Mana mechanics with almost exact numbers

[Damirius]

I’m starting a new guide topic, so I can add put results of my research to the top post later and it’s easier to find.

I created a small program that can analyze screenshot from the game and measure almost exact amount of mana that heroes have.

This topic summarizes with (almost exact) numbers mana mechanics of different heroes that can add mana directly (like Misandra, Alberich or Fenrir).

I use team of heroes with different mana speed, paired with troops with no mana benefit.

Direct mana-giving hero specials

Misandra gives exactly 0.5 of tile per successful hit, up to 2 tiles (direct link to post: Mana mechanics with almost exact numbers - #2 by Damirius )

Fenrir gets 1.7 of a tile per each killed enemy and 0.85 of a tile per each minion at 8 special (direct link to post: Mana mechanics with almost exact numbers - #3 by Damirius )

Alberich gives exactly 0.8 tiles per turn (direct link to post: Mana mechanics with almost exact numbers - #4 by Damirius )

Margaret - each dodge gives flat 24% of mana regardless of hero’s mana speed, and this is affected by other mana bonuses like spells and class talents. (direct link to post: Mana mechanics with almost exact numbers - #6 by Damirius)

Sumitomo - first counterattack in a round gives 1 tile of mana, second gives 0.7 of a tile (direct link to post: Mana mechanics with almost exact numbers - #9 by Damirius )

PvE mana mechanics

Current theory is:

Each enemy receives constant bonus at the end of each turn. The bonus is equal to 150% of amount of mana the enemy would receive from 1 hit from combo 1 tile.
Mana from Combo 2 hits is 90% of mana from Combo 1 hit.
Different bosses have different numbers for amount of mana for Combo 1 hit.

PvP Mana mechanics

Current theory is:

combo 1 tile (1c1) is 66.66% of a tile in offense, and End of Turn (EOT) bonus is 1.30 of a 1c1. This gives (without any mana bonus):

Mana Speed	Predicted 1c1	Predicted EOT	Measured 1c1	Measured EOT
Very Fast	10.256%	13.333%	-	13.42%
Fast	8.33%	10.83%	8.2%	10.5%
Average	6.666%	8.666%	6.5%	8.5%
Slow	5.555%	7.222%	-	-
Very Slow	4.938%	6.420	-	-

Mana gained from hits depends on current number of combo. Combo 2 hit gives 90% of Combo 1 hit, and Combo 3 hit gives 90% of Combo 2 hit, and so on.

[Damirius]

For Misandra, here’s my team setup (all heroes without talents or mana troops):

On processed screenshots, mana meter is in range from 0 (empty) to 1000 (full).

Here’s the result after 1 hit:

Here’s the result after 2 hits:

Here’s the result after 4 hits:

According to these numbers, each Misandra hit gives exactly 0.5 of a tile.

[Damirius]

Fenrir’s team:

Fenrir has his special maxed.

Number after killing exactly 1 enemy with no minions:

Kill without minions gives 21.3% of mana. One tile for Fenrir is 12.5%. So it gives 1.7 tiles.

Number after killing exactly 1 minion:

So, each minion gives exactly half of mana for monster/hero, 0.85 of a tile.

[Damirius]

Alberich’s team:

After 1 turn of his mana regeneration ability:

So Alberich gives everyone exactly 0.8 tiles per turn.

[EC1]

Tks damiris!

Really helpful and informative!

[Damirius]

With Margaret, getting the numbers is very tricky, because it requires raiding to get the specials fired at my heroes at certain time, but I managed to get some screenshots to establish some facts:

Here’s the screenshot of single mana gain after dodge with no mana bonus (look at Margaret’s mana):

After that, I played with my regular mono team, which has mana troops and mana spirit link bonus:

Here are numbers after Evelyn and Margaret dodged (no spirit link bonus, just lvl 11 mana troops):

And here’s when Telluria dodged with lvl 17 mana troops and spirit link bonus (it expired after she dodged):

So it looks like Margaret’s dodge bonus is flat 24% (23.8 ~ 24.2) regardless of hero’s mana speed, but it is affected by mana bonuses from troops and skills.

[Damirius]

Now I want to measure mana mechanics in PvE (against map bosses). I took Season 1 7-4 and mono team, so bosses can survive more hits.

