DefensePer2

A quick blast of numbers for the 2nd period (as of Dec 13, 2010)

Our arsenal lv 3 will add 45 * 5 / 50 = 4.5 to our protection value by the time the Barbs attack. This is a constant regardless of any other factor.

Remaining protection must come from donations. SInce we will require many donations, will a wall help? Or rather, will the help be cost effective compared to the cost of building?

Assumptions:

  • We will have 35 Active Citizens, producing an ACF of 31
  • The average house will be 123 CP's (Level 11)… meaning some will have lv12, and many will still be down around lv 8
  • » 123 of persoanl CP's adds just under 139 CP's to the town. I.E., I expect to see '139' under 'C: Housing' in the town hall come attack #2
  • Most Citizens will remain at lv3 clothing, but those that are expanding will contimue to. They are in the minoriy, so clothing average will be 24 CP's (just over lv4)
  • » THis is just over 27 CP's to the town
  • Setting the Garden CP's to the town at 5. So far, the garden isn't a big factor
  • Since the 1st attack, we build a Town Hall, Library and a Market (75 CP's)
  • We will also assume that 100% of donations to the guard occur after the wall is built up to its desired level (unrealistic, but the minimal donations made prior are not worth worrying about)

Known factors:

  • Adding a level to the wall adds 5 CP's to the City (will be factored in calculations)
  • A level 1 wall is what we have now - 0% bonus
  • Level 2 wall will add 20% to any donation… so we effectivley donate at 1.2 per donation at this level
  • L3 = 40% and L4 (the max) = 60%
  • Our Danger Value must be 20 or less if we want "whole town protection"
  • To build a new city building costs 2 x ACF… which basicly means each AC needs to make about 2 donations each (with an AC of 35, it's actually 1.77 donations per citizen - but some will not donate, so 2 is a good enough to be "known")

Equasions

First we need our Protection Value (or PV)

(1)
\begin{eqnarray} \lefteqn{ PV = Arsenal_Contribution +\frac{Donations + WallBonus}{ACF} } \end{eqnarray}

Since we already know our ACF and Arsenal contributions, this becomes:

(2)
\begin{eqnarray} \lefteqn{ PV = 4.5 +\frac{Donations + WallBonus}{31} } \end{eqnarray}

Next we have Danger Value. This is what we need to be below 20. The equasion is:

(3)
\begin{eqnarray} \lefteqn{ DV = \frac{CPtown + (CPcitzn / ACF)}{PV} } \end{eqnarray}

Since we know the CP of the town is 75 + any extra added by the wall, and we defined the CP of citizen possesions (after factoring the ACF), we can plug in the assumptions and get this:

(4)
\begin{eqnarray} \lefteqn{ DV = \frac{(75 + W) + (139 + 27 + 5)}{((D + (D*B)) / 31) + 4.5} } \end{eqnarray}

Where W = extra wall culture points (0 for lv1,… , 15 for lv 4) and D = Guard donations made by citizens and B = the bonus from the wall (0% for lv1, …, 60% for lv4)

Example with no wall

Lets start by looking at a wall level 1 (W = 0, B = 0%) and donations from Citezens = 170 (D = 170).

(5)
\begin{eqnarray} \lefteqn{ DV = \frac{(75 + 0) + (139 + 27 + 5)}{((170+ (170*0.0)) / 31) + 4.5} = \frac{75 + 171}{((170+ 0) / 31) + 4.5} = \frac{246}{5.4839 + 4.5} = \frac{246}{9.9839} = {24.6} } \end{eqnarray}

As we can see, 170 total donations is not enough to make our safety goal of DV = 20. In fact, we would need 242 total donations to just squeek under a DV 0f 20.

With 35 AC's, 242 / 35 = about 7 Guard donations per AC. Since no walls were built, there were no additional city donations needed by the citizens.

Another example with a Lv 4 Wall

This time, we've built a wall level 4 (W = 15, B = 60%) and donations from Citezens = 170 (D = 170).

(6)
\begin{eqnarray} \lefteqn{ DV = \frac{(75 + 15) + (139 + 27 + 5)}{((170+ (170*0.6)) / 31) + 4.5} = \frac{90 + 171}{((170 + 102) / 31) + 4.5} = \frac{261}{(272 / 31) + 4.5} = \frac{261}{8.7742 + 4.5} = \frac{261}{13.2742}= {19.7} } \end{eqnarray}

In this case, 170 total donations gets the job done (Actually, 166 would get us at 19.99). With 35 citizens, 166 / 35 = 4.75 donations each - a savings of 2.25 donations (or total, 242 - 166 = 76 doantions). However, we would have to build 3 city expantions to get the wall to level 4, at a cost of 2 donations x 3 = 6 donations per citizen. This would make the total true cost 10.75 donations (or if you want to get picky about the 1.77 donations for a city expantion per citizen, it could be an even 10 donations).

Here is a more exact breakout:

Wall Level Donatins to Guard Donations to City Total donations
1 6.92 0 6.92
2 5.95 2 7.95
3 5.29 4 9.29
4 4.74 6 10.74

So, the wall is of no help to us this period - its cost outweighs its benefit. But what if we include the benefit gained by already having the wall in place in time for the third barbarian attack?

Wall's value including all periods upto the 3rd attack

Assumptions

  • 40 Active Citizens (ACF = 35)
  • Average house level at 13 (CP = 178) for CP's to city of 203.5
  • Average clothing level at 5 (CP = 40) for CP's to city of 45.7
  • Gardens at CP 12
  • It is tough to imagine what else we might build in the city… so lets assume 125 INCLUDING the wall - I.E. for wall level 1 we have upgraded other buildings (or focused on other personal expantion for which this can compinsate for) and for wall level 4, we are still at 125 with less upgrades to other buildings (or personal expantion to compinsate).

Known factors

  • Same Arsenal protection at +4.5 as days in period 3 are the same as in period 2
  • Same everything, really

Lets skip the equasions and get right to the breakdown. Remember, there is no donation to the city this time as we assume all donations are done in Period 2:

Wall Level Donatins to Guard Total savings Donations to Wall in P2 *Grand Total Savings*
1 14.81 0 0 (Baseline)
2 12.39 2.42 2 1/2 a donation
3 10.59 4.22 4 1/4 a donation
4 9.28 5.53 6 - 1/2 a donation

So looking at line 2, we save 2.5 donations because we upgraded the wall to level 2 in the second period. But, since we paid 2 doantions each to upgrade this wall, we really ony net 1/2 a donation (1.5 resourses) over the course of the WHOLE REST OF THE GAME!! In fact, with wall level 4, it actually costs us.

CONCLUSION

The wall, for the sake of protection, appears to be "take it or leave it". We can build it for the sake of building it, or we can not. It appears that it just boild down to something to do with our donations.

PROS:

  • The walls will add 15 CP's that become self protected - it is like getting these CP's at a zero defense cost

CONS:

  • We could also get another 15 CP's from 1 market upgrade for the price of 3 wall upgrades - the remaining donations would easily cover the extra guard donations needed to defend that 15 CP plus have leftovers

So I (Fleet) do not see the wall as a question of "do we need it for protection" but rather a "what do we want to spend our money on". If we have lots of things we'd rather spend it on, then we can forget the wall. If we are done upgrading city buildings until after the 3rd attack and don't want to get our housing too high, then the wall is a nice neutral item to build up.

Suggestion: Build the wall to level 2 and then lets be done with it. It minimizes wasted donations in period 2 and gets them back in period 3 - it, in combination with other city upgrades, will help divert too much housing expantion so we meet our protection goals for the 2nd attack.

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