Saturday, February 26, 2011

Analysis of Defense Options by qwe4rty

I'd promised my tribe I'd write up an analysis of the different defensive options, and now that it's done, I felt like I should share it. This is a long post, and I encourage you to read each and every part of it. If you have constructive criticism, I'd love to hear it.

Each defensive village assumes a 20,000 population size available for troops. This is sufficient to show my intent.

Base build time:
Spear: 1:19 = 79 seconds
Sword: 1:56 = 116 seconds
HC: 6:14 = 374 seconds

a) 10k/10k spear/sword, lvl 3/3 - Standard
General Defense: 910,000
Cavalry Defense: 980,000
Time to build: 1,950,000 seconds = 32,500 minutes

b) 7k/7k/1k spear/sword/hc, lvl 3/3/3,-Hybrid 1 rams lvl 1
General Defense: 917000 --> 100.7% of a)
Cavalry Defense: 798,000 --> 81% of a)
Time to build: 1,365,000 seconds = 22,750 minutes
--------b.1) 7k/1k spear/hc, lvl 3/3
--------General Defense: 427,000
--------Cavalry Defense: 553,000

c) 7k/7k/1k lvl 3/2/2,-Hybrid 2 rams lvl 2
General Defense: 838,000 --> 92% of a)
Cavalry Defense: 758,000 --> 77% of a)
Time to build: 1,365,000 = 22,750 minutes
--------c.1) 7k/1k spear/hc, lvl 3,2
--------General Defense: 397,000
--------Cavalry Defense: 541,000

d) 8k/2k spear/HC, spear/HC
General Defense: 728,000 --> 80% of a), 79% of b), 86% of c)
Cavalry Defense: 728,000 --> 74% of a), 91% of b), 96% of c)
Time to build: 748,000 seconds = 12,466.7 minutes


First off, there are several interesting things of note when you look at the different defense options.

Comparison: a) and b)
Build b) shaves off about 10,000 minutes of build time, which is a hefty amount. What are the payoffs? Surprisingly, you actually gain a slight amount of General Defense. However, percentage wise, it is rather insignificant. The main pay off is you lose Cavalry Defense (b) is only 81% as effective as build a) in this regard). In addition, build b) is slightly more flexibly, as it employs a fair number of HC, gaining a little bit more mobility.

However, thought your defense villages will be able to supply these research levels with no problem, you will have to sacrifice a research level in your offense villages to be able to have this defensive arrangement. The only likely one would be rams, dropping you from lvl 2 rams to lvl 1

Comparision: c) to b), with respect to a)
If you're not one of the people who wants to have a weaker nuke just so that you can have full research levels in every village, build c) would be the research levels you take in your offensive villages. Upon inspection, you will notice the General Defense of c) is 92% of a) while the Cavalry Defense of c) is 77% of a).

You have still shaved off about 10,000 minutes of build time. It is slightly weaker then b), but provides you with a slightly stronger nuke.

Comparison: d) to everything else
Finally, we get to the build I've been trying to sell. First off, you'll notice that it shaves another 10,000 minutes off of a). It is almost twice as fast to build as b) and c), and approaches 3 times as fast to build as a).

Now looking at the relative strengths. First off, when you compare cavalry defense of the 8k/2k spear/hc, you'll notice it is almost as strong as any of the hybrids. However, what you lose from changing from a Hybrid to pure spear/hc is General Defense. The 8k/2k is 80% as effective as a straight up 10k/10k, and 79% as effective as the stronger of the two hybrids.

Quick Summary.
The hybrid loses out on Cavalry Defense vs the Standard defense while gaining increased build time. The spear/HC has a comparable Cavalry Defense to the Hybrid, but loses out on General Defense to the Standard and Hybrid (80% as effective as standard, and 79% as effective as Hybrid, a comparable loss in General Defense), all the while, shaving off even more time.

Final (and Selling) point
So far however, this post has only gone into the relative strengths of the ratios, and has not taken into consideration one other crucial advantage the spears/HC has over any of the other defense options: movement speed.

To fully understand this, I'm going to go into a bit of geometry. Take the scenario that a village is under attack and you need to draw support from nearby villages. The attack is incoming in X minutes, and so you can only draw support from villages that are less then or equal to X minutes away. The border of the area that fulfills this constraint is a circle (all points in a plane at a constant distance, called the radius, from a fixed point, called the center), with the center being the village under attack.

