King's Bounty Grand Slam Open

[pavned]

Following Lord Ludwig's Teana's Open tournament where KBAP untis were going 1 on 1, I decided to put a tournament where units would face each other base on a Leadership value instead of just 1 on 1. So here it is, the KB Grand Slam open where the leadership value for the whole tournament is 10 000.

But no like Lord Ludwig tournament, I'll need your help to determine the winners, cause with all the units involve it's not as easy going as a 1 vs 1 match-up.

So here is the draw (base on the US OPEN Male tennis tournament of 2009! :grin:) To help you I put the number of units going face to face, the total health of the stack, (the health of 1 unit) and the total damage dealt by the stack (damage of 1 unit). As for Lord_Ludwig tournament, seed are base on the leadership of a single unit.

Black Dragon (1) 4 units, 4000 Total HP (1000 HP for 1) and 480 total dam (120 dam for 1)
Bye

Decaying Zombie 250 units, 12000 HP (48), 1375 Dam (5,5)
Furious Goblin 250 units, 10500 HP (42), 1250 Dam (5)

Hunter 66 units, 7260 HP (110), 627 Dam (9,5)
Lake Fairy 1428 units, 11424 HP (8), 2142 Dam (1,5)

Bye
Black Knight (31) 66 units, 10 560 HP (160), 924 Dam (14)

Chosha (21) 45 units, 8550 HP (190), 1350 Dam (30)
Bye

Cave Spider 714 units, 9996 HP (14), 2142 Dam (3)
Catapult 83 units, 6649 HP (80), 705,5 Dam (8,5)

Ghost 125, units, 5000 HP (40), 750 Dam (6)
Pirate 400 units, 10000 HP (25), 1600 Dam (4)

Bye
Demon (14) 33 units, 7920 HP (240), 792 Dam (24)

Royal Thorn (12) 26 units, 9360 HP (360), 650 Dam (25)
Bye

Snake 333 units, 9990 HP (30), 1498,5 Dam (4,5)
Ancient Bear 125 units, 8750 HP (70), 1312,5 Dam (10,5)

Gorguana 83 units, 6640 HP (80), 664 Dam (8)
Undead Spider 769 units, 9997 HP (13), 1922,5 Dam (2,5)

Bye
Demonologist (22) 47 units, 7520 HP (160), 611 Dam (13)

Horseman (26) 55 units, 8250 HP (150), 880 Dam (16)
Bye

Fire Dragonfly 1000 units, 8000 HP (8), 2500 Dam (2,5)
Foreman 76, units, 9120 HP (120), 1026 Dam (13,5)

Bear 142 units, 8520 HP (60), 1207 Dam (8,5)
Marauder 333 units, 9990 HP (30), 1498,5 Dam (4,5)

Bye
Bone Dragon (8) 7 units, 5530 HP (790), 455 Dam (65)

The rest will come later, but for now I think we got some good matchs and thinking to do before setteling all the matches. How about that Famous MArauder vs Bear, will it end up like the 1 vs 1 match-up, the Bear win? Not sure! What about those Fire Dragonfly, they look mighty impressive! And they do fire damage!

[Lord Ludwig]

Glad to see I'm making proselytism! :-D

And now I will have a closer look at those match-ups...

[pavned]

I think the biggest difficulty will be to estimate the effect of Att and Def, cause a lot of small uinits won't be doing as much damages as their numbers show!

Didn't need you for that Lord_Ludwig, it's just fun, Paris (Rolan-Garros) is still so far!
;-)

[MaroonMaurader]

If the Archdemon meets the Bone Dragon or Emerald Dragon, he's going to absolutely stomp them because you happened to pick 10,000 leadership - he has 9600 leadership, they have 9100 and 9500 respectively. It's your tournament, but were I running it I would make an exception to the rules for those two fights - for those fights IF they should arise, and those fights only, I'd adjust the leadership to 20,800 and 30,400 respectively so there's an honest equal-leadership fight.

[Petwin]

Maybe you could play every match with both contenders having the same (minimal) amount of leadership.

So 16 Pirates vs. 5 Ghosts (400 leadership), 25 Green dragons vs 19 Black dragons (47.500 lead), 100 Pirates vs 1 Black Dragon (2.500 lead).

