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

[Zack]

Update:
Found a fast wing 5* Tahir with no mana bonus in my watchtower to fight and also had set up two fast 4*, Heifeng Guai and Scarlett without any mana bonuses.

Expectations:

• 1 tile of mana per turn and 8 tiles in total, so all 3 charge in 8 turns
• my new hypothesis: 4* charge in 9 turns or under, 5* in 10 turns or under, so 4* charge in 9 turns, 5* in 10 turns
• my previous hypothesis: all fast heroes charge with 9.08 turns, so all 3 of them charge in 10 turns

defending team 1:

defending team 2:

results:
5* Tahir charged in 10 turns
4* Scarlett charged in 9 turns
4* Heifeng Guai charged in 9 turns

Screenshots:
Tahir charging

During turn 10 Tahir got the mana generation buff from Odin, but at this point it doesn’t matter anymore because Tahir wasn’t charged in 9 turns (and was nearly full so he would have charged in turn 10 anyway).

Scarlett charging

Heifeng Guai charging

=> For me this looks like sufficient evidence that there is more to the new hypothesis that 4* charge faster than 5* (I like that this presents an possible explanation for the outliers, but I’m not a fan of the necessary investigative work to find out the details)
=> it can be expected that other mana speeds are also effected, which also would require more investigation

Questions:
If it is not about 4* and 5* (and possibly 3* charge also differently), what alternative explanation is there for this different charging behaviour on defense for these fast heroes?

Are there other fast 4* and 5* heroes that are special and really should be investigated as well to see how fast they charge on defense?

[G_H_O_S_T]

All right Zack I’m doing super refined testing of one hero very close up. This test was against a right-wing Jove with no talent grid bonus, 5% bard bonus because an additional Jove on opposite wing they’re not counted as a duplicate hero and a 15% mana troop. Which gives us a 20% Mana gen Jove.

Showing Active Bard Bonus

Attack Team

Ability achieved on 8th turn with no tiles contacting

Results

Looks like 8 turns exactly give or take which with the 20% bonus would be a speed of 9.6 turns in which The additional 20% would have him fire in exactly eight turns.

[Damirius]

As I stated earlier, end-of-turn bonus in defense is 0.8(6) of the tile in offense.

With that in mind, here’s the theoretical table on how many turns it would take on defense to fully charge, assuming no mana bonuses except for class bonus (if the hero wasn’t hit at all):

So assuming no constume/family bonus:

Number of turns in defense = ceiling[number of tiles in offense / (0.86666666) / (1 + class bonus/100)].

This is the table, according to those calculations:

You can verify how this data correlates to the actual game.

With 0.75 (as claimed by @Elioty33 ), the table would look like:

Which, as we know, wrong, since fast heroes with no bonus charge in 10 turns, not 11.

@Zack

So when defending without any mana generation bonuses

• some fast heroes charge in 10 turns in 2019
• Fogg charges in 10 turns in 2022 and 2023
• Elkanen charges in 10 turns in 2022
• Woolerton charges in 9 turns in 2023
• Chao charges in 9 turns in 2023

An explanation could be that (fast) 4* get a small mana generation bonus on defense so that they charge in 9 turns instead of 10.

This could be explained with the fact that class bonus was not working in 2019, but was secretly fixed in 2020, and the staff first acknowledged the bug, but then denied that bug even existed.

Mana Class Talent and Costume Mana Bonus DO Work in Defense - Staff Response Post #90

With this news, I think mana bonus description from emblems and costumes is VERY irritating to say the least. It should imo explicitly say that this mana bonus is only for offense and NOT for defense. Please fix wording asap to prevent any further major confusion!! [IMG_0162] [IMG_0161] When clicking on a defending costumed hero, it is even plain wrong!! [image]

After they fixed the bug, I has confirmed independently, that class bonus in defense started working.

[Zack]

@Damirius

So assuming no constume/family bonus:

Number of turns in defense = ceiling[number of tiles in offense / (0.86666666) / (1 + class bonus/100)].

This is the table, according to those calculations:

You can verify how this data correlates to the actual game.

It looks to me like the defending heroes charge even faster than that. For example, a fast 5*, without any mana generation bonuses and without mana from any other source than turns, charged in 9.36 turns, but wasn’t charged yet in 9.07 turns.

@Damirius

This could be explained with the fact that class bonus was not working in 2019, but was secretly fixed in 2020, and the staff first acknowledged the bug, but then denied that bug even existed.

If it was working correctly from 2020 onwards, my investigation in 2022 and my current investigation should be based on correct charging behaviour for the defense.

