Defensive Mana - Troops/Differences/Turn- Based Mana Calculations and it's Discovery

[Zack]

@Elioty33

For Changing Tides mana speed, it seems from my data that the “uneven” (first, third, fifth…) mana bars require 800mp (this indeed matches fast mana speed; FYI 1400mp for PvE bosses) but for the even charges (second, fourth, sixth…), it’s not actually 1000mp (like average) but again, like mana speeds with charges, it’s still 800mp with a -25% mana generation modifier (so with no manage generation bonus, it makes it actually 10.67 tiles to charge on offense).

Time for a surprise. [edit: nope]

Let’s verify the 800 for offense first on offense first, should be easy.
My Bagreg with 0% mana generation bonus gets mana from 8 tiles for 800 MP - and his fast Buddy Tudan is in the same position.
800 = 800 x 1.0

=> fast tide speed is charged with 800 MP on offense

Let’s check 799 MP:
My Bagreg has +12% +13% mana generation bonus from mana troops level 23 (+13%) and gets mana from 5 regular tiles and 2 tiles with +4%:
799 = 500 x 1.13 + 200 x (1.13 + 0.04)

=> fast tide speed is not charged from 799 MP on offense, just like regular fast speed

Now onwards to the average speed on offense, should be easy since I had already prepared setups for my attacking team for 1067 MP and 1066 to test this evening. [edit: bad idea and it was clearly too late at night right before bed time]

And then my Bagreg charges with 1067 MP as expected
and with 1066, of course, he is…also charged!? Why?

Okay, of course, the 800/(1 - 0.25) = 1066.7 gets rounded down, so I go for 1065 MP next and verify that Bagreg is indeed…charged again!?

Well, no idea what’s going on, but let’s just test 1064 MP then and see that Bagreg is finally…charged as well!?

Okay, time for the standard approach.
Let’s check 1000 MP: not charged
Then let’s check something in between like 1026 MP: Bagreg is charged
Ha! There we go! Next stop: 1017 MP and Bagreg is…not charged
Hmmm, might the “25” be a fixed amount of 25 MP maybe?
Then let’s see 1024 MP: Bagreg is not charged
Gotcha! And finally 1025 MP: Bagreg is drumroll charged

=> so on offense the average mana speed is actually 1025 MP [edit: nope, wrong, should have immediately compared to the -25% mana modifier approach and done some more testing. In my next post I check and the 1025 MP is clearly wrong and there is definitely a mana modifier, for which the -25% fit very well, so 800 MP with -25% is the go to for average tide speed]

What does that mean for Tide heroes on defense?
The fast tide speed should act the same as regular fast speed and 5* should charge with 934 MP.
The average tide speed of 5* could charge in 1197 MP, if 1025 is the basis. 4* would then charge with 1152 and 3* with 1108 MP. [edit: the average tide speed should charge with 934 MP as well but with a fixed -25% mana modifier always active]

I found a Phorcys 1-1 that I can set up in my alliance for tests. Well, not a perfect target with his minions that give +5% mana each turn - I guess I’ll have to prevent that with my Proteus when I want to test the average tide speed on defense. But first I’ll focus on magic heroes and styx, so @G_H_O_S_T please go ahead and test the mana from tiles for the 4* and then test the mana gain from 5* tide heroes.

Here’s the details: [edit: added one column for the MP with -25% mana modifier]

charged?	regular tiles	initial mana generation	tiles with +4%	tiles with +10%	tiles with +24%	mana points	MP with -25%
not full	10	0				1000	750
not full	9	13				1017	792
not full	5	12	4			1024	799
						0	0
full	7	13	2			1025	800
full	9	14				1026	801
full	10	5				1050	800
full	3	18			5	1064	864
full	4	5			5	1065	840
full	6	5	4			1066	816
full	4	13		5		1067	842