[KongMysen]

Maybe you could play every match with both contenders having the same (minimal) amount of leadership.

So 16 Pirates vs. 5 Ghosts (400 leadership), 25 Green dragons vs 19 Black dragons (47.500 lead), 100 Pirates vs 1 Black Dragon (2.500 lead).

You should be in the King's Bounty Gran Slam board with this constructive idea:) Obviously it's a much better way of making the draw fair..

[pavned]

Like your ideas, but the logic behind my choice is on the game experience. Meaning when you're playing you got a total amount of leadership and have choices to do. Even if you miss 20 points in leadership you just can't get that 1 additional unit.

The results of that tournament will declare the best single stack units you can have with a 10000 leadership. I'm just curious to see how those level 3-4 units cna faire against level 4-5 units.

[pavned]

Here are the results:

Black Dragon (1)
Bye

Decaying Zombie
Furious Goblin

Hunter
Lake Fairy

Bye
Black Knight (31)

Chosha (21)
Bye

Cave Spider
Catapult

Ghost 125
Pirate 400

Bye
Demon (14)

Royal Thorn (12)
Bye

Snake
Ancient Bear

Gorguana
Undead Spider

Bye
Demonologist (22)

Horseman (26)
Bye

Fire Dragonfly
Foreman

Bear
Marauder

Bye
Bone Dragon (7)

- For the Zombie vs Goblin, their stats are so alike that it's only a matter of which one got the most total health, in this case de Decaying Zombie.

- For the Lake Fairy vs Hunter, I had to do some calaculation and here is the total dmage for the 1sr blow each unit is dealing with the hunter double attack and the Attk and Def stats accounted for:
Hunter: 2257,2 Total damage for a total of 282 Fairies killed
Fairy: 1146 total damage for a total of 10 hunters killed

The fact that the fairy got no-retaliation enables it to win this match. But can be different if the hunter got other Double damage attack, I consider it a one time action.

- The Catapult range attack and reloaded sepcial fire/burning attack makes it enable to overcome the deficit in the starting potential damage dealing.

- The Ghost life sucking and 50% less damage from physical attack makes it a tougher opponent for the Pirate that I would have tought.

- Ancient Bear vs Snake, this one is a marathon. To give a chance for the snake I consider the 2 space special bite and running away strategy. This mean that the snake got 2 attack for 1 attack by the bear (snake 2 hexes bite, then AB attack then Snake retaliate). Because of this, after 2 special bites by the snake and running away combo, the AB have lost half his forces, going from 125 to 66 while the Snake go from 333 to 240. After that the clock is slowly ticking for the AB.

- Those Gorguana have just so many great abilities. Combine with great Def and attk stats, the Undead spider got no chance at all.

-The Foreman Def and Attk stats are proving too strong for the Firy Dragonfly. The FD is seeing is amazing 2500 potential damage dealing reduce to 1388,9 because of it's opponent stats.

- Like the Snake match-up, the Marauder 2 hexes attack and running away strategy is proving too strong for the Bear aggressive strategy. This one is even easier because of the less difference in the Attk and Def stats between each units.

[Lord Ludwig]

- For the Lake Fairy vs Hunter, I had to do some calaculation and here is the total dmage for the 1sr blow each unit is dealing with the hunter double attack and the Attk and Def stats accounted for:
Hunter: 2257,2 Total damage for a total of 282 Fairies killed
Fairy: 1146 total damage for a total of 10 hunters killed

The fact that the fairy got no-retaliation enables it to win this match. But can be different if the hunter got other Double damage attack, I consider it a one time action.
.

As much as I like it to have inspired others to launch their own Teana grand slam tournaments, and as much as I know I too made some miscalculations in the original one, I fear you'll have to be more careful if you want this "thought experiment" to be meaningful. Some of your results don't persuade me, but I took time to check only the one that struck me as most unlikely.

Let's consider the lake fairies vs hunters match.

