The Optimal Purchase Guide [Efficiency Guide Revamped] First, I'd like to give credit both to TERRA's original Building Efficiency Guide and to CraCkFaRrOkH's Efficiency guide 2.0. Both are outdated now with the release of the new lands, so I thought I'd pick up the ball and roll with it while adding some new information about efficiency. I would also like to give a massive thank you to chocolate23 for compiling the ❰ Buildings & Lands ❱ guide, which is incredibly comprehensive and provided me with all the numbers I needed to crunch. Foreword For those of you who don't know me, hi, I'm Koyuki. I used to play this game quite a while back before returning a few weeks ago, and since I first played I've gained 1) a healthy appreciation for maths, and 2) a working knowledge of Excel. One of the things I'm most concerned about when upgrading buildings is picking the most optimized path and getting the most stats out of my money as quickly as possible. I originally used the efficiency guides for this, but ran into a problem quite quickly: both guides fail to take upgrades into account. What do I mean by this? Well, let's use an example from the original efficiency guide. Just looking at the numbers for Highland buildings and upgrades shows us that buying highlands and placing a Lv1 building on them is them most efficient choice until land 12, after which upgrading all buildings to level 2 is more efficient. After buying land 13, it becomes more efficient to upgrade all buildings to level 3 before buying land 14. Here is where the problem lies. We now have our buildings all upgraded to level 3, correct? So it stands to reason that, after buying a building, we will upgrade it to level 3 to match all of the other buildings we own. The efficiency guides do not take this into account. They instead assume that all new buildings placed on land will be level 1, and thus distort our results and deviate from the most optimal path. All of the numbers provided by the efficiency guide after HL land 13 are thus inaccurate, and following them is suboptimal. So what I've endeavored to do is crunch all the numbers I could get my hands on and work out the most optimal path of buying land and upgrading. How did I do this? A spreadsheet. The SpreadsheetIf you aren't interested in understanding the math behind this, feel free to skip down to the Purchase Guide. The Spreadsheet. For ease of use (read: my sanity), I've used efficiency values from spy buildings rather than begin to dissect the differences between offensive, balanced, and defensive troop buildings. I've plugged in various sets of numbers into the spreadsheet just to verify that nothing is glaringly different between spy buildings and troop buildings, and was gratified to find that, while troop buildings have greater efficiency, the purchase guide is still accurate. Feel free to download the spreadsheet and fiddle around with it - any feedback would be much appreciated. While the older efficiency guides calculated efficiency for level 1 buildings and then for their subsequent upgrades, I went a little bit further. I've defined something I call an "optimal" upgrade level. This is an upgrade level that provides an exceptionally high gold spent per stats accumulated efficiency when compared to further levels. For example, the level 3 upgrade for Volaries has an efficiency of 2036.9, but the level 4 upgrade has an efficiency value of 506.5, nearly 4 times less. Meaning that, past land 13, the most optimal upgrade for Volaries is level 3 rather than level 1 or level 4. This same trend is evident in troop buildings too - Upgrades 1 to 3 of all Highland buildings provide much greater efficiency than Upgrade 4. There are similar trends in the Hoarfrost too. Upgrades 1 and 2 provide a much greater efficiency ratio when compared to Upgrades 3-10, for all buildings. For Osmon Rai and for the Abyss, however, the most significant difference is between Upgrade 1 and Upgrades 2-9. Meaning that the most optimal upgrade is level 1. After buying a new land and placing a level 1 building on it becomes less efficient than upgrading to level 2, then it becomes best to upgrade vertically - upgrading the previous building to the max possible level before buying a new land and placing a new building on it. Hence the "optimal" upgrades are as follows: Level 3 for Highlands (after land 13), Level 2 for Hoarfrost (after land 8), and Level 1 for both the Abyss and for Osmon Rai. To hammer out the most efficient purchase guide, I crunched the efficiency of buying a building and upgrading it to its optimal level versus buying a building and immediately upgrading it to the maximum level. For Highlands, after land 13, it is strictly better to leave all buildings at level 3, since upgrade level 4 is so inefficient. For Hoarfrost, Abyss, and Osmon Rai, however, there are defined changeover points - places where it becomes more efficient to begin to purchase upgrades vertically rather than to purchase land horizontally. For Hoarfrost, that changeover point is land 17; for Abyss, land 4; and for Osmon Rai, land 2... in theory. As Sethosaurus_ pointed out in the comments, fully upgrading Osmon Rai lands is impractical at the CS count implied by the changeover point. Since upgrades 5, 6, and 10 of Osmon Rai are noticeably less efficient, the changeover point splits into several - a changeover point at land 2 to from level 1 to level 4, another point at land 5 from level 4 to level 8, and another at land 10, from level 8 to level 9. But wait. What do all these changeover points actually mean? What they mean is that, before purchasing that specific land (land 17 HF, land 4 AB, lands 2/5/10 OR), it becomes more efficient to max out all your buildings and then continue to max out the subsequent buildings on each new land you purchase before buying another one. These so called optimal upgrade levels and changeover points are new data that I've introduced into the calculations, and are my major gripe with the original efficiency guides. They simply don't take enough variables into account, and I wanted to remedy that. So I did. And now, without further ado, here's the most optimal path for purchasing all lands, buildings, and their upgrades from the Highlands onwards, updated as far as Osmon Rai. Enjoy. The Purchase GuideI had to pick a color that wasn't white for Osmon Rai, so I went with yellow. Note: Hoarfrost land 15 is quite inefficient. However, the Abyss and Osmon Rai lands it unlocks are significantly more efficient, and thus is bumped a little higher up the priority order of the Purchase Guide. Highlands: Land 1 to Land 12 Highlands: Upgrade all buildings to level 2 Highlands: Land 13 Highlands: Upgrade all buildings to level 3 Highlands: Land 14 to Land 15 Hoarfrost: Land 1 to Land 8 Hoarfrost: Upgrade all buildings to level 2 Hoarfrost: Land 9 to Land 10 Highlands: Land 16 Hoarfrost: Land 11 Highlands: Land 17 to Land 19 Hoarfrost: Land 12 Highlands: Land 20 Hoarfrost: Land 13 Highlands: Land 21 to Land 22 Hoarfrost: Land 14 to Land 15 ***(see note above) Abyss: Land 1 to Land 2 Osmon Rai: Land 1 Osmon Rai: Upgrade all buildings to level 4 Abyss: Land 3 Osmon Rai: Land 2 Osmon Rai: Land 3 Abyss: Upgrade all buildings to level 10 Abyss: Land 4 Osmon Rai: Land 4 Osmon Rai: Upgrade all buildings to level 8 Osmon Rai: Land 5 Abyss: Land 5 to Land 6 Highlands: Land 23 Osmon Rai: Land 6 Abyss: Land 7 Osmon Rai: Land 7 Abyss: Land 8 Osmon Rai: Land 8 Abyss: Land 9 to Land 10 Osmon Rai: Land 9 Osmon Rai: Upgrade all buildings to level 9 Osmon Rai: Land 10 Abyss: Land 11 Osmon Rai: Land 11 Abyss: Land 12 Osmon Rai: Land 12 Highlands: Land 24 Osmon Rai: Land 13 Abyss: Land 13 Osmon Rai: Land 14 Abyss: Land 14 Osmon Rai: Land 15 Abyss: Land 15 Hoarfrost: Land 16 Abyss: Land 16 Osmon Rai: Land 16 Highlands: Land 25 Osmon Rai: Land 17 Abyss: Land 17 Osmon Rai: Land 18 Abyss: Land 18 Osmon Rai: Land 19 to Land 20 Abyss: Land 19 Osmon Rai: Land 21 to Land 25 Abyss: Land 20 to Land 21 Osmon Rai: Upgrade all buildings to level 10, Osmon Rai build complete Hoarfrost: Upgrade all buildings to level 10 Hoarfrost: Land 17 Abyss: Land 22 Hoarfrost: Land 18 Abyss: Land 23 Hoarfrost: Land 19 Abyss: Land 24 Hoarfrost: Land 20 Abyss: Land 25, Abyss build complete Hoarfrost: Land 21 to 22 Highlands: Upgrade all buildings to level 4, Highlands build complete Hoarfrost: Land 23 to 25, Hoarfrost build complete Changelog 20/05: Changed Osmon Rai buildings to be more practical when taking CS and total cost into consideration. Spreadsheet is not yet updated. Spreadsheet updated!