Here’s my Bagreg with +12% mana generation bonus from mana troops level 6 (+7%) and Zhabog (+5%) as he gains mana from 5 regular tiles and 4 tiles with +4%
1024 = 500 x 1.12 + 400 x (1.12 + 0.04) [edit: or
799 = 500 x (1.12 - 0.25) + 400 x (1.12 + 0.04 - 0.25) and updated the screenshots with the mana for the -25% mana modifier]

=> average tide speed is not charged yet with 1024 [MP or 799 MP] on offense

Then Bagreg with +13% mana generation bonus from mana troops level 23 (+13%) as he gains mana from 7 regular tiles and 2 tiles with +4%
1025 = 700 x 1.13 + 200 x (1.13 + 0.04) [edit: or
800 = 700 x (1.13 - 0.25) + 200 x (1.13 + 0.04 - 0.25)]

[edit: average tide speed is charged with 1025 MP or 800 MP on offense]

[CrazyChemist3891]

Well, no real surprise there.
What Elioty33 said (1067mp) is only valid for the 0%.
Actually I think, it is a nice confirmation of the Breakpoints I posted earlier.

[Elioty33]

@Zack

+12% mana generation bonus from mana troops level 23 (+13%)

As @CrazyChemist3891 said, you got it wrong because the max mana is still 800mp for even Changing Tides. There is just an hidden -25% mana generation effect which throws off your calculation as soon as you don’t run with +0% mana generation otherwise.
And if we do the correct math with your breakpoints, it actually matches my expectations:

@Zack

Here’s the details:

charged?	regular tiles	initial mana generation	tiles with +4%	tiles with +10%	tiles with +24%	mana points
not full	5	12	4			1024
						0
full	7	13	2			1025

5 x (100 - 25 + 12) + 4 x (100 - 25 + 12 + 4) = 799mp < 800 max mana: not charged as I expected
7 x (100 - 25 + 13) + 2 x (100 - 25 + 13 + 4) = 800mp >= 800 max mana: charged as I expected

It’s totally the same kind of hidden mana generation effect as for magic and styx mana speeds which I think you understood from your previous tests on them.

[Zack]

@Elioty33

As @CrazyChemist3891 said, you got it wrong because the max mana is still 800mp for even Changing Tides. There is just an hidden -25% mana generation effect which throws off your calculation as soon as you don’t run with +0% mana generation otherwise.
And if we do the correct math with your breakpoints, it actually matches my expectations:

@Elioty33

It’s totally the same kind of hidden mana generation effect as for magic and styx mana speeds which I think you understood from your previous tests on them.

@CrazyChemist3891

Well, no real surprise there.
What Elioty33 said (1067mp) is only valid for the 0%.
Actually I think, it is a nice confirmation of the Breakpoints I posted earlier.

Right, I messed up. Got the wrong idea in my head right before bed time and went along with it the next day.
But I like this blunder, because we can make the mana modifier case even stronger with it.

@Elioty33

5 x (100 - 25 + 12) + 4 x (100 - 25 + 12 + 4) = 799mp < 800 max mana: not charged as I expected
7 x (100 - 25 + 13) + 2 x (100 - 25 + 13 + 4) = 800mp >= 800 max mana: charged as I expected

The numbers work perfectly for the -25% mana modifier as well. So to remove all doubts all we need to do is show that the 1025 MP is wrong for average tide speed.

To test this I take my Bagreg, give him 25% mana generation bonus from styx troops level 27 (+20%) and from Zhabog (+5%) and get him 8 tiles.

• In case of the 1025 MP mana bar this would give 1000 MP (= 800 x 1.25) and Bagreg wouldn’t be charged yet
• in case of the -25% mana multiplier this would give 800 MP (= 800 x (1.25 - 0.25)) and Bagreg would be charged
  
  
  
  => Bagreg is charged from the 8 tiles with +25%
  => the 1025 MP for average tide speed is incorrect
  => the -25% mana modifier works perfectly again here

I’ll correct my post above accordingly and correct a typo

[Elioty33]

@Zack

Right, I messed up. Got the wrong idea in my head right before bed time and went along with it the next day.