First of all hunters do NOT have the double shot talent. However, they still should win easily. Considering 10,000 leadership you line up 1428 LF against 66 H, total health 11424 and 7260 respectively. Damage ranges 1-2 for the LF, 9-10 for the H. Leaving criticals aside and considering average damage, considering relative AT and DE the H always does triple damage, the LF always do 1/3 damage. On a medium grid the LF can't close distance on round 1 so the H strikes first.

Thus we have:

round 1 LF moves, H hit for 1881 killing 235

total health and number of troops: LF 9543 (1192) H 7260 (66)

round 2 LF hit for 596 killing 5, H step away and hit for 1738 killing 217

total health and numbers of troop: LF 7805 (975) H 6664 (61)

round 3 LF hit for 487 killing 5 H step away and hit for 1596 killing 199

total health and numbers of troop LF 6209 (776) H 6179 (56)

round 4 LF hit for 388 killing 3 H step away and hit for 1510 killing 189

total health and numbers of troop LF 4699 (587) H 5791 (53)

You can go on, but since after four rounds the LF have been reduced to about 40% of their original strength while H are still at 80% I think it's pretty clear who's the winner. The only variables are: 1) average damage is slightly limiting for the LF. their first strike ranges from 397 to 794, crit 1191. The first hit of the H in comparison ranges from 1782 to 1980, crit 2970. So the LF could strike lucky, but the H have also a slightly higher crit chance, and their critical is a lot more impressive 2) dust fairy (30%) could change something, but not nearly enough 3) the only real option for the LF, if the grid is very peculiar maybe they can lock the H in a corner forcing them to go melee; no penalties anyway but at least the LF gain counterstrike. Even so, I think the numbers show there's really no chance at all of the LF winning this. I would urge you to take a closer look also at some other results I think smell a bit fishy, like the ancient bear losing to the snake. However I've got no time right now to make those calculations as well, so my gut feeling may prove wrong on that one.

[pavned]

I did made some calculation, and I use Zechnophobe formulas to determine the damage dealt when accounting Attk and Def stats.
http://forum.1cpublishing.eu/showthread.php?t=10991&page=2

Using this formula the Fairies are delaing more Damage and receiving less (much less without the Double Attack)

Thus we have:

round 1 LF moves, H hit for 1129 killing 141

total health and number of troops: LF 10295 (1287) H 7260 (66)

round 2 LF hit for 1287 killing 11, H step away and hit for 940,5 killing 117

total health and numbers of troop: LF 9355 (1170) H 5973 (55)

round 3 LF hit for 1170 killing 10 H step away and hit for 769,5 killing 96

total health and numbers of troop LF 8585,4 (1074) H 4803 (45)

round 4 LF hit for 1074 killing 9 H step away and hit for 615,6 killing 76

total health and numbers of troop LF 7969,8 (998 ) H 3729 (36)

The Hunter casualties makes them unable to get rid of Fairies fast enough and they keep hitting them, next round they wipe another 9 hunters making it 27.

It appears that the main issue here is how do we calculate damage dealt. Like I said I use the formula posted by Zechnophoe which:

For the fairies, the damages dealt are:
[100/(100+((10/3)*(DIFFERENCE_F)))] * Damage

where Difference_F is the difference between the Hunter Defence and the Fairy attack --> 15

that means the Fairies are doing only 66,6% of their normal damage. Since they are doing 1,5 mean damage, the total damage dealt is equal to the number of fairies units left in the stack

For the hunter the damages dealt are:

[(DIFFERENCE_H * (10/3))/100] * Damage + Damage
where DIFFERENCE_F is the difference between attack of the Hunter and defence of the Fairy --> 24

That means the hunter are doing 80% more damages.

Maybe this formula is wrong. Cause your numbers means they are doing 300%. But Zechnophobe said that
"Both of these calculations max out at 60 difference. At 60 greater attack you will do 300% of base damage (three times normal damage) and at 60 greater defense you will take 33% of normal damage (67% less than normal)."

[pavned]

I'll wait for comments about this before posting next match-ups and results

[Lord Ludwig]

It's certainly possible that I am mistaken. I did not know about Zechnophobe's formula, I just interpreted what the game states when you read about the effects of DE and AT. I always understood it as being based upon the ratio between AT and DE rather than upon plain difference. It makes more senso to me that AT 12 vs DE 4 should be equal to AT 90 vs DE 30 rather than AT 90 vs DE 82, but if Zech says so I suppose it's all another bad translation or just a misinterpretation on my part.

