I don’t understand your “optimum level” concept. I approached the math a little differently. I simply calculated the incremental cost per stat point for each individual transaction and then sorted the transactions in ascending order. Then I grouped transactions together with their more expensive (per stat point) prerequisites if they had any. I also grouped consecutive transactions together if they had a prerequisite relationship. I matched up with your purchase guide with a few exceptions up until the Abyss/Osmon Rai unlock. After that point, I couldn’t find a good correlation. All calculations have been done using the Balanced Troop building and it is assumed the results can be applied to all building types. For Lowlands and Highlands, the highest available building tier for each map was used for the calculations. Upgrades listed with multiple level increases should be done vertically (one Land at a time) not horizontally (one Level at a time). The numbers preceding each upgrade combination are the calculated cost in gold per stat point. For the sake of being thorough, I added Lowlands at the beginning: 12,669 – Lowlands: Land 2 to Land 25 (Level 1) 27,586 – Highlands: Land 1 to Land 2 (Level 1) 29,551 – Lowlands: Upgrade all buildings to Level 3 (Lands 2-25), Lowlands build complete Hoarfrost Land 1 + Level 1 (57,764) is a better value than Highlands Level 2 (71,971), so it would be more efficient to hold on Highlands Level 2 and Level 3 until after Highlands Land 15 (Hoarfrost unlock). 136,915 – Highlands: Land 3 to Land 15 (Level 1), Hoarfrost unlock 61,776 – Hoarfrost: Land 1 to Land 2 (Level 1) 71,971 – Highlands: Upgrade all buildings to Level 2 (Lands 1-15) 90,497 – Hoarfrost: Land 3 to Land 5 (Level 1) 111,930 – Highlands: Upgrade all buildings to Level 3 (Lands 1-15) Hoarfrost Level 2 (119,170) is a better value than Hoarfrost Land 6 + Level 1 (121,947), so it would be more efficient to upgrade to Level 2 after Hoarfrost Land 5 rather than Land 8: 119,170 – Hoarfrost: Upgrade all buildings to Level 2 (Lands 1-5) 178,333 – Hoarfrost: Land 6 to Land 11 (Level 2) Hoarfrost Land 11 + Levels 1-2 (246,120) is a better value than Highland Land 16 + Levels 1-3 (250,535). 282,518 – Hghlands: Land 16 to Land 18 (Levels 1-3) Hoarfrost Land 12 + Levels 1-2 (308,693) is a better value than Highland Land 19 + Levels 1-3 (314,502). 308,693 – Hoarfrost: Land 12 (Levels 1-2) 335,824 – Highlands: Land 19 to Land 20 (Levels 1-3) 371,266 – Hoarfrost: Land 13 (Levels 1-2) Highlands Level 4 (375,845) is a better value than both Highlands Land 21 + Levels 1-3 (399,790) and Abyss Land 1 + Level 1 (402,638), so it would be more efficient to upgrade to Level 4 after Hoarfrost Land 13 rather than wait until both Abyss and Osmon Rai are build complete (!?!?!): 375,845 – Highlands: Upgrade all buildings to Level 4 (Lands 1-20) 394,707 – Highlands: Land 21 (Levels 1-4) Abyss Land 1 + Level 1 (402,638) is a better value than Highlands Land 22 + Levels 1-4 (411,503), so it would be more efficient to hold on Highlands Land 22 until after Hoarfrost Land 15 (Abyss & Osmon Rai unlock). 