Ah, that explains it. It didn’t seem like you to me, knew something was off

[G_H_O_S_T]

@Zack

Right! The magic1 and styx 1 should be simple to verify. Same with the Tides, except that I’ll probably have to rely on @G_H_O_S_T for this since my alliance lacks 5* tide heroes and finding a suitable target in the wild is very hard nowadays.

Luckily the great @Cheds has agreed to help me test the tide heroes so we’ll be able to test all of them from three four and five stars

[Zack]

@Elioty33

Ah, that explains it. It didn’t seem like you to me, knew something was off

Haha, yes, it just happens sometimes.
Well, my post can act as an example on how to calculate and not calculate the average tide speed

[CrazyChemist3891]

So we can conclude, that Changing Tides is understood and the ingame description of fast and average is misleading.
Thank you very much @Zack and @Elioty33 !

[Zack]

As a next step I would like to show that magic2 indeed has a mana multiplier.

For the test I’m using my Anton with 0% mana generation bonus, give him temporary 10% from Delilah, then charge mana1 with 5 tiles, then wait for Delilah’s +10% to run out, then get 7 tiles with 0% which will give Anton’s magic2 either 700 MP or 546 MP.

So without mana modifier he should be charged, but with a -22% mana multiplier he should be close to being charged as the 550 MP wouldn’t be full yet.
700 = 700 x 1.0 or
546 = 700 x (1.0 - 0.22)

=> Anton’s magic2 is not charged yet, but nearly charged
=> mana modifier is active for magic2, as expected, and it fits very well with -22%

Actually, I think it has to be -22% for magic 2, unless we have to consider decimals for the mana modifiers:

• With a mana modifier of -23% the charged Ray in my post 128 in this thread (10 MP from overflow + 6 tiles with 12%) wouldn’t be charged
  10 MP + 600 x (1.12 - 0.23) = 544 MP = not charged
  => cannot be -23%
• With a mana modifier of -21% non-charged Anton in this post would be charged from the 7 tiles at 0%
  700 x (1.0 - 0.21) = 553 MP = charged
  => cannot be -21%

@CrazyChemist3891

So we can conclude, that Changing Tides is understood and the ingame description of fast and average is misleading.

Definitely! The “fast” is indeed fast, but the “average” is just “kinda like average, but a bit slower”, but that wouldn’t sound very convincing

[u2371]

@Zack

Definitely! The “fast” is indeed fast, but the “average” is just “kinda like average, but a bit slower”, but that wouldn’t sound very convincing

I don’t understand. Didn’t you already test that “Bagreg is charged from the 8 tiles with +25%” mean the tide’s 2nd charge is at least as fast as average ?

@Zack

• In case of the 1025 MP mana bar this would give 1000 MP (= 800 x 1.25) and Bagreg wouldn’t be charged yet
• in case of the -25% mana multiplier this would give 800 MP (= 800 x (1.25 - 0.25)) and Bagreg would be charged

=> Bagreg is charged from the 8 tiles with +25%
=> the 1025 MP for average tide speed is incorrect
=> the -25% mana modifier works perfectly again here

[Zack]

@u2371

I don’t understand. Didn’t you already test that “Bagreg is charged from the 8 tiles with +25%” mean the tide’s 2nd charge is at least as fast as average ?

