Sioux Exponential Unit Stats
Posted: 27 Apr 2019, 12:39
As a humble lowly 1st lieutenant I always wonder why top players do not use teepees for tactical purposes like map control and gold starving, these days on EP it is a case of drop 5 teepees near your town centre, push out in fortress age and then type 'GG' in the chat box.
Although I do appreciate the ESOC patch redesign of the teepee, I also appreciate that they have not Altered the RE version of What teepees were meant to to in general.
The following information was conducted on the latest ESOC patch, where No war chief benefiting cards were used, no team game cards sent from other allied civs and no upgrades researched from Native Trading Post minor civs (like lakota, cheyenne and comanche). I also appreciate that it may be impractical to clump 20 teepees together in a real match but treat the below as more of a thought experiment instead of a hard guide.
what's the idea? The idea is that sioux could also have a map control based agenda instead of a fast fortress nature and possibly win some matchups in a different way instead of right clicking the opponents TC.
Teepee HP boost on Axe Riders
Lets consider the colonial Axe rider with Stats of HP:250, SD: 20, HD: 38. If we built an Axe rider next to a teepee we observe that its HP increases to 267HP, only a modest 7% / 17HP increase. However when multiple teepees are used its effects are profound. {Note there is a card which increases teepee build limit from 10 to 20)
0 'teepee' HP = 250
1 'teepee' HP = 267
5 'teepee' HP = 350
10 'teepee' HP = 491
15 'teepee' HP = 689
20 'teepee' HP = 967
This is incredible, it shows that the teepee exponentially affects the stats of the unit by HP=base*(1.07^n) where n is the number of teepees in range of the selected unit. I believe many people didnt realise this about the sioux and thought that the HP gain was linear I.e HP = base * n * 1.1 ( which is not the case). As i write this i wonder whether this was intentional as it has a massive difference. Also the 7% health gain is questionable compared to 10% many people think it actually is.
Attack Card on Axe Riders
The fun really starts when you send the teepee attack aura card: Again considering colonial Axe Riders.
0 'teepee' SD: 20 HD: 35
1 'teepee' SD: 22 HD: 38
5 'teepee' SD: 32 HD: 56
10 'teepee' SD: 51 HD: 90
15 'teepee' SD: 83 HD: 146
20 'teepee' SD: 134 HD: 235
This exponential growth behaves the exactly the same way as the HP, however the growth percentage is 10%. Not linear 10% but exponential 10%! Total damage = base*(1.1^n).
At this point the colonial units max stats are:
Axe Rider : HP: 967 SD: 134 HD: 235
Bow Rider : HP: 851 SD: 67 RD: 134
Dog Soldier : HP: 2,128 SD: 201 HD: 188
Upgrade Cards, Techs, Unit Upgradess
After sending the following cards: Cav Attack, Cav HP and Euro Arsenal, its affect on the the units stats were observed.
Firstly the Cav HP card changed the Axe rider HP from 967HP to 1112HP. On the face of it this sounds normal. "If i send a 15% HP upgrade for my cav then my HP will increase by 15%" - the answer is TRUE.
This means the teepees affect and change the base stats of a unit before any other upgrades are applied to the increased stats.
so final HP is = BASE*upgrades where BASE = base*(1.07^n) as before. The example written out with symbols substituted is:
final HP, 1112 = {250*(1.07^20)}*1.15.
This increases to 1209HP with cav HP tech from arsenal. (Who says this tech is just for french cuirs?)