485,984 – Hoarfrost: Land 14 to Land 15 (Levels 1-2), Abyss & Osmon Rai unlock 402,638 – Abyss: Land 1 (Level 1) Highlands Land 22 + Levels 1-4 (411,503) and Hoarfrost Level 3 (440,141) are both better values than Abyss Land 2 + Level 1 (473,691). 411,503 – Highlands: Land 22 (Levels 1-4) 440,141 – Hoarfrost: Upgrade all buildings to Level 3 (Lands 1-15) 473,691 – Abyss: Land 2 (Level 1) Highlands Land 23 + Levels 1-4 (478,687) is a better value than Osmon Rai Land 1 + Level 1 (533,753). 478,687 – Highlands: Land 23 (Levels 1-4) 533,753 – Osmon Rai: Land 1 (Level 1) Osmon Rai Levels 2-4 (770,959) is far less efficient than just about any other option at this point. Osmon Rai Level 2 (602,526) should happen after Abyss Land 3 + Level 1 (544,745) and Highlands Land 24 + Levels 1-4 (545,872). Osmon Rai Level 3 (777,960) should happen after Abyss Land 8 + Levels 1-6 (699,921). Osmon Rai Level 4 (824,896) should happen after Hoarfrost Land 18 + Levels 1-5 (801,887). 544,745 – Abyss: Land 3 (Level 1) 545,872 – Highlands: Land 24 (Levels 1-4) 602,526 – Osmon Rai: Level 2 (Land 1) 615,331 – Osmon Rai: Land 2 (Levels 1-2) Osmon Rai Land 3 + Levels 1-2 (681,259) should not happen until after Abyss Land 5 + Levels 1-6 (674,269). Abyss Levels 2-6 (650,290) should not happen until after Hoarfrost Land 16 + Levels 1-3 (620,531), Highlands Land 25 + Levels 1-4 (629,852), and Hoarfrost Level 4 (631,134). Abyss Levels 7-10 (835,783) should not happen until after Hoarfrost Levels 6-7 (832,164). 615,799 – Abyss: Land 4 (Level 1) Osmon Rai Land 4 + Levels 1-3 (785,904) should not happen until after Osmon Rai Level 3 (777,960). Osmon Rai Levels 5-8 (960,502) should not happen until after Hoarfrost Land 20 + Levels 1-10 (959,402). At this point everything is sufficiently scrambled in your guide, so I will list the remainder in the order that I came up with: 620,531 – Hoarfrost: Land 16 (Levels 1-3) 629,852 – Highlands: Land 25 (Levels 1-4), Highlands build complete 631,134 – Hoarfrost: Upgrade all buildings to Level 4 (Lands 1-16) 650,290 – Abyss: Upgrade all buildings to Level 6 (Lands 1-4) 674,269 – Abyss: Land 5 (Levels 1-6) 681,259 – Osmon Rai: Land 3 (Levels 1-2) 683,402 – Hoarfrost: Upgrade all buildings to Level 5 (Lands 1-16) 699,921 – Abyss: Land 6 (Levels 1-6) 723,709 – Hoarfrost: Land 17 (Levels 1-5) 743,895 – Abyss: Land 7 to Land 8 (Levels 1-6) 777,960 – Osmon Rai: Upgrade all buildings to Level 3 (Lands 1-3) 785,094 – Osmon Rai: Land 4 (Levels 1-3) 798,863 – Abyss: Land 9 (Levels 1-6) 801,887 – Hoarfrost: Land 18 (Levels 1-5) 824,896 – Osmon Rai: Upgrade all buildings to Level 4 (Lands 1-4) 832,164 – Hoarfrost: Upgrade all buildings to Level 7 (Lands 1-18) 835,783 – Abyss: Upgrade all buildings to Level 10 (Lands 1-9) 846,583 – Abyss: Land 10 (Levels 1-10) 867,331 – Osmon Rai: Land 5 (Levels 1-4) 868,346 – Abyss: Land 11 (Levels 1-10) 876,944 – Hoarfrost: Upgrade all buildings to Level 9 (Lands 1-18) 888,378 – Hoarfrost: Land 19 (Levels 1-9) 906,431 – Abyss: Land 12 to Land 13 (Levels 1-10) 939,980 – Hoarfrost: Upgrade all buildings to Level 10 959,402 – Hoarfrost: Land 20 (Levels 1-10) 960,502 – Osmon Rai: Upgrade all buildings to Level 8 (Lands 1-5) 960,839 – Abyss: Land 14 (Levels 1-10) 978,203 – Osmon