• With 0% mana generation bonus an average hero needs 1000 MP (= 10 tiles) on offense, while average tide needs 1067 MP (= 800 / (1.0 - 0.25)), i.e. 67 MP more
• If you want the average tide to charge with 1000 MP you need 5% mana generation, which is 5% more than what you need for average
• With 12% mana generation bonus an average hero needs 893 MP (= 1000 / 1.12 = 9 tiles), while average tide needs 920 MP (= 800 / 1.12 - 0.25), i.e. 27 MP more
• If you want the average tide to charge with 899 MP (= 9 tiles) you need 14% mana generation, which is 2% more than what you need for average
• With 25% mana generation bonus an average hero needs 800 MP (= 1000 / 1.25 = 8 tiles), while average tide needs 800 MP (= 800 / 1.25 - 0.25), i.e. the same
  With 43% mana generation bonus an average hero needs 700 MP (= 1000 / 1.43 = 7 tiles), while average tide needs 678 MP (= 800 / 1.43 - 0.25), i.e. 22 MP less, but you basically still need 7 tiles here
• If you want the average tide to charge with 696 MP (= 7 tiles) you need 40% mana generation, which is 3% less than what you need for average

=> due to the -25% mana modifier the average tide is usually slightly slower than average speed
=> at >25% mana generation bonus the average tide becomes slightly faster than average speed

Imho the average tide speed is slightly slower than average speed in most situations. You may take advantage of the >25% range if you manage to get +40% mana generation bonus, which I would only be able to do with styx3 from Thanatos or in a tower event.

[Elioty33]

@Zack

=> at >25% mana generation bonus the average tide becomes slightly faster than average speed

You mean slightly faster than fast speed?! The >25% mana generation bonus totally counter-act the hidden -25% mana generation modifier so you are back to roughly equivalent to fast speed (800mp).

[Zack]

@CrazyChemist3891

And one more test for Magic on offense:

0% Mana Bonus at all, 5 tiles hitting the enemy, 6th tile ghosted, how many more hitting tiles to get to the 2nd charge loaded?
Assumption is 6 tiles.

Repeat the former test with 2% Mana Bonus.
Now the assumption is 5 tiles!
Yes, I know, that that is only a total of 12!
But prove me wrong!

Will test this in the next days.
Is there a reason why that one tile should be ghosted? Or is it okay to just throw 7 tiles while charging magic1?

@Elioty33

@Zack

=> at >25% mana generation bonus the average tide becomes slightly faster than average speed

You mean slightly faster than fast speed?! The >25% mana generation bonus totally counter-act the hidden -25% mana generation modifier so you are back to roughly equivalent to fast speed (800mp).

I was comparing average tide speed to an average speed hero with the same mana generation bonus. For example, average tide speed with +30% mana generation bonus (762 MP) is slightly faster than average speed with +30% (770 MP), but fast speed with +30% (616 MP) is even faster.

[Zack]

One more test for styx heroes to confirm the +100% mana modifier for styx3.

Arges with +20% from magic troops level 29 (+20%) gets styx 1 charged with 5 tiles, then 3 tiles with +30% from troops (20%) and Delilah (+10%), then 2 tiles with +54% from troops (20%), Delilah (+10%) and Phoenicus (+24%)

styx1 = 600 = 500 x 1.2
styx2 = 690 = 600 + 90 = 300 x (1.2 + 0.1 + 1.00)
styx3 = 598 = 90 + 508 = 90 + 200 x (1.2 + 0.1 + 0.24 + 1.00)

=> Arges’ styx3 is not charged yet, as expected

Now, the point of this was to see, if Arges is charged or not. Because if he would have been charged, then the mana modifier of styx3 would have been >100%
styx2+styx3 = 1200 MP = 300 x (1.2 + 0.1 + 1.00) + 200 x (1.2 + 0.1 + 0.24 + 1.01)
=> but Arges wasn’t charged
=> styx3 mana modifier cannot be 101% (or more)

It is well known that styx heroes with 0% mana generation charge with 6 tiles for exactly styx1, with 3 more styx2 is exactly charged and with another 3 tiles styx3 is charged. For styx2 this wouldn’t be possible, if not for a mana modifier of exactly 100%. Also styx3 wouldn’t be charged then, if the modifier was lower than 100%

=> styx 2 mana modifier = 100%
=> styx 3 mana modifier = 100%

(edit: would be nice, if I didn’t mess up this time, because it’s late here )

[Elioty33]

@Zack

I was comparing average tide speed to an average speed hero with the same mana generation bonus. For example, average tide speed with +30% mana generation bonus (762 MP) is slightly faster than average speed with +30% (770 MP), but fast speed with +30% (616 MP) is even faster.