On the first turn I fired 3 tiles to the left boss, and then both bosses receive end-of-the-turn bonus:

Assuming end-of-the-turn bonus is the same for both bosses, this gives following numbers:
Each hit gives 10% of mana
End-of-turn bonus gives 15% of mana

On the second turn, I fired 3 tiles to the right boss, and then end-of-turn bonus applied:

So far the numbers are the same as predicted.

After that, I fired 3 tiles into left boss, and the mana was not full (presumably 90%), but then end-of-turn bonus kicked in, and left boss was fully charged (ignore the 1022 number, that’s just a measurement error).

After that, left boss was killed, and right one was charged and fired his special. Here’s the look after right boss received the end-of-turn bonus:

So, the conclusion is, for PvE (1-7-4), each hit from combo 1 gives 10% of mana, and end-of-turn bonus is 15% of mana.

Now to measure combo effects.

Here’s the screenshot (another battle) when on first turn, right boss was hit with Combo - 3 tiles (combo 1), and then 3 more tiles (combo 2), and then end-of-turn applied:

As measured before, each combo 1 hit is 10%, and end-of-turn is 15%. This means, that 3 tiles from Combo 2 give (72 - 30 - 15 = 27%), so every hit from Combo 2 gives 9% of mana.

Here’s another example of Combo 2:
Left boss was hit with 2 tiles from Combo 1 and 1 tile of Combo 2 + end of turn bonus (2 * 10 + 9 + 15 = 44%).
Right boss was hit with 2 tiles from Combo 1 and 4 tiles from Combo 2 + end of turn bonus (2 * 10 + 4 * 9 + 15 = 71%).

So, the current theory can correctly predict the numbers.

[Damirius]

Continuing with PvE, now against emblem challenge bosses:

On turn 1, left boss was not hit at all, only end-of-turn bonus. Right boss was hit with 4 tiles from combo 1, then 3 tiles from combo 2, and end of turn bonus.

So for left boss, EOT bonus is 11%.

On turn 2, left boss was hit with 3 tiles from combo 1 and EOT bonus, and right one wasn’t hit at all, only EOT bonus:

So for right boss, EOT bonus is 12.5%
Now we can deduce, that for left boss (Domitia), 3 tiles from combo 1 hits for (44.5-11-11 = 22.5), so each tile hits for 7.5%
And for right boss, 4 tiles from combo 1 and 3 tiles from combo 2 hit for (68.1 - 12.5 = 55.6%).
Assuming that each hit from combo 2 gives 10% less mana than hit from combo 1 (established in previous post), we can deduce that for right boss (Scarlett), each hit from combo 1 gives (55.6 / (4 + 3*0.9) = 8.3%

So, for Domitia boss, EOT bonus is 11% and 1 hit from combo 1 is 7.5%
For Scarlett boss, EOT is 12.5% and 1 hit from combo 1 is 8.3%

So Scarlett receives 10% more mana from each hit, and 10% more mana for EOT.

Here’s my current theory for PvE:

End of Turn mana bonus is 150% of a combo 1 tile.
Combo 2 tile gives 90% of a combo 1 tile.
Different bosses have different numbers for combo 1 tile.

[Damirius]

Now to measure Sumitomo. It’s hard to get Sumitomo attacked several times in a single round, so far I managed to get 2 attacks.

Here’s Sumitomo after 1 attack:

Here’s Sumitomo after 2 attacks on the same round:

So, first attack in a round gives 1 tile, second gives 0.7 of a tile.

[Damirius]

I’m back with some preliminary analysis of PvP (raids). This analysis is a little harder than usual because I fight in upper diamond arena, where most enemies are 4500+ with heavy emblems and troops, so mana bonus needs to be assumed.

So, today I fought this team:

Here’s assumed mana bonus for heroes in this team:

Dalilah: no class bonus, lvl 19 mana troop = 11%
Hel: no class bonus, no mana troops = 0%
Richard: no class bonus, lvl 22 mana troop = 11%
Marjana: assumed class bonus, no mana troop = 2%
Lianna: assumed class bonus, no mana troop = 2%

Long investigation

Turn 1

On the first turn, three yellow tiles were thrown at Marjana. All other heroes are untouched and receive only EOT mana bonus:

This allows calculating of EOT bonus for all heroes except Marjana:

Dalilah - 9.6 %
Hel - 8.8 %
Richard - 9.6%
Lianna - 10.5%

Turn 2

On the second turn, three purple tiles were thrown at Richard, no other heroes were touched.