Up to now I thought that fast heroes all charge at the same speed on defense. But in my recent tests from a few days ago a fast 4* Woolerton, a fast 4* Chao, a fast 4* Scarlett and a fast 4* Heifeng Guai, all of them without any mana generation bonuses and without mana from any other source than turns, charged in 9 turns. I’ve never seen any information indicating that fast 4* charge faster on defense than 5*, so I was very surprised when this possibility popped up.

I’m currently collecting more data slowly and so far I have some more new data for fast 5* on defense:

• In a friendly battle my Kadilen 4-80 with +15% mana generation from a mana troop level29, with only turns as mana source and no other mana effects present, charged in 9 turns, so she wasn’t charged in 8 turns: 8 x 1.15 = 9.2 (insufficient)
• In a friendly battle my costume Sartana 4-80 with +16% mana generation (11% from a magic troop level11, 5% from the bard Zarel), with only turns as mana source and no other mana effects present, charged in 9 turns, so she wasn’t full in 8 turns: 8 x 1.16 = 9.28 (insufficient)
• same mana situation in a friendly battle for my costume Magni 4-80+20 with +34% mana generation (20% from styx troop, 4% from class, 5% from costume, 5% from Phenexa) who charged in 7 turns: 7 x 1.34 = 9.38 (charged) (for confirmation of my 2022 results)
• @G_H_O_S_T has reported a fast 5* Jove with +20% mana generation bonus that charged with only 8 turns: 8 x 1.2 = 9.6 (charged)

I also now have on test for a 3* on raid defense:

• in a friendly battle my Whacker 3-50 with 0% mana generation bonus, with only turns as mana source and no other mana effects present, charged in 9 turns, just like the 4* heroes

Please feel free to check these situations.

[Elioty33]

Thank you for your experiments @G_H_O_S_T, @Damirius and more importantly @Zack, I finally understood how to apply one parameter that was bugging me and which totally explain your observations.

First off, let’s talk in absolute amount of mana and not in whacky tiles or % values which is good only for displaying a mana bar and because that’s how the game works (outside of the final UI computation).

So, a fast hero needs 800 mana points to charge (average 1000, ninja 490 per charge, etc).
On attack, a tile hit or miss gives 100 mana points. A tile reaching the end of the field (ghosted tile) gives 200 mana points.
On defense, the end of the turn gives, to PvP heroes, I insist, 100 mana points as well. BUT, there’s a maximum mana (the amount of mana required to charge) multiplier of 4% per rarity-level (multiplicative: base max mana * 1.04 * 1.04 * … (rarity minus 1 times, with a rounding down after each step)). So a 1* fast hero still needs 800mp, a 2* 832mp, a 3* 865mp, a 4* 899mp and a 5* 934mp. Which seems to match @Zack observations, thank you again for those.
For information, for monsters, the end of the turn gives 150mp (they use the same mana speeds as heroes with two extra one: one requiring 1600mp and another one 4000mp).

[u2371]

@Zack

If it is not about 4* and 5* (and possibly 3* charge also differently), what alternative explanation is there for this different charging behaviour on defense for these fast heroes?

I think no. It is very likely that 4* really charge faster than 5*. Also from what SG say that

@Zack

In the test, we are slightly reducing the buff for most legendary Heroes in the game. The higher stats the Hero has the larger the reduction is. Although the reduction is larger, a Hero with higher stats will remain more powerful than one with lower stats, but not as much as before. We will start with a slight reduction, keep monitoring what the effects are, and do changes until we have found a better balance that is more suitable for the game at this point of its life cycle.

It is very likely that SG make legendary heroes charge slightly slower on defense.

I am not sure what is actually is now. That say “most legendary Heroes” but I think they apply the effect to all legendary heroes. (Because if they don’t, it will be unfair.)

So, from your second question.

@Zack

Are there other fast 4* and 5* heroes that are special and really should be investigated as well to see how fast they charge on defense?

I think we might need to teat the effect of stat of heroes. As SG say before that “The higher stats the Hero has the larger the reduction is”, so 5* with higher stat might get more reduction than 5* with lower stat.

For 3* and 4*, it is also possible that they charge at the same rate. Because from what SG say is that they slightly reduce the buff for most legendary Heroes. It is possible that they just do it on only legendary heroes and leave 3* and 4* uneffected.

---

From that, it remind me about the damage calculation result. From what SG say, it is possible that 5* might get less buff on defense than 4* (It is possible that 5* do slightly less slash damage and receive slightly more damage than 4* at the same stat.). It will be pretty bad if that is true .

