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Kaelin -> RE: =AQ= Houses With Estates - Discussion (5/22/2009 9:36:49)
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I've collected some data from two different estates during this past war and decided to try to see if a noticable difference in performance emerged.
First, let's describe the estates:
Owner: Kaelin Alvein
Attack: 843
Resources used per attack: 1008
Tower Level: 12
Total Waves Sent: 24
Wins: 437
[Note: An extra half-wave was sent at the end of the war but is omitted from calculations. This omission was decided in advance to avoid confounding the impact of the number of guards sent, and it turns out the data would have had an insignificant impact on the data anyway.]
Owner: Never Gonna Give You Up
Attack: 223
Resources used per attack: 264
Tower Level: 9
Total Waves Sent: 84
Wins: 491
Method: I recorded wins, gold, and XP earned for each wave sent. Since XP rewards round to relatively small intervals (and XP is probably the most important thing to players here), I focus my analysis on said rewards. Since Captain Rhubarb has announced that rewards are granted according to a normal distribution, I assume the data for each estate fits a normal distribution. The ultimate measure of effectiveness for each estate in terms of XP is how much XP is earned per resource spent, so I produce a list of XP/resource for each estate. I then run a t-test (one-tail, unequal variance) to test whether Kaelin's estate seems to give better rewards than Never Gonna Give You Up's estate.
Statistical Information of Data:
For Kaelin Alvein
Average XP Earned Per Resource Used: 4.311
Standard Deviation of XP Earned Per Resource Used: 1.457
Number of Full Waves (n): 24
For Never Gonna Give You Up
Average XP Earned Per Resource Used: 4.095
Standard Deviation of XP Earned Per Resource Used: 1.147
Number of Full Waves (n): 84
P-value (t-test result): 0.254
Analysis: Kaelin seems to have a better average than Rick Astley (albeit a fairly weak one), so the difference in there, right? Well, no, not necessarily. Even if the reward system treats both estates equally, Kaelin would have beaten Rick by an even larger margin about 25.4% (0.254) of the time. For a "statistically significant" difference to arise, we instead need to get that number under 5% (0.05).
The problems with producing a stronger result are that our observed difference is fairly small, the variation in the data points is very large, and our sample sizes (especially for Kaelin's estate) are rather small. Even if our XP/resource numbers were to stay the same, I'd have to send hundreds of waves for each estate to have sufficient evidence of a difference. Considering that Rhubarb can change formulas at any time (which would render previous data worthless for future war participation), I elect to make do with the data I have.
As mentioned earlier, even if our observed difference is representative, it's not a particularly major difference. If we had expected that the number of house guards would affect the rewards won, we would be highly disappointed after taking into account the resources consumed for each wave of house guards; considering the huge difference in the number of house guards per estate (843 versus 223), if there is an impact, it seems to be negligible. If we are looking to see if there is a difference in effectiveness according to guard tower level, the effect remain unclear; the difference in the levels of the towers is relatively small (12 versus 9), so our data is insufficient to rule out that guard level has a significant effect on rewards.
Recommendations:
#1) If you want to get house guards, do it for the purpose of protecting your flow of resources and challenging other players, not for the purpose of enhancing the effect of sending your house guards to war. Using ten times as many guards to get ten times as many rewards doesn't help if you are consuming ten times as many resources to do it, and this sort of scenario seems to be the present reality.
#2) If you want to upgrade your guard tower, be advised that its impact on war performance is unknown. Certainly the guard tower is effective in protecting your resource producers, but the tower itself consumes more resources as it is upgraded. A level 3 tower carries no penalty and a level 7 tower eats up very little (-1 Food and -1 Energy). However, be adviced the penalties (and costs of upgrading) grow considerably at higher levels, and upgrading above level 9 will cost you dearly in gold, and upgrading above level 12 will cost you dearly in resources, probably more than any reasonable improvement you could hope to obtain.
As an extra note, Kaelin's estate has all of the Darkovia resource-gathering properties plus one fully-developed Storage building (and again, a L12 Guard Tower). She earned 104300 XP and 35730 Gold over the course of the war and was fairly diligent in keep invaders away. If you are considering building properties on an estate and what to know what sort of rewards you could reasonably expect to earn, these are your numbers. Keep in mind this entails considerable Token and gold investments up front, and unless you have your house swamped with guards, keeping your estate clear of invaders will also take a significant time investment (you will earn XP and gold for defeating invaders, although probably at a rate lower that your regular play style). Still, Estates do entail a particular amount of fun in your own right, but you should not look to them as an important source of XP and Gold; in fact, it may take dozens of wars just for Kaelin to break even on gold.
As another note, even though Kaelin earned a lot more in rewards, Rick had a lot more defeated enemies. Yikes!
My hope for this (limited) study is that helps players make informed purchases regarding some mysterious elements of estates. However, I also hope this information allows people to have a relatively-informed discussion on the direction that estates should take.
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