Final Colonial Max Stats
At this point the colonial units max stats with cards and arsenal tech: {without WC cards}
War chief: HP: 3385 SD: 166 HD: 66
Axe Rider : HP: 1209 SD: 154 HD: 270
Bow Rider : HP: 979 SD: 84 RD: 168
Dog Soldier : HP: 2,660 SD: 232 HD: 216
Imperial Dog Soldier Max Stats with Cav combat
Imp Dog Soldier: HP: 5,107 SD: 464 HD: 433
War dance and Siege Dance
ladies and gentleman we are not done yet! It appears that the War dance and siege dance apply a multiplier to the final stats (and not the base stats or the 'BASE' stats as defined earlier. this means that the maximum bonuses from War dance {25%} and Siege dance {~199%} are added after everything else is calculated,
'Final Form' Imperial Dog Soldier Max Stats with all cards/techs and Dances
(both siege and war are shown together for illustrative purposes)
Imp Dog Soldier: HP: 5,107 SD: 1,389 HD: 541
Therefore equation for attack damage is DAMAGE = {[base*(1.1^n)]*(Cards&Upgrades)}*WarOrSiege dances
.............. Oh dear god what have I done!
Update 1 25/8
*bump* lol. I was giving this a little thought and possibly I tried to push this idea as a colonial / late colonial strategy but have realised since that this has more use in the late fortress age. Reasons are: You have already sent your important cards, the wood needed to construct them is less significant, The attack/HP buffs multiply off of any upgrades (Elite Axe rider / Cav combat) and that wakinas and war hut units can build them instead of villagers.
To give good comparison to what affect these teepees have I have answered the question, How many teepees to I need to get Imperial stats on my units. (Note in EP& beta there is talk of reverting the HP buff back to 10%. With the attack policy card each teepee will increase the final unit stats by 10%.) I the number of teepees required is valid for the attack and will be valid for the HP if the 10% revert is implemented.
The results are true for all sioux units as this is about stat upgrades and not base stats.
Colonial Axe Rider
HP: 250
Attack: 35
Number of Teepees needed for Imp stats. 8
Elite Axe Rider (Base +25%)
HP: 312
Attack: 43
Number of Teepees needed for Imp stats. 5
Elite Axe Rider + Cav combat (Base + 40%)
HP: 350
Attack: 49
Number of Teepees needed for Imp stats. 4
Champion Axe Rider + Cav combat (Base + 65%)
HP: 412
Attack: 57
Number of Teepees needed for Imp stats. 2
What i am trying to suggest is that as the game goes on, this card with a small number of teepees can have large bonuses on units with upgrade cards already sent.
Although I do appreciate the ESOC patch redesign of the teepee, I also appreciate that they have not Altered the RE version of What teepees were meant to to in general.
The following information was conducted on the latest ESOC patch, where No war chief benefiting cards were used, no team game cards sent from other allied civs and no upgrades researched from Native Trading Post minor civs (like lakota, cheyenne and comanche). I also appreciate that it may be impractical to clump 20 teepees together in a real match but treat the below as more of a thought experiment instead of a hard guide.
what's the idea? The idea is that sioux could also have a map control based agenda instead of a fast fortress nature and possibly win some matchups in a different way instead of right clicking the opponents TC.
Teepee HP boost on Axe Riders
Lets consider the colonial Axe rider with Stats of HP:250, SD: 20, HD: 38. If we built an Axe rider next to a teepee we observe that its HP increases to 267HP, only a modest 7% / 17HP increase. However when multiple teepees are used its effects are profound. {Note there is a card which increases teepee build limit from 10 to 20)
0 'teepee' HP = 250
1 'teepee' HP = 267
5 'teepee' HP = 350
10 'teepee' HP = 491
15 'teepee' HP = 689
20 'teepee' HP = 967
This is incredible, it shows that the teepee exponentially affects the stats of the unit by HP=base*(1.07^n) where n is the number of teepees in range of the selected unit. I believe many people didnt realise this about the sioux and thought that the HP gain was linear I.e HP = base * n * 1.1 ( which is not the case). As i write this i wonder whether this was intentional as it has a massive difference. Also the 7% health gain is questionable compared to 10% many people think it actually is.
Attack Card on Axe Riders
The fun really starts when you send the teepee attack aura card: Again considering colonial Axe Riders.