[Zack]

That is a very interesting and elegant defense mana formula. Let me check against my data to try and poke holes in it

fast 5* prediction: 9.34 turns with no other mana than from turns
fast 5* my data: 9.33 turns < X < 9.36 turns

(Today I got data on a Freya with +25% mana generation that got mana from 6 regular turns and 3 turns with a -64% mana generation debuff from Mist and was nearly charged: 9.33 = 6 x 1.25 + 3 x (1.25 - 0.64))

ninja 5* prediction: 5.72 turns (from 4.90 as the basis)
ninja 5* my data: 5.72 turns
=> I’m really impressed and love it

magic 1 5* prediction: 6.41 turns (from 5.50 as the basis)
magic 1 5* my data: 6.23 turns < X < 6.54 turns

styx 1 5* prediction: 6.99 turns (from 6.00 as the basis)
styx 1 5* my data: 6.97 turns < X < 7.02 turns

very fast 5* prediction: 7.60 turns (from 6.50 as the basis)
very fast 5* my data: 7.58 turns < X < 7.63 turns

average 5* prediction: 11.68 turns (from 10.00 turns as basis)
average 5* my data: 11.53 turns - hmm, this was against a Devana. Unfortunately I can’t check again as I can’t find the video for this anymore => I’ll deem this as a mistake in my notes and will do some more testing soon on this speed. Without this Devana data, this becomes:
average 5* my data: 11.52 turns < X < 11.77

slayer 5* prediction: 12.85 turns (from 11.00 as basis)
slayer 5* my data: 11.65 turns < X < 13.04 turns

slow 5* prediction: 14.01 turns (from 12.00 turns as basis)
slow 5* my data: 14.01 turns
=> very impressed again

very slow 5* prediction: 15.78 turns (from 13.50 turns as basis)
very slow 5* my data: 15.26 turns < X < 15.76 turns
The 15.76 come from an Alfrike 4-73 with a crit troop level 5 and 0% mana generation bonus in a raid battle dated 11.09.2022 - I still have the video. She charged from 15 regular turns and finally 1 turn with -24% mana generation from my Orla. 15.76 = 15 x 1.0 + 1 x (1 - 0.24). She only got hit from one special (Kingston) to reduce the attack of her neighbours to let my heroes survive a bit longer.
=> maybe the 13.50 is minimally incorrect and is actually 13.49? With 13.49 I derive 15.76 turns for the defense

Here are the screenshots for each turn:

Summary:
Excellent precision from this new formula for the 5* defense mana predictions!

Final test:
5* are at one end of the range, what about the other end?
Fast 1* heroes are now predicted to charge in just 8 turns.
I’ve put my Aife 1-1 to the test.
She got a crit troop, no mana generation bonuses and was only allowed to get mana from each turn.

Fast Aife charged in 8 turns, as predicted.
=> This new formula works GREAT!
=> Excellent work @Elioty33

[Zack]

@u2371

I think no. It is very likely that 4* really charge faster than 5*. Also from what SG say that

@Zack

In the test, we are slightly reducing the buff for most legendary Heroes in the game. The higher stats the Hero has the larger the reduction is. Although the reduction is larger, a Hero with higher stats will remain more powerful than one with lower stats, but not as much as before. We will start with a slight reduction, keep monitoring what the effects are, and do changes until we have found a better balance that is more suitable for the game at this point of its life cycle.

It is very likely that SG make legendary heroes charge slightly slower on defense.

Not just 4*, even Aife charges faster than 5*! She was always special!

My data now shows that 1* charge faster than 3* and 4*, which in turn charge faster than 5*.
Imho the data gives strong support to the new defense mana formula that @Elioty33 suggested here.

@u2371

I am not sure what is actually is now. That say “most legendary Heroes” but I think they apply the effect to all legendary heroes. (Because if they don’t, it will be unfair.)

The only buff that I found for the defending team was the +20% damage increase. Their statement fits with an adaptation of this +20% damage buff, but we don’t know how and when the buff is adapted.

@u2371

From that, it remind me about the damage calculation result. From what SG say, it is possible that 5* might get less buff on defense than 4* (It is possible that 5* do slightly less slash damage and receive slightly more damage than 4* at the same stat.). It will be pretty bad if that is true .

Yes, that would make it really tedious to investigate. But it looks very much like we now have a very precise formula for mana on defense \ /

We “just” need to verify the exact values.

