300 * (1.009^19) -> 355 * 1.25 -> 443 * 1.18 -> 522 * 1.06 -> 553 * .95 -> 525 * .96 -> 504

So each turn that extra 82gp gets eaten away, slowly at first until it's essential no bonus at turn 20.

Even in your capital, which is by far the most favourable province to do this in, you make probably an extra 1000gp before you start losing money.

I'm not sure it's worth being 2 mages and about 300 research points down.

Re: Income and population mechanics
 

Nightfall, are you saying its NOT worth over taxing?

If so under what circumstances? Like growth 3?

Dooley

Re: Income and population mechanics
 

Given the scales in the original post it's of dubious value doing it perpetually in the capital, and even worse anywhere else.

Overtaxing certainly has uses, first turn in capital, low pop provinces with mines and provinces that you expect to lose in the next few turns, but I don't think this is a good one.

Re: Income and population mechanics
 

Thx Nightfall for your thoughts and advice. A lot in this game to get your head around.

Re: Income and population mechanics
 

Thx for all this, very enlightening.
I will go over it myself, when I have the time, but for now it seems my strategy was not perfect.

Re: Income and population mechanics
 

http://dl.dropbox.com/u/10701954/Tax...culations.xlsx

Just made up a spread sheet to calculate this out. Adjust assumptions and scales as desired. I have it set for a build I was trying out for man. O3P1C3G3

Bottom line is that overtaxing at 1.2 in your capital brings in about 1000 gold extra within around 20-25 turns at which point the total difference begins to decrease. At 1.3 its around 1500 gold extra by around turn 20. Your talking about an extra fort or two within the first 20 turns. That's a pretty big deal.

Overall I would say its worth it. Especially in CBM. In vanilla the trade off is a bit more questionable since foresters have a lower patrol and you almost always need 2.

However, as MA Man you also have an incentive to get up a lot of extra forts. You don't quite live and breath the stink of castle walls the same way was LA Man, but you do have some advantages they don't. Namely nature mages coming out you ears to provide supplies, and a bunch of stealthy, high strength wardens (if you're playing CBM) to sneak in and hold up the walls. Given this you can probably have a couple forts crank out a forester or two for 20 gold to patrol some provinces, leading to more gold, leading to more forts, leading to more mages. True if you used a capital recruitment turn to pick up another forester you would lose some research, but ultimately you get more if you have more castles cranking out mothers and bards.

As far as optimizing the strategy, you want as many positive scales as possible. Since the tax rate is multiplicative with any scales, the more positive modifiers you have the more this trade off tilts in favor of over taxing. For instance with O3P3G3 you can get almost 1800 extra gold by turn 21 at 1.3 tax. Take it up to 1.5 and you can get almost 2700 extra by turn 20. That's two extra forts, two labs, and almost half a temple.

Re: Income and population mechanics
 

GREAT!!
I wanted to do it just like that, but between job, 3 children and building a house I just barely have enough time to play one dom3 MP game and read the forum.
So many thanks to you!
This should definitely go to the strategy index, I'll send a PM to Valerius.

By the way: The exponential effect can only be seen very slightly....

Re: Income and population mechanics
 

I had surprisingly little to do today, which was quite a rarity. I have everything except the building a house.

http://dl.dropbox.com/u/10701954/Tax...ions%20v2.xlsx

Made a couple changes just to make it clear what actually needs to be input.

I have to say I'm a little surprised at how effective overtaxing is. And more surprised that more people don't use it, especially given the relative importance of gold in the early game.

For instance, just with O3G3 if you tax at 200% continuously you can get almost 4000 extra gold within the first 17 turns. Sure you've trashed your capital but you'll end up with almost 50% more gold during that time period. And with a 50% advantage in numbers/forts/labs you should be able to more than make up for the reduction in you capital through expansion.

Re: Income and population mechanics
 

Maybe because in reality your going to get nothing like that...

Basic testing shows you need 6 foresters patrolling to overtax at 200% without causing unrest problems...

Re: Income and population mechanics
 

Basic testing in CBM shows that you do need 2.