Ah OK, makes sense indeed. It’s me who gotta go to bed tonight haha.

@Zack

(edit: would be nice, if I didn’t mess up this time, because it’s late here )

Seems all good to me this time

@Zack

Will test this in the next days.
Is there a reason why that one tile should be ghosted? Or is it okay to just throw 7 tiles while charging magic1?

This is to show/verify that the overspilling MPs don’t have the -22% mana generation penalty.

[CrazyChemist3891]

Correct.
For Magic Charge 1 we calculate with 550MP,
while Charge 2 has also 550MP but hidden -22% Mana Generation Debuff. Resulting in more than 12 tiles at 0% Mana Bonus.

The overspill from Charge 1 should charge Charge 2 faster than expected without such Debuff.

[Zack]

Here you go:
2 Lucys, one with just the +2% mana generation bonus from the mana node, the other one with 0%.

The first test is with 4+1 tiles, then 2 tiles, then 6 tiles.

=> both Lucys’ magic2 is charged

Second test is with 5 tiles, then 2 tiles, then 5 tiles.

=> magic2 of the Lucy with 2% is charged, magic2 of the Lucy with 0% is not charged yet

[CrazyChemist3891]

Conclusion:

1. Magic 2 has a hidden -22% Mana Generation Debuff.
2. Overspill mana points of tiles, which contribute to Magic 1, do not get affected by the debuff and count fully for Magic 2.
   Thank you very much @Zack

[Elioty33]

Psst, you forgot the “as expected”, thank you

[u2371]

@Zack

• With 0% mana generation bonus an average hero needs 1000 MP (= 10 tiles) on offense, while average tide needs 1067 MP (= 800 / (1.0 - 0.25)), i.e. 67 MP more
• If you want the average tide to charge with 1000 MP you need 5% mana generation, which is 5% more than what you need for average
• With 12% mana generation bonus an average hero needs 893 MP (= 1000 / 1.12 = 9 tiles), while average tide needs 920 MP (= 800 / 1.12 - 0.25), i.e. 27 MP more
• If you want the average tide to charge with 899 MP (= 9 tiles) you need 14% mana generation, which is 2% more than what you need for average
• With 25% mana generation bonus an average hero needs 800 MP (= 1000 / 1.25 = 8 tiles), while average tide needs 800 MP (= 800 / 1.25 - 0.25), i.e. the same
  With 43% mana generation bonus an average hero needs 700 MP (= 1000 / 1.43 = 7 tiles), while average tide needs 678 MP (= 800 / 1.43 - 0.25), i.e. 22 MP less, but you basically still need 7 tiles here
• If you want the average tide to charge with 696 MP (= 7 tiles) you need 40% mana generation, which is 3% less than what you need for average

=> due to the -25% mana modifier the average tide is usually slightly slower than average speed
=> at >25% mana generation bonus the average tide becomes slightly faster than average speed

Imho the average tide speed is slightly slower than average speed in most situations. You may take advantage of the >25% range if you manage to get +40% mana generation bonus, which I would only be able to do with styx3 from Thanatos or in a tower event.

Oh, thank you. That is interesting. I really look like the average tide is actually fast tide but with -25% mana regen bonus.

Could you test using x4 small mana pot vs the average tide at 0% mana generation bonus and Ludwig’s 6th mana buff vs the average tide at 0% mana generation bonus ?

If the -25% mana regen bonus really exist, x4 small mana pot and Ludwig’s 6th mana buff should unable to charge the average tide at 0% mana generation bonus.