[Elioty33]

@Zack

(Today I got data on a Freya with +25% mana generation that got mana from 6 regular turns and 3 turns with a -64% mana generation debuff from Mist and was nearly charged: 9.33 = 6 x 1.25 + 3 x (1.25 - 0.64))

THIIIIIIIS CLOSE to getting charged.

@Zack

average 5* my data: 11.53 turns - hmm, this was against a Devana. Unfortunately I can’t check again as I can’t find the video for this anymore => I’ll deem this as a mistake in my notes and will do some more testing soon on this speed.

Phew, dodged a bullet here.

@Zack

very slow 5* prediction: 15.78 turns (from 13.50 turns as basis)
very slow 5* my data: 15.26 turns < X < 15.76 turns
The 15.76 come from an Alfrike 4-73 with a crit troop level 5 and 0% mana generation bonus in a raid battle dated 11.09.2022 - I still have the video. She charged from 15 regular turns and finally 1 turn with -24% mana generation from my Orla. 15.76 = 15 x 1.0 + 1 x (1 - 0.24). She only got hit from one special (Kingston) to reduce the attack of her neighbours to let my heroes survive a bit longer.
=> maybe the 13.50 is minimally incorrect and is actually 13.49? With 13.49 I derive 15.76 turns for the defense

Doh, right in the kokoro this time. I kept looking around, at those heroes’ description, your screenshots and trying to tweak my formula but can’t figure out what’s wrong here. Also regarding your last comment, I can confirm that very slow is 1350mp on offence and applying my formula, it indeed gives 1578mp for a very slow 5* hero on defense. You are sure that no big combo happened during the fight with one tile at a high combo value hit her (which would give a minimal amount of mana)? At least you have the video recording so you can double check

@Zack

Fast Aife charged in 8 turns, as predicted.

ONE STAR heroes for the win

@Zack

=> This new formula works GREAT!
=> Excellent work @Elioty33

Thank you but you are also doing a tremendous data collection work that I wouldn’t have the patience to do and yet it helped me understand how that parameter (the per-rarity-level max mana multiplier for heroes on defense) works in the game
I guess you’re going to enjoy some more time collecting more data to polish your estimate and my formula.

[u2371]

@Zack

Not just 4*, even Aife charges faster than 5*! She was always special!

@Zack

The only buff that I found for the defending team was the +20% damage increase. Their statement fits with an adaptation of this +20% damage buff, but we don’t know how and when the buff is adapted.

I mean that I wonder if the effect(the damage buff and mana regen reduction) is depend on heroes stat or not. For example, 5* at 1-1 vs 5* at 80-20. 5* at 1-1 might get more damage buff and charge faster.

[Elioty33]

For the mana speed penalty, it’s solely depending on the hero rarity.

[u2371]

I know that is very likely to be but do we really test that ?

[G_H_O_S_T]

Damn @Zack You’ve been put in work I’ve been busy and I’m going to try to get caught up with all this and see if I can help refine anything. I’ve been testing and just haven’t been able to document and post with the Alliance quest and everything else going on. Amazing job though brother!

I am starting to spreadsheet though to keep track of:

Class
Hero
Speed
Troop Type/Level
TG Bonus or range for unknown
Tiles Contacted
Turn Special Achieved

Given what I’ve seen so far It seems pretty conclusive based on the research that you’ve done but I want to be able to make sure that if anything changes that I have at least a record of it.

I did just run a test head-to-head with a cMarj on left wing with lv 20 Mana troop vs Zekena on right wing with Lv 20 Ninja troop and she was faster but just slightly. She fired in nine and he would have fired in 10 but a tile made contact.

[G_H_O_S_T]

The man that definitely has a factor, It’s really hard to say just how big of a factor and at what point is it worth just running a ninja troop or even a crit for that matter? Where’s that line is what I want to know but we’ll figure it out

[Zack]

@Elioty33

THIIIIIIIS CLOSE to getting charged.

It actually doesn’t look that close in the game, here’s Freya in turn 9 with 9.33 mana:

I’ll show all 10 turns when I have the data on the 9.34 turns to finish the fast 5* investigation.

One possible situation for that is:
fast 5* hero with exactly +18% mana generation that gets mana from 7 regular turns, then gets hit by Mist for 2 turns with -64%: 9.34 = 7 x 1.18 + 2 x (1.18 - 0.64)

I won’t have time for more investigations during the weekend, so maybe someone else can check on this situation in the meantime?

@Elioty33

Phew, dodged a bullet here.