The time of the incoming attack will be directly proportional to the distance from the villages on the outermost edge of that "circle" of villages that can get support to the one being attacked. Time is therefore proportional to the radius.

The area of the circle corresponds to the number of all villages able to get support to the village under attack under the time constraints. The formula for the area of a circle is A=pi*r^2

What does this mean in terms of tribal wars? It means as the max distance from the village under attack to villages that are able to provide support (radius) increases, the total number of villages able to provide support exponentially increases.

In terms of tribal wars, the faster your defense can move, the more defense you can stack in a single village, minimizing losses. Time is therefore a limiting factor. We can eliminate a), the Standard Defense, because it fails this miserably. Both its time to build and time to move are abysmal.

The hybrid defense improves upon the time factor of the Standard defense, building 10,000 minutes faster, and employing a number of HC able to provide support to a village. However, it still contains 7,000 swords, and this becomes a problem. While it takes longer to build, it also simultaneously slows down the speed of your support. Depending upon the length of time you have until an attack hits, you may not be able to send the swords with the rest of your support, it would have to arrive after. This significantly diminishes the strength of your defense. You move from a General Defense of 917000 and a Cavalry Defense: 798,000 to a General Defense of 427,000 and a Cavalry Defense of 553,000. Not as impressive looking as before.

The spear/HC defense on the other hand is more likely to be able to get its full defense power as support to a village before an attack lands.

Very last (I promise) point/comparison
With all this being said, it seems beneficial to compare the Hybrid with Spear/HC one last time, taking into consideration the movement speed.

Remember that the only two things significantly different between these 2 builds were the following:
1) spear/HC builds about 10,000 minutes faster
2) spear/HC is only 80% as effective in General Defense as the Hybrid (Cavalry defense is highly comparable, and as stacking increases, this difference diminishes to 0 faster).

Looking at this, one notices one important factor. The only thing spear/HC really lacks is the General Defense contained by the Hybrid. Guess what, Heavy Cavalry provides General Defense! By employing a much larger number of Heavy Cavalry then the hybrid, the chances that you can draw support from another village even further away increases.

Remember, there are several layers of defense that can be sent. The hybrid can send a full D from villages close by (7k spears, 7k swords, 1k HC), a half D from villages slightly farther away (7k spears, 1k HC), and a fractional D (1k HC) from villages extremely far away). Spears/HC on the other hand can send a full D from villages close by (8k/2k), a full D from villages slightly farther away (8k/2k), and a half D from villages extremely far away (2k HC).

By employing a larger number of HC, you can draw MORE support from further differences, and since it is HC, it provides a greater proportion of General Defense, which is the only thing that the Spears/HC lacked that the Hybrid had. (The small fraction of Cavalry Defense that the Hybrid had over the Spears/HC is further minimized by the small amount of Cavalry D provided by the HC).

This specific difference between hybrid and spears/hc is then evened out, and spears/hc are still left with the advantage of building almost twice as fast as the hybrid.

Also, remember that you have the full defense capabilities of the spear/HC after 12,466 minutes of building. At this point in time, the Hybrid will have only slightly more then half of the defensive power. The Hybrid's defense doesn't surpass the defense offered by spears/HC until around 18,000 minutes (this is a guesstimate, I'm tired of writing).

So basically, when you're in a war heavy environment and are being attacked, you may not have the time to even build a full farms worth of D. Each individual hybrid village will have LOWER total defense then spears/HC simply because of the time taken to build. Spears/HC contains all of the advantages of time, and can make up any slight difference in defense power through manipulation of the additional time you have at your disposal to build troops and send them.


As a note, I've never used a hybrid before, and there are all types of variations. For this analysis, I had just taken the first hybrid build one of my tribemates had posted. However, my end conclusion still remains the same. The mathematical comparisons I had made between the spear/HC and the hybrid build could change depending on if you went for a more spear heavy hybrid build in an attempt to balance the defense more (which would be a better hybrid build in my eyes), yet the maneuverability of spears/HC still makes it superior in my eyes.

--Researched and written by qwe4rty

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