Rai: Land 6 to Land 8 (Levels 1-8) 1,009,806 – Abyss: Land 15 to Land 16 (Levels 1-10) 1,034,641 – Osmon Rai: Land 9 to Land 10 (Levels 1-8) 1,042,450 – Abyss: Land 17 (Levels 1-10) 1,042,540 – Hoarfrost: Land 21 (Levels 1-10) 1,064,213 – Abyss: Land 18 (Levels 1-10) 1,078,951 – Osmon Rai: Land 11 (Levels 1-8) 1,085,976 – Abyss: Land 19 (Levels 1-10) 1,115,876 – Osmon Rai: Land 12 (Levels 1-8) 1,125,677 – Hoarfrost: Land 22 (Levels 1-10) 1,129,502 – Abyss: Land 20 (Levels 1-10) 1,152,801 – Osmon Rai: Land 13 (Levels 1-8) 1,167,100 – Osmon Rai: Upgrade all buildings to Level 9 1,173,028 – Abyss: Land 21 (Levels 1-10) 1,203,573 – Osmon Rai: Land 14 (Levels 1-9) 1,216,555 – Abyss: Land 22 (Levels 1-10) 1,229,598 – Hoarfrost: Land 23 (Levels 1-10) 1,248,803 – Osmon Rai: Land 15 (Levels 1-9) 1,281,844 – Abyss: Land 23 (Levels 1-10) 1,316,648 – Osmon Rai: Land 16 to Land 18 (Levels 1-9) 1,347,133 – Abyss: Land 24 (Levels 1-10) 1,361,878 – Osmon Rai: Land 19 to Land 20 (Levels 1-9) 1,375,088 – Hoarfrost: Land 24 (Levels 1-10) 1,399,570 – Osmon Rai: Land 21 to Land 23 (Levels 1-9) 1,412,422 – Abyss: Land 25 (Levels 1-10), Abyss build complete 1,425,200 – Osmon Rai: Land 24 to Land 25 (Levels 1-9) 1,443,579 – Osmon Rai: Upgrade all buildings to Level 10, Osmon Rai build complete 1,499,794 – Hoarfrost: Land 25 (Levels 1-10), Hoarfrost build complete
This might be why our results differ so much. I was using spy buildings to calculate efficiency for a hansel build. Balanced buildings give the most stats output per gold input, which changes the order of purchasing some of the lands. This is even more obvious on Hoarfrost. Elven Temple (HF Balanced) gives 50% more stats than Unkari Ice Tree (HF Spy) - 1.2mil mcs compared to 0.8mil mcs respectively, for the exact same price. This is why I think the purchase paths we've each reached differ so much - for spies, it is in no way efficient to purchase any of the HF upgrades until Abyss and OR are LC, simply because you get so little stats from them. This is definitely worth looking into. I've actually been communicating with a number of BC players in an attempt to work out which upgrades are better both in terms of stats and in terms of plunder, so this guide will probably be tweaked in the near future. I may also create additional segments of the spreadsheet for troop buildings, since now that I have all the formulas down, it's simply plugging in numbers. Thank you for bringing this up and making me aware of this info
You are quite right. There is a HUGE difference in the most efficient purchase order between balanced buildings and spy buildings. I redid my calculations using spy buildings and this is what I came up with: 97,778 - Lowlands: Lands 2-25 (Level 1) 113,214 - Highlands: Land 1 (Level 1) 113,700 - Lowlands: Upgrade all buildings to Level 3 (Lands 2-25), Lowlands build complete 263,274 - Highlands: Lands 2-15 (Level 1), Hoarfrost unlocked 288,707 - Hoarfrost: Lands 1-6 (Level 1) 368,824 - Highlands: Upgrade all buildings to Level 2 416,994 - Hoarfrost: Lands 7-8 (Level 1) 480,154 - Hoarfrost: Upgrade all buildings to Level 2 486,618 - Hoarfrost: Land 9 (Levels 1-2) 490,940 - Highlands: Upgrade all buildings to Level 3 532,238 - Hoarfrost: Land 10 (Levels 1-2) 566,657 - Highlands: Land 16 (Levels 1-3) 577,859 - Hoarfrost: Land 11 (Levels 1-2) 628,870 - Highlands: Land 17 (Levels 1-3) 821,168 - Hoarfrost: Lands 12-15 (Levels 1-2), Abyss and Osmon Rai unlocked 632,440 - Abyss: Land 1 (Level 1) 675,529 - Highlands: Lands 18-20 (Levels 1-3) 744,048 - Abyss: Land 2 (Level 1) 799,953 - Highlands: Lands 21-22 (Levels 1-3) 823,633 - Abyss: Upgrade all buildings to Level 6 (Lands 1-2) 827,751 - Abyss: Land 3 (Levels 1-6) 833,333 - Osmon Rai: Land 1 (Levels 1-2) 861,244 - Abyss: Lands 4-5 (Levels 1-6) 897,436 - Osmon Rai: Land 2 (Levels 1-2) 912,661 - Osmon Rai: Upgrade all buildings to Level 8 (Lands 1-2) 913,876 - Abyss: Land 6 (Levels 1-6) 919,275 - Osmon Rai: Lands 3-5 (Levels 1-8) 939,931 - Highlands: Land 23 (Levels 1-3) 943,258 - Osmon Rai: Land 6 (Levels 1-8) 944,228 - Abyss: Upgrade all buildings to Level 10 (Lands 1-6) 945,068 - Abyss: Land 7 (Levels 1-10) 950,453 - Osmon Rai: Land 7 (Levels 1-8) 957,874 - Abyss: Land 8 (Levels 1-10) 964,843 - Osmon Rai: Land 8 (Levels 1-8) 983,486 - Abyss: Lands 9-10 (Levels 1-10) 1,000,817 - Osmon Rai: Land 9 (Levels 1-8) 1,010,812 - Osmon Rai: Upgrade all buildings to Level 9 (Lands 1-9) 1,013,379 - Osmon Rai: Land 10 (Levels 1-9) 1,021,903 - Abyss: Land 11 (Levels 1-10) 1,034,395 - Osmon Rai: Land 11 (Levels 1-9) 1,047,515 - Abyss: Land 12 (Levels 1-10) 1,055,411 - Osmon Rai: Land 12 (Levels 1-9) 1,064,355 - Highlands: Land 24 (Levels 1-3) 1,076,427 - Osmon Rai: Land 13 (Levels 1-9) 1,085,932 - Abyss: Land 13 (Levels 1-10) 1,118,458 - Osmon Rai: Land 14 (Levels 1-9) 1,130,752 - Abyss: Land 14 (Levels 1-10) 1,160,490 - Osmon Rai: Land 15 (Levels 1-9) 1,175,573 - Abyss: Land 15 (Levels 1-10) 1,186,131 - Hoarfrost: Land 16 (Levels 1-2) 1,201,184 - Abyss: Land 16 (Levels 1-10) 1,202,521 - Osmon Rai: Land 16 (Levels 1-9) 1,219,886 - Highlands: Land 25 (Levels 1-3) 1,223,537 - Osmon Rai: Land 17 (Levels 1-9) 1,226,796 - Abyss: Land 17 (Levels 1-10) 1,244,553 - Osmon Rai: Land 18 (Levels 1-9) 1,252,407 - Abyss: Land 18 (Levels 1-10) 1,265,568 - Osmon Rai: Lands 19-20 (Levels 1-9) 1,278,019 - Abyss: Land 19 (Levels 1-10) 1,310,122 - Osmon Rai: Lands 21-25 (Levels 1-9) 1,354,854 - Abyss: Lands 20-21 (Levels 1-10) 1,393,090 - Osmon Rai: Upgrade all buildings to Level 10 (Lands 1-25), Osmon Rai build complete 1,400,909 - Hoarfrost: Upgrade all buildings to Level 10 (Lands 1-16) 1,406,723 - Hoarfrost: Land 17 (Levels 1-10) 1,431,689 - Abyss: Land 22 (Levels 1-10) 1,450,102 - Hoarfrost: Land 18 (Levels 1-10) 1,508,524 - Abyss: Land 23 (Levels 1-10) 1,518,269 - Hoarfrost: Land 19 (Levels 1-10) 1,585,358 - Abyss: Land 24 (Levels 1-10) 1,611,224 - Hoarfrost: Land 20 (Levels 1-10) 1,662,193 - Abyss: Land 25 (Levels 1-10), Abyss build complete 1,797,135 - Hoarfrost: Lands 21-22 (Levels 1-10) 1,974,063 - Highlands: Upgrade all buildings to Level 4 (Lands 1-25), Highlands build complete 2,220,597 - Hoarfrost: Lands 23-25 (Levels 1-10), Hoarfrost build complete
As you can see, I am matching you exactly from Abyss Land 7 on. However, prior to Abyss Land 7, there are some pretty major differences.