0 'teepee' SD: 20 HD: 35
1 'teepee' SD: 22 HD: 38
5 'teepee' SD: 32 HD: 56
10 'teepee' SD: 51 HD: 90
15 'teepee' SD: 83 HD: 146
20 'teepee' SD: 134 HD: 235
This exponential growth behaves the exactly the same way as the HP, however the growth percentage is 10%. Not linear 10% but exponential 10%! Total damage = base*(1.1^n).
At this point the colonial units max stats are:
Axe Rider : HP: 967 SD: 134 HD: 235
Bow Rider : HP: 851 SD: 67 RD: 134
Dog Soldier : HP: 2,128 SD: 201 HD: 188
Upgrade Cards, Techs, Unit Upgradess
After sending the following cards: Cav Attack, Cav HP and Euro Arsenal, its affect on the the units stats were observed.
Firstly the Cav HP card changed the Axe rider HP from 967HP to 1112HP. On the face of it this sounds normal. "If i send a 15% HP upgrade for my cav then my HP will increase by 15%" - the answer is TRUE.
This means the teepees affect and change the base stats of a unit before any other upgrades are applied to the increased stats.
so final HP is = BASE*upgrades where BASE = base*(1.07^n) as before. The example written out with symbols substituted is:
final HP, 1112 = {250*(1.07^20)}*1.15.
This increases to 1209HP with cav HP tech from arsenal. (Who says this tech is just for french cuirs?)
Final Colonial Max Stats
At this point the colonial units max stats with cards and arsenal tech: {without WC cards}
War chief: HP: 3385 SD: 166 HD: 66
Axe Rider : HP: 1209 SD: 154 HD: 270
Bow Rider : HP: 979 SD: 84 RD: 168
Dog Soldier : HP: 2,660 SD: 232 HD: 216
Imperial Dog Soldier Max Stats with Cav combat
Imp Dog Soldier: HP: 5,107 SD: 464 HD: 433
War dance and Siege Dance
ladies and gentleman we are not done yet! It appears that the War dance and siege dance apply a multiplier to the final stats (and not the base stats or the 'BASE' stats as defined earlier. this means that the maximum bonuses from War dance {25%} and Siege dance {~199%} are added after everything else is calculated,
'Final Form' Imperial Dog Soldier Max Stats with all cards/techs and Dances
(both siege and war are shown together for illustrative purposes)
Imp Dog Soldier: HP: 5,107 SD: 1,389 HD: 541
Therefore equation for attack damage is DAMAGE = {[base*(1.1^n)]*(Cards&Upgrades)}*WarOrSiege dances
.............. Oh dear god what have I done!
Update 1 25/8
*bump* lol. I was giving this a little thought and possibly I tried to push this idea as a colonial / late colonial strategy but have realised since that this has more use in the late fortress age. Reasons are: You have already sent your important cards, the wood needed to construct them is less significant, The attack/HP buffs multiply off of any upgrades (Elite Axe rider / Cav combat) and that wakinas and war hut units can build them instead of villagers.
To give good comparison to what affect these teepees have I have answered the question, How many teepees to I need to get Imperial stats on my units. (Note in EP& beta there is talk of reverting the HP buff back to 10%. With the attack policy card each teepee will increase the final unit stats by 10%.) I the number of teepees required is valid for the attack and will be valid for the HP if the 10% revert is implemented.
The results are true for all sioux units as this is about stat upgrades and not base stats.
Colonial Axe Rider
HP: 250
Attack: 35
Number of Teepees needed for Imp stats. 8
Elite Axe Rider (Base +25%)
HP: 312
Attack: 43
Number of Teepees needed for Imp stats. 5
Elite Axe Rider + Cav combat (Base + 40%)
HP: 350
Attack: 49
Number of Teepees needed for Imp stats. 4
Champion Axe Rider + Cav combat (Base + 65%)
HP: 412
Attack: 57
Number of Teepees needed for Imp stats. 2
What i am trying to suggest is that as the game goes on, this card with a small number of teepees can have large bonuses on units with upgrade cards already sent.