This allows calculating EOT bonus for Marjana:
Marjana - 45.6% - 35.1% = 10.5% (equal to Lianna’s bonus)

This also allows calculating mana from 3 hits of combo 1 (3c1 for short) for both Richard and Marjana.

For Marjana - after first round she had 35.1%, EOT bonus is 10.5%, this leaves 3c1 = 35.1 - 10.5 = 24.6%, then 1c1 should hit for 8.2%

For Richard - he had 40.4% of mana after two EOT and 3c1. His EOT is 9.6%, so 3c1 = 40.4 - 2 * 9.6 = 21.2%, then 1c1 should hit for 7.1%

EOT for other heroes can be refined here as well:

Dalilah: 2 EOT = 19.3%, one is 9.6% (same as before)
Hel: 2 EOT = 16.7%, one is 8.4% (was 8.8% on previous screen)
Lianna: 2 EOT = 21.1%, one is 10.55% (almost same as before)

Turn 3
On third turn, three rightmost heroes were hit with 1 tile from Combo 1.

Let’s do some prediction (assuming Lianna has the same mana behavior as Marjana):
Dalilah should have only EOT bonus, so 9.6 * 3 = 28.8%
Hel should also have only EOT bonus, so 8.4 * 3 = 25.2%
Richard should have 40.4% from previous turn + EOT (9.6%) + 1c1 (7.1%) = 57.1%
Marjana should have 45.6% from previous turn + EOT (10.55%) + 1c1 (8.2%) = 64.35%
LIanna should have 21.1% from previous turn + EOT (10.55%) + 1c1 (assumed 8.2%) = 39.85%

As you can see, the prediction works well, but some numbers are off (Lianna, Marjana).

Few refinements are possible here:
Dalilah EOT bonus can be refined to 28.1 / 3 = 9.4%
Hel’s EOT bonus can be refined to 25.4 / 3 = 8.5%
Richard’s EOT bonus should be equal to Dalilah’s bonus, so this gives refined EOT of 9.4% and 1c1 as 7.2%
Lianna’s and Marjana’s assumption of 1c1 are different, varying from 8.1% to 8.8%. Probably measurement error.

Turn 4
On fourth turn, Richard was hit with 3 green tiles and died. Others were not affected.

Prediction:
Dalilah: 28.1 + EOT (9.4%) = 37,5%
Hel: 25.4 + EOT (8.5%) = 33.9%
Marjana: 64 + EOT (10.5%) = 74.5%
Lianna: 40.4 + EOT (10.5%) = 50.9%

And here is the screenshot:

Bingo! All the numbers are very close, few refinements possible:

Dalilah: 37.7% = 4EOT, so EOT is 9.42%
Hel: 34.2% = 4EOT, so EOT = 8.55%

Partial conclusion:
Observed End of Turn bonus and 1 hit from combo 1 (1c1) gains for heroes:

Dalilah: EOT 9.42%, 1c1 assumed 7.2%
Hel: EOT 8.55%, 1c1 unknown
Richard: EOT 9.42%, 1c1 = 7.2%
Marjana: EOT 10.55%, 1c1 = 8.2%
Lianna: EOT 10.55%, 1c1 assumed to be 8.2%

Subtracting mana bonus from troops:
Dalilah: EOT 8.5%, 1c1 = 6.5%, EOT/1c1 = 1.30
Hel: EOT 8.5%, 1c1 assumed 6.5%, EOT / 1c1 = 1.30
Richard: EOT 8.5%, 1c1 = 6.5%, EOT / 1c1 = 1.30
Marjana: EOT 10.33%, 1c1 = 8.04%, EOT / 1c1 = 1.28 (assumed)
Lianna: EOT 10.33%, 1c1 = 8.04%, EOT / 1c1 = 1.28 (assumed)

Cross-check
I have a table (in Russian) with turns to completely charge depending on mana bonus, assuming heroes were not hit:

Let’s cross check it:

Average heroes

So, I measured that Average heroes get 8.5% of mana every turn, and 6.5% of mana for each hit from combo 1.

My prediction for turns to fully charge Average hero without being hit:
No bonus: 12 turns (cross-checks)
7% bonus: 11 turns (cross-checks)
17% bonus: 11 turns (differs)

If EOT for average is refined to 8.6%, this cross-checks with the table completely.

So, current theory is for Average, EOT is 8.6% (0.86 of an offence tile) and 1c1 is 6.6% (0.66 of an offence tile)

Fast heroes

I measured fast heroes EOT to be 10.33%, and 8% of mana for each hit from combo 1.