@Koyuki You have a great guide, it makes players aware of which build route to use the silver bars. There is just one statement that I don't totally agree: You said it's better to LC the Abyss and OR first before upgrading HF buildings. Efficiency-wise, this could be possible but the costs of land unlocks from Abyss15+ and OR15+ is just too colossal. You would need lots of gold out or bank on expensive allies or stockpile sb just to unlock and place a new building on Ab15+ or OR15+. Meanwhile, the upgrade cost of HF building from level2 to level10 is 900Bil. I wouldn't stockpile SBs from event just to wait for next Ab15+ unlock and OR15+ unlock. I believe, there are situations that a player needs to build towers on Ab and OR and needs SOME HF buildings to max upg to boost plunder to grow. Being LC on Ab and OR is situational, it depends on each player's goals or priorities.
That's very interesting, actually. I'm not sure why exactly we differ so much in Highlands - I'll run some tests on it when I have time. The Abyss level 6 and level 8 are actually explainable... I made a mistake. I didn't account for level 6 Abyss as an optimal level, so my guide overprioritizes OR and underprioritizes Abyss. I feel your method may be a more accurate version of the one I'm currently using. I'd be very grateful if you could compile a sample spreadsheet page and link it to me, so I'd be able to see what your numbers look like pre-crunched and post-crunched. I had some problems with the "efficiency" equation - hence the "optimal level" construct - and anything that improves on that is a step forward in my book. The feedback I've gotten so far has been incredible and has proven that this guide is in need of a semi-revamp for the earlier segments, and I'd be very interested in attempting to use your method while doing so.
Here is a link: http://tinyurl.com/OptimumBuildCalcs Parts of the order were derived by trial and error. I didn't feel like writing a lengthy subroutine to produce the optimum order automatically There are some interesting implications to consider. Spy buildings are slightly more efficient in Osmon Rai than balanced buildings. However, balanced buildings are way more efficient than spy buildings in Highlands and Hoarfrost. The "slight" advantage for spy buildings in Osmon Rai amounts to a considerable difference in total stats for that map - over 25m. I need to look into this further for all building types on each map to arrive at a more optimized build which uses multiple building types.
This is very very useful, thank you. Something interesting to note - I have it on good authority that the optimal plunder levels for Abyss are 6 and 10, and for Osmon Rai, 5 (very inefficient in terms of gold) 8 and 10. A lot of BC players got to where they are by leaving OR at level 8 as they bought up the lands, since upgrades 9 and 10 are so costly. Seems that people worked out an order very similar to the spreadsheet order simply through trial and error rather than relying on simple math ;D
So you are telling me it's fastest to get level 9 buildings on rai lands then buy all the lands up to 25 before putting buildings on them? Or am I reading this wrong?
Do you do private efficiency tutoring for people that are a decent way into building randomly, that have been around for years?