Re: Income and population mechanics
 

Two will basically ensure that unrest never builds up. But in general I've found that one keeps unrest at 0 when taxing at 120% probably 90% of the time. Every once in awhile you miss a turn, but you're still only getting up to 2-4 unrest usually before it drops back down to zero. Still even if you insist on using two, that extra 1100 in gold income over the first 20 turns is still worth it. Its an extra fortress + part of a lab to crank out bards.

Lets assume you need one forester for every +10 in taxes. If you're taxing at 150 you get an extra 2390 gold within the first 20 turns, with the advantage dropping off after that. It hits gold parity around turn 40. Each forester costs 20 gold, 1.3 upkeep. Lets just say 2 for simplicity sake. That's 10 gold per turn in upkeep. So at turn 20 your still sitting at +2190 gold. Which would be about 2 extra castles and a lab, or 16 extra mothers, or 62 extra wardens, or 39 extra Knights of Avalon. It seems like this is well worth it. And that assumes the foresters are completely worthless other than for patrolling. They're still scouts, and they's also precision 12, a pretty good chassis for some magic bows (thunder bows in CBM 1.92 are wicked).

And if it takes 6 foresters then stick 6 foresters on it. Are you really saying that you're not going to have a few fortress turns free here and there at some point? Fortress completed prior to a lab going up? spend 20 gold for a forester. Left with an odd amount of gold at the end of a turn and cant afford another mother or bard? Spend the 40 gold and buy a couple foresters. Seems pretty easy to get a few of these guys, and once you do crank up the taxes, and even if you have to actually recruit one INSTEAD of a mother or bard, they pay for themselves rather quickly. And with the extra gold you get from overtaxing you can get more mothers and bards in the long run. Yes, it might take awhile before you end up with the six needed to tax at 200%, but that doesn't counter the overarching point: gold now is worth MUCH more than gold later since it lets you expand now.

Re: Income and population mechanics
 

And if you really have a problem with using two at 120%. Then just use one at 110%. Still nets you an extra 600 gold in the first 24 turns, and doesn't reach gold parity until turn 46.

It just seems sort of strange that there are plenty of people out there who are willing to take death scales in order to get an advantage early at the cost of some gold later in the game, but very few are willing to do the same with overtaxing. 120% taxing along with patrolling kills off less % population than death 3 scales, but actually nets you more gold than 3 scales of order.

Re: Income and population mechanics
 

Or, in CBM, you could take O3/P3 instead of O3/G3, have a similar income and be in a better position to leverage it. In all cases holding your first army back for 1-3 turns, overtaxing high and then going to normal tax is better than a perpetual 10/20/30% in both the short and long term.

I agree taking death for order is also a bad decision, not what death scales should be used for. Death scales are really only viable for big bless or blood strategies and should always be combined with luck.

Re: Income and population mechanics
 

Alright. Assume no growth and O3P3 (But for MA man thats pretty sub-optimal since all your crones are old and without growth will be seriously hurting) Tax at 120. You still end up with 1073 more gold by turn 22 with gold hitting parity at turn 45. As I said before, since all the math is multiplicative, an extra multiplier like production scales increases the effectiveness as well.

And yes, I would agree that overtaxing even higher while holding your intial army back is even better, but that doesn't change the fact that perpetual overtaxing is also effective.

Answer this question with actual numbers. Why is temporary overtaxing at 200% an effective strategy but temporary taxing at 200% followed by long term overtaxing at 120% not an effective strategy? Obviously, it not as effective if you have to use 10 x 10 GP units plus a 40 GP commander to do it. But if you can do it with a 20 GP unit the math works out pretty well it its favor. You keep saying that its not effective, but I haven't seen any actual numbers illustrating why its not.

It seems like the real downside is not the amount of gold you generate, but rather the micromanagement that the strategy entails.

Re: Income and population mechanics
 

Note that the discussion, from my side, has always been that overtaxing like this is a bad use of Growth 3.

I have not disputed the fact that you can get an extra 1000-1500gp doing it, I actually stated that before you did, but the biggest cost in doing so is the 120 pretender points you have wasted. There are just plain better ways to spend those points if your not going to take advantage of the exponential nature of the Growth scale.