My prediction for turns to fully charge Fast hero without being hit:
No bonus: 10 turns (cross-checks)
5% bonus: 10 turns (differs)
17% bonus: 9 turns (differs)

If EOT bonus is refined to 10.75%, this cross-checks with the table completely. I think my assumption that both Marjana and Lianna had 2% class mana bonus can be wrong.

Then current theory is for Fast heroes, EOT bonus is 10.75% (0.86 of an offence tile), and 1c1 is 8.27% (0.66 of an offence tile).

Current PvP mana theory
Each tile from combo 1 (1c1) is 2/3 of a tile in offense.
End of turn bonus is 1.30 of a 1c1 tile.

Further speculations
Let’s cross check the theory for Slow heroes.
My prediction for slow heroes is: 1c1 is 0.6666 of an offence tile = 5.56%, and EOT is 7.2215%
To fully charge Slow hero without being hit:
No bonus: 14 turns (table suggests 15 turns)
5% bonus: 14 turns (cross-checks)
9% bonus: 13 turns (cross-checks)
13% bonus: 13 turns (cross-checks)
17% bonus: 12 turns (cross-checks)

I think table is wrong about no-bonus turns (need to check again).

Very Fast
Theory predicts 10.256% for 1c1 and 13.333% for EOT

To fully charge Very Fast hero without being hit:
No bonus: 8 turns (cross-checks)
5% bonus: 8 turns (cross-checks)
7% bonus: 8 turns (cross-checks)
9% bonus: 7 turns (cross-checks)
13% bonus: 7 turns (cross-checks)
17% bonus: 7 turns (cross-checks)
The theory cross-checks fully.

Very Slow

Theory predicts 4.938% for 1c1 and 6.420% for EOT

To fully charge Very Slow hero without being hit:
No bonus: 16 turns (cross-checks)
5% bonus: 15 turns (differs)
7% bonus: 15 turns (cross-checks)
9% bonus: 15 turns (cross-checks)
13% bonus: 14 turns (cross-checks)
17% bonus: 14 turns (cross-checks)
19% bonus: 14 turns (differs)

So this needs to be checked again.

Current theory: in raids, combo 1 tile is 66.66% of a tile in offence, and EOT bonus is 1.30 of a combo 1 tile. This gives (without any mana bonus):

Mana Speed	Predicted 1c1	Predicted EOT	Measured 1c1	Measured EOT
Very Fast	10.256%	13.333%	-	-
Fast	8.33%	10.83%	8.2%	10.5%
Average	6.666%	8.666%	6.5%	8.5%
Slow	5.555%	7.222%	-	-
Very Slow	4.938%	6.420%	-	-

[Damirius]

Yet another quick battle with following team:

Assumed mana bonus for heroes:
Seshat: 13% from troops + 2% class bonus = 15%
Gravemaker: 11% from troops + 2% class bonus = 13%
Telluria: 13% from troops + 2% class bonus = 15%
Vela: 13% from troops + 2% class bonus = 15%
Joon: 13% from troops + 5% costume bonus + 2% class bonus = 20%

Long description of battle

Turn 1
Three tiles to Seshat. All other heroes received only EOT.

Prediction:
Seshat: (10.83%( EOT) + 3 * 8.33% (1c1)) * 1.15 = 41.193% (measured 39.5%, error 1.6%)
Gravemaker: 13.333% (EOT) * 1.13 = 15.06% (measured 14.9%, error 0.16%)
Telluria: 8.666% (EOT) * 1.15 = 9.967% (measured 9.6%, error 0.367%)
Vela: 10.83% (EOT) * 1.15 = 12.458% (measured 12.3%, error 0.158%)
Joon: 10.83% (EOT) * 1.20 = 13.000% (measured 12.3%, error 0.7%)

Reality:

It’s weird that Joon got the same amount of mana as Vela, because Joon should have consume bonus.

My hypothesis is that COSTUME MANA BONUS DOESN’T WORK ON DEFENSE - this needs some extra checking.

Turn 2 - big combo
Telluria was hit with 3 tiles from Combo 2, and 4 tiles from combo 4
Vela was hit with 2 tiles from Combo 2 and 1 tile from combo 4
Joon was hit with 1 tile from Combo 2 and 1 tile from combo 4
Seshat and Gravemaker wasn’t touched at all.