Haha! Well, it IS very easy to overlook something

@Elioty33

Doh, right in the kokoro this time. I kept looking around, at those heroes’ description, your screenshots and trying to tweak my formula but can’t figure out what’s wrong here. Also regarding your last comment, I can confirm that very slow is 1350mp on offence and applying my formula, it indeed gives 1578mp for a very slow 5* hero on defense. You are sure that no big combo happened during the fight with one tile at a high combo value hit her (which would give a minimal amount of mana)? At least you have the video recording so you can double check

Checked the video again and again. No tiles hit Alfrike. No other mana source to be found for her than mana from each turn. If the basis is not 13.49 than I have no other idea right now

@Elioty33

ONE STAR heroes for the win

Wasn’t there a thread about “don’t nerf Aife” quite a while ago? I hope that not too many people will put her in defense again now

@Elioty33

Thank you but you are also doing a tremendous data collection work that I wouldn’t have the patience to do and yet it helped me understand how that parameter (the per-rarity-level max mana multiplier for heroes on defense) works in the game

Thank you! Everybody’s teamwork has lead to this result

@Elioty33

I guess you’re going to enjoy some more time collecting more data to polish your estimate and my formula.

Will do for sure.
It may take me a while, though, because in my alliance I’m by far the most eager member to keep investigating, setting up teams and moving lots of tiles in ways that do not seem to help to win the battle, combined with madly throwing mana debuffs here and there.

Searching for certain heroes with certain mana generation percentages with suitable team members that allow the science team to survive long enough, all while trying to charge 1-2 mana debuff heroes in time for very special mana debuff combinations, all while trying to avoid pesky cascades, the life of a modern E&P mana generation hunter is filled with lots of adventure. Join now!

[Zack]

@u2371

I mean that I wonder if the effect(the damage buff and mana regen reduction) is depend on heroes stat or not. For example, 5* at 1-1 vs 5* at 80-20. 5* at 1-1 might get more damage buff and charge faster.

Since Aife 1-1 can survive long enough to charge, we can get 5* 1-1 to survive long enough as well.

Should be relatively easy to test.

[Zack]

@G_H_O_S_T

You’ve been put in work I’ve been busy and I’m going to try to get caught up with all this and see if I can help refine anything. I’ve been testing and just haven’t been able to document and post with the Alliance quest and everything else going on. Amazing job though brother!

Thank you! Only possible due to everybody’s teamwork

@G_H_O_S_T

I am starting to spreadsheet though to keep track of:

Class
Hero
Speed
Troop Type/Level
TG Bonus or range for unknown
Tiles Contacted
Turn Special Achieved

Yes, updating all of the tables on the required mana bonuses for the defense to accomodate for this new dependency on the hero rarity looks complicated. I’m not sure yet, how I’ll update my own tables.

@G_H_O_S_T

I did just run a test head-to-head with a cMarj on left wing with lv 20 Mana troop vs Zekena on right wing with Lv 20 Ninja troop and she was faster but just slightly. She fired in nine and he would have fired in 10 but a tile made contact.

With the +16% mana generation bonus she should charge in 9 turns, which she did.
=> fits well with the new formula
With +17% she should be able to charge in 8 turns.

[G_H_O_S_T]

Then I shall test a 16% Mana bonus for a fact hero. I just wish there was a way to test without needing friendly attacks. I mean I can run the stats and figure out what they have. I do want to start checking those brake points though of make it or break it.

@Zack and @Elioty33 I’m going to get to work on the tedious chart using the new 1.04 formula and see what the full range of values are and then we can really test.

So I have to start every calculation for defense at a one star and work my way up correct?

FAST FOR EXAMPLE

1* - 8 × 1.04 = 8.32
2* - 8.32 × 1.04 = 8.65 and so on for every speed.

My chart just got a lot bigger…lol

I will only do the calculations for three four and five star since that’s the only thing that’s relevant

9.358 = 9.35 or 9.36?

[G_H_O_S_T]

Well I got to start on it and I kept it out a thousandth decimal because I didn’t know whether it around up or not but I think we just leave it at the hundredth decimal, but I want to verify first before I I had to go back through and recalculate

[G_H_O_S_T]

So I went against a GP at 25%.

She was set to fire in 8 turns but I wanted to check on the .75 tile value.

I fed her seven tiles and she fired on turn 3 which was accurate.

Then I fed her eight tiles and she fired on turn two which is also accurate.

Just the first round of testing but I want to find one that’s right at the The point of make or break on a turn and see if it’s 100% accurate at .75 per tile. I’m sure it is though.