Re: Income and population mechanics
 

My point about overtaxing has nothing to do with growth vs. no growth. Its about gold now vs. gold later. The growth is mainly there for MA Man because your crones need it. As I said the math is similar without the growth and just O3P3 scales. Because of the mechanics if you have fewer positive multipliers the value of overtaxing is less. But as long as you have those multipliers the amount of gold you can get early is very significant, leading to a significant force advantage early on. Basically as long as you have fairly positive scales you should overtax if possible (i.e. have a cheap unit with a high patrol value), if you have neutral scales the question is more difficult. With negative scales the calculation starts to tip back in favor of normal tax rates.

If you want another good look at this check out Executor's recent guide for Bogarus. Basically the same idea but it uses Simargls for the patrolling.

Re: Income and population mechanics
 

And this is why we are never going to agree, you believe that the opportunity cost of this unit, which can easily be raised in a captured province, is lower than the opportunity cost of a mage.

Every forester you hire is a mage you aren't hiring if you had played efficiently.

And I would say it's about mages now vs. mages later. The difference is that gold doesn't win games, mages and research do.

The value of taxing high early for the first couple of turns isn't that it gives you extra gold; It's that you can convert that gold quickly into an early second castle with lab, and recruit 2 mages a turn.

Re: Income and population mechanics
 

I agree. Mages now vs. mages later are much better. However, what you're saying is that you have to give up mage recruitment in order to recruit a few foresters. I'm saying that isn't the case. One, you don't have to give up mage recruitment and two you end up with more mages very quickly.

First, you probably don't have to give up mage recruitment, one of several things could occur:

1. You have a fortress up but have not had a chance to build a lab yet.

2. You have some gold left over and can't afford to recruit another mage.

3. You have a fortress up that you don't intend to put a lab in at least for a few turns.

Two, you end up with more mages, faster. Just 4 turns of overtaxing at 120 can net you +300 gold. Which = 2 additional mothers of Avalon. So even if you had to give up one turn of mage recruitment to get the forester, you end up being able to afford 2 additional mages within 4 turns.

Re: Income and population mechanics
 

Do you think I don't understand this? I'm not just hoarding gold and sitting on the piles laughing maniacally. Overtaxing high early helps you do this, as does overtaxing high continuously. Gold now vs. gold later by default means you'll end up with more mages now vs. later. With more gold you get more fortresses and labs, and thus more mages.

Re: Income and population mechanics
 

None of these things should ever happen if your playing well.

Re: Income and population mechanics
 

Not exactly, a second early fortress and lab is a great start, a third early fortress and lab makes you a big fat target at exactly the time rush builds are looking for one.

Re: Income and population mechanics
 

Then don't build the third fortress until turn 20 or whenever to avoid looking like a target. It doesn't change the fact the more gold early = more fortresses and labs earlier and more mages earlier. Start over taxing on turn 15 after you've had a chance to crank out a forester instead of immediately. Adjust accordingly.

Are you really saying that you never, ever, ever end a turn with 50 gold left over after mage recruitment, troop recruitment, infrastructure development, with a fortress that hasn't produced a mage? I find that statement somewhat ridiculous. At some point in the first 20 turns you're going to have a chance to recruit a forester, and prior to that use the one you start with. I may not be the most min-max player ever, but I hardly think I'm coming out of nowhere with this.

I already pointed to one strategy guide written by a very good player (much better than myself) that's not to far off exactly this. Yes your using a summons rather than a recruit-able, but you're still using a mage turn + gems to get them.

The difference between recruiting a patrol unit for 1 mage turn and 1 mage is, actually, very far off from being the same thing.

I stand by my original conclusion, recruiting one extra forester and perpetually patrolling (20%-30%) in the capital is a close call, you could go either way; trying to do it everywhere is a bad idea.

I did make one mistake in that post, in forgetting that man got a forester for free, which makes it more viable. I still think it's a mistake with G3 though; by turn 50 your capital is worth about 660 a turn under the original scales if you don't overtax.

Note that turn 50 is usually about the point that your upkeep starts to get close to your income if your doing well and you have neutral scales.

