[Guide] Assessment of Seed Vault

[DeletedUser27525]

Introduction
The Seed Vault is a GB with 2 effects: supplies and "helping hands." It is also the only GB to date that has a chance of producing diamonds.

In this guide, we shall ignore the supplies production and only compare the effect of "helping hands" with wishing wells (or fountain of youths), since SV and WW give very similar resources. Intuitively, as "helping hands" relies on aiding, the GB is more powerful if the owner has more players to aid. This guide provides a quantitative assessment of SV with respect to WW. It does not take into account of other factors such as fps for leveling and goods for building.

Method
The "helping hands" probability is denoted as p. The number of aidable players per day is denoted as N, which cannot exceed

79 (neighbors excluding self)
+ 79 (guildmates excluding self)
+ 140 (friends)
= 298.​

(For people who attack all their neighbors, the maximum N is 219.)

We make 3 observations:

1. The equivalent number of WWs is Np by the law of large numbers (think long-term averaging).
2. The spatial efficiency of SV relative to WW is Np * (area of WW) / (area of SV) = 0.323 Np. (Roads are included.) Break-even occurs when this value is 1.
   
3. At every level there exists a minimum number of aidable players to reach break-even, i.e. Nmin = Ceiling( 1 / 0.323p ), where Ceiling() rounds a number to the smallest integer greater than (or equal to) it.

Values for p are taken from wikia.

Note: In the upcoming Soccer event, WW can be upgraded to Little Wishing Well, which gives the same resources but occupies only 6 tiles. The spatial efficiency relative to LWW is 0.215 Np. The number of aidable players at break-even becomes Ceiling( 1 / 0.215p ).

Results
1. Equivalent number of WWs
The figure below shows the number of WWs the SV is equivalent to depending on its level (x-axis) and the number of players aidable by the owner, chosen from 100 (small guild, few friends) to 298 (maximum possible).

At level 1, the SV is equivalent to 2-6 WWs (for 100-298 players). At level 10, the multiplier effect is amplified: SV is equivalent to 8 WWs with 298 aidable players, but still just slightly more than 2 WWs with 100 aidable players.

What this implies is that increasing the number of aidable players is much more effective than leveling. E.g., as we have seen above, the extra benefit of bringing SV to level 10 with 100 aidable players is negligible compared to increasing the number of aidable players to 298 but simply remaining at level 1 (3x increase in helping hands effect).

Formally, compare the case of increasing aidable players, (N+dN)p, with that of leveling, N(p+dp). Below level 11, dp is almost constant at 0.1%, which is about 0.1 / 2 = 5% relative to p. Therefore, as long as dN is bigger than 5% of N, increasing the number of aidable players will be more effective than leveling. This can be achieved, at least in principle, if the owner has less than 284 aidable players (i.e., >5% from maximum).




2. Spatial efficiency relative to WW
The relative spatial efficiency can be taken as a measure of whether the owner is better off having WWs for the same space instead. From our previous definition, break even occurs when this value is 1 (for LWW the value is 1.5), which means that the owner should stay above the horizontal line (solid for WW; dashed for LWW) in the following figure. Otherwise, the owner should not build SV at all.



3. Number of aidable players at break-even
The following figure shows the number of aidable players needed at each level to obtain a relative spatial efficiency of at least 1 for WW or 1.5 for LWW in the previous figure. It is advisable to have at least around 160 (when compared to WW) or 240 (when compared to LWW) aidable players before building SV.


Conclusions
To enjoy the most benefit of SV, you really need to aid a lot of players (at least around 160). If you're in a small guild with few friends you may not want to build it at all. One should also try to eliminate as much as possible any overlap between neighbors, guildmates, and friends. Increasing aidable players is much more effective than leveling unless you already have close to 298 aidable players.

 

[DeletedUser26965]

Not sure why you say 2-6 wishing wells for a level 1, it's 2% of 298 so the average over the long run converges on 6 so might as well just say 6, of course any given trial of 298 can result in 0 or 12 or whatever so in that sense it's like having 0 wishing wells that day or 12 another day or whatever.

No fp's though like WW so that's a big negative. I built it anyway since I aid a lot, I'll just leave it at level 1.

Of course WW's are mainly used for diamond farming on alt worlds so can't really compare on that basis 1% chance for diamonds of the 6 long term average plus having to aid, eesh, can't imagine what that comes out to lol.

 

[DeletedUser27525]

Not sure why you say 2-6 wishing wells for a level 1, it's 2% of 298 so the average over the long run converges on 6 so might as well just say 6, of course any given trial of 298 can result in 0 or 12 or whatever so in that sense it's like having 0 wishing wells that day or 12 another day or whatever.

Yes, I meant 2 WWs, if the owner has 100 players, up to 6 WWs, if the owner has 298.

Thanks for your input.

 

[DeletedUser26965]

Yes, I meant 2 WWs, if the owner has 100 players, up to 6 WWs, if the owner has 298.

Thanks for your input.

ah, my misread I see, unless you just changed that or something, bah, lol very good though, always enjoy data.

 

[DeletedUser27525]

ah, my misread I see, unless you just changed that or something, bah, lol very good though, always enjoy data.

Yeah I edited to clarify. Your comments are very helpful!

 

[Agent327]

Conclusions
To enjoy the most benefit of SV, you really need to aid a lot of players. If you're in a small guild with few friends you may not want to build it at all. One should also try to eliminate as much as possible any overlap between neighbors, guildmates, and friends. Increasing aidable players is much more effective than leveling.

I like the way you made this comparison and how you came to your conclusion. I never thought of it this way. I compared the Vault with the Dynamic Tower and focussed only on the goods it gives. For that reason I replaced my DT with the SV. Same size, so no hassle and anything else the SV gives besides goods is extra.

 

[DeletedUser27525]

I like the way you made this comparison and how you came to your conclusion. I never thought of it this way. I compared the Vault with the Dynamic Tower and focussed only on the goods it gives. For that reason I replaced my DT with the SV. Same size, so no hassle and anything else the SV gives besides goods is extra.

Comparing DT with SV is another interesting perspective. I focused on WW because it's very similar to SV and, most importantly, free. So one must have compelling reasons to justify the construction of SV (costs fps and goods) which prompted me to do this analysis.

 

[Emberguard]

I like the way you made this comparison and how you came to your conclusion. I never thought of it this way. I compared the Vault with the Dynamic Tower and focussed only on the goods it gives. For that reason I replaced my DT with the SV. Same size, so no hassle and anything else the SV gives besides goods is extra.

Hmm. Never thought of doing it that way, and it'd probably be more relative for later aged players. But given the amount of goods Dynamic Tower gives and a guild friend of mine reckoned they get several hundred refined goods a week at lvl 10, it does sound like the SV would be better after reaching refined goods age