Prediction:
Seshat : 41.193 (previous) + 10.83 (EOT) * 1.15 = 53.6475% (measurement lost)
Gravemaker: 13.3333 * 2 * 1.13 = 30.133% (measured 28.9%, error 1.23%)

Others cannot be predicted yet, because mana decrease from combos is not known.

Here’s the actual result:

Let’s do some deduction, starting with Joon. He ends up with 40.4% of measured mana.
This mana is result of 2 EOT bonuses ( 12.3 * 2), 1 tile from combo 2 (1c2), and one tile from combo 4 (1c4)
1c2 + 1c4 = 40.4 - 12.3 * 2 = 15.8%. To deduct the troop/class bonus, let’s divide it by 1.15, the result is 13.740%
My previous prediction says, that 1c1 for Fast hero is 8.33%. So, if 1c2 and 1c4 would be the same as 1c1, the resulting mana would be 16.6666%. The measured mana is less, so as in PvE, mana from combo 2 is less than mana from combo 1.

In PvE, 1c2 = 1c1 * 0.9. Let’s guess that the same decay rate is applied to raids as well. Then for Fast hero, 1c2 would be 8.333 * 0.9 = 7.5%. Then 1c4 = 13.74% - 7.5% = 6.24%.
1c4 / 1c2 = 6.24% / 7.5% = 0.83 (this is very close to 0.81).

So, the theory is, that tile from combo 2 gives 0.9 of mana from a tile from combo 1. Tile from combo 3 gives 0.9 of mana from a tile from combo 2 etc.

Basically, 1cN = 1c1 * 0,9^(N-1).

Let’s predict Vela and Telluria based on this numbers:

Vela: (2 * 10.83% (EOT) + 2 * 8.33% * 0.9 (2c2) + 8.33% * 0.9^3 (1c4)) * .1.15 (assumed mana bonus) = 48.765%. Measured - 47.4%, error 1.36%
Telluria: (2 * 8.666% (EOT) + 3 * 6.666 % * 0.9 (3c2) + 4 * 6.666% * 0.9^3 (4c4)) * 1.15 (assumed mana bonus) = 62.983%. Measured - 61.4%, error 1.583%

Let’s count the same numbers, but only counting troops, not class bonus (so both Telluria and Vela would have 13% bonus, not 15% bonus):
Vela: predicted without class bonus: 47.067%, Measured 47.4%, error 0.33%
Telluria: predicted without class bonus: 61.88%, Measured 61.4%, error 0.48%

So, the data fits better if class bonus is not counted!

Current theory is then modified to: mana bonus for heroes depends only on mana troop level, ignoring mana bonus from class talents and costumes

This definitely needs to be investigated further.

Current theory is:

• Mana class talent and costume bonus don’t work in defense, only bonus from troops counts
• Each hit from combo 2 gives 10% less mana than hit from combo 1, as in PvE. This continues in geometrical progression, so each hit from combo 3 gives 10% less mana than hit from combo 2 and so on

That definitely needs some extended testing.

[touka]

amazing work!
thanks for sharing!

out of curiosity, have you tested the recently HOTMs that have element link for “small amount of mana”? the description is similar to Misandra’s spell effect but I wonder if the effect is the same.

I’ve tested pairing Frosth (lvl 1 spell) with a Richard (lvl 1):

• using 5% mana troop: 9 tiles + element link 1 turn → almost full. 9 tiles + element link 2 turns → full
• using 7% mana troop: 9 tiles + element link 1 turn → full

I don’t have a Misandra to test with and I’m curious if recent HOTMs can work as sort-of a replacement for Misandra for boosting a team of avg-speed heroes.

[jinbatsu]

Thank you very nice demonstration and detail mana on defense.
Just a little correction.

@Damirius

Vela: 13% from troops + 2% class bonus = 15%

Vela is druid, and it is at node 20.

@Damirius

Mana class talent and costume bonus don’t work in defense, only bonus from troops counts

Not sure if it is correct, but staff already demonstrate it, result is talent and costume bonus does have a little advantage.

Here is the thread.

@jinbatsu

For illustration purposes, please see this example below with a Quintus defense team:

1. Defense & attack teams used:

2. Same defense team order, 1 turn of passive mana gain (no tiles used, just skipping attack teams turn, attack team mirror of the defense team):

3. After 9 turns of passive mana gain (no tiles used, just skipping attack teams turns):

Source

But, let assume if it can be changed from that time, maybe they adjust hidden update, who know.

[ALX]

here correct numbers from Alberich without and with troops/class bonus.