Re: Income and population mechanics
 

I agree. Trying to do it everywhere is not viable. But I stand by the assertion that you probably can get a few more than one forester out, and if you have them you might as well overtax your high pop provinces to get the income boost.

As I said before MA Man is not quite as castle ready as LA Man but they're moving in that direction, and putting up a slightly higher number than the average nation is far from worthless. Especially in CBM 1.92 where your wardens and lord wardens become recruit anywhere. With large number of high strength stealthy troops + large numbers of stealthy nature mages + normal units with a castle defense bonus + relatively high defense cheap castles you can exert a lot of control over the landscape. And as long as you're putting a few extra castles up, you might as well churn out a forester or two.

The G3 point is somewhat irrelevant to whether you overtax or not. Whether its O3G3 or O3P3 or just O3 the math doesn't work out to be wildly different. The more positive scales you have the better overtaxing is, but its hardly useless even with neutral scales. The G is not really about income its more about keeping your crones healthy, and without it they tend to get diseased WAY too often. I've lost far too many precious E2, W2, A4 or N5 crones to disease, and loosing one of them is a pretty huge blow.

As to what your capitals worth by turn 50, I'd rather sink my capital to get more gold now thus enabling me to grab someone else's capital. MA Man is not exactly a late game powerhouse (somewhat better with CBM but still not great), and unless you're expanding early your probably not going to fare well. I'd rather do everything I can to front load my income and expansion, thus overtaxing where you can.

Re: Income and population mechanics
 

Actually, I'd say the more fortresses you have the less you look like a rush target. In the early game, sieges are a pain in the neck.
It's even less of a concern for Man because a) everyone knows their fortresses are going to be even harder to break than average and b) everyone assumes they're gimps in the late game.

Which, y'know, they probably are at that.
But more often than not they do get to see it, because in my experience people try to snuff either easier or more ultimately dangerous targets first.
It doesn't help that Man's early game is actually pretty strong - longbows and knights with magic weapons shut down many different sacred rushes, air magic stops elephant rushes dead in their tracks, a handful of spies quickly make rushes that depend on cap-only units or mages unsustainable.

Re: Income and population mechanics
 

A mod I have been contributing to was released recently which introduces a new nation which has high admin castles, a cheap patrol-bonus unit, a cheap patrol-bonus commander and a cap-only mage who reduces unrest in the province by 4/turn. While I didn't set out to make that nation eminently over-taxable, things did end up evolving that way. For those folks who really want to test the viability of growth + over-taxation, MA Jomon would be a good place to try it.

I noticed elsewhere in the forum a bit of misinformation I want to disabuse people of: having a unrest reducing unit in a province does NOT reduce population as though you had been patrolling it. Again, that theory was posted elsewhere and I have personally tested it and found it wrong (test data will be provided upon request).

However, unrest reduction does behave a little differently than you might expect. Say you have a province that has an initial unrest of 50 (say from previous over-taxation or a bad event or something), is being taxed at 110% (which generates 2 unrest/turn), and contains a unit which reduces unrest by 4/turn. You'd expect to have the unrest there be reduced by 2 a turn (plus any unrest reduction you get from having friendly dominion) and you would be right. However, say that same province has 0 initial unrest, 110% tax and that same unit stationed there. You'd expect to have 0 unrest each turn (since it's being increased by 2 and decreased by 4) but instead you'll have 2 unrest at the start of each turn. That's because the unrest reduction of your unit happens before the unrest increase of your over-taxation. In fact, it seems to work like this:
1) lower unrest from abilities
2) collect income
3) raise unrest from taxation
?) I'm not sure where in all this lowering unrest from patrolling goes...

So, say you have a province with 100 of these unrest reducing units and you are running 200% taxation. What that means is that you will be getting money from that province at 200% each turn (as though you had zero unrest) but the province will have 20 unrest. That will reduce the number of resources that province has to recruit units but it will NOT reduce the income that province is generating. In that situation you are effectively trading some of your recruitment capacity for extra money.

This presents a new taxation scenario for you number-crunchy folks to chew on. Oh and try the new mod out; I think you'll find it interesting.