It DOES make sense to me to operate on ratio rather than absolute difference... 30 people fighting 60 are more comparable to 30,000 fighting 60,000 than to 59,970 fighting 60,000. But if the game mechanics are different than I imagined them and would like them to be than that's just the way it is. Means I have to check back on those old semifinals of mine as well :-(

I certainly apologize for thinking you were not careful when it seems I am the one who erred. I'll look again at the data considering this different interpretation of the AT and DE effects.

[KongMysen]

Imo King's Bounty took a lot of things from Heroes of Might and Magic. I know that they initially started the genre, but the 3DO crew jest evolved it. However HOMM have never been so balanced and fun as King's Bounty is.

That said HOMM have always been using this formula or a formula close to it.

With a higher attack than defence:
Dmg output = Number of units*base dmg* (1+difference*0,05)

With a higher defence:
Dmg output = Number of units*base dmg* (1-difference*0,02)

In homm1 and 2 the numbers where 0,10 and 0,05 but the last 3 games have been more balanced.
HoMM also decided that max and minimum dmg should be 33,3% and 300%

I know these games aren't excactly the same, but since there are so many similarities I'm guessing Zechnophobe's calculations are correct, and that the lvl 1 units can get far in this Gran Slam, because of their large numbers. They do however fail to spells and skills like Lullaby, fear, Blind lvl 1, sheep lvl 1 etc.
The system works perfectly I think, and I do agree that ATT 12 DEF 4 doesn'e seem the same as ATT 90 DEF 82, but if they changed it, the balance of the game would dissappear.

An example could be Hunters (27ATT) vs Miners (8DEF)

The hunters dmg would be 337,5% but capped to 300%. A hero with 10 defence could lower the number to 150%.
A hero with 10 attack wouldn't be doing any more dmg.

[pavned]

Emerald Dragon (4) 5 units, 4000 total HP (800 HP for 1 unit) 475 total damage (95 damage for 1 unit)
Bye

Swordman 285 units, 9975 total HP (35 for 1), 1282,5 toal dam (4,5 dam for 1)
Bowman 200 units, 6800 total HP (34 for 1), 700 total dam (3,5 for 1)

Black Unicorn 66 units, 9240 total HP (140 for 1), 1089 total dam (16,5 for 1)
Thorn Hunter 1250 units, 7500 total HP (6) 1875 total dam (1,5)

Bye
Knight (29) 62 units, 9920 total HP (160 for 1), 1054 total dam (17 for 1)

Archmage (23) 50 units, 7000 total HP (140), 325 total dam (6,5)
Bye

Skeleton 833 units, 11662 total HP (14), 2082,5 total dam (2,5)
Guard Droid 83 units, 8300 total HP (100), 996 total dam (12)

Elf 125 units, 7500 total HP (60), 562,5 total dam (4,5)
Robber 500 units, 10000 total HP (20), 1500 total dam (3)

Bye
Royal Griffin (15) 33 units, 7260 total HP (220), 825 total dam (25)

Troll (10) 9 units, 7020 total HP (780), 630 total dam (70)
Bye

Fire Spider 333 units, 9990 total HP (30), 1498,5 total dam (4,5)
Orc 133 units, 9310 total HP (70), 1130,5 total dam (8,5)

Inquisitor 100 units, 7000 total HP (70), 600 total dam (60)
Skeleton Archer 714 units 7140 total HP (10), 1785 total dam (2,5)

Bye
Cannoneer (20) 45 units, 6300 total HP (140), 360 total dam (8)

Evil Beholder (28) 55 units, 5500 total HP (100), 660 total dam (12)
Bye

Lake Dragonfly 1111 units, 7777 total HP (7 for 1), 2222 total dam (2 for 1)
Veteran Orc 71 units, 9230 total HP (130), 1029,5 total dam (14,5)

Royal Snake 166 units, 10624 total HP (64), 1328 total dam (8)
Goblin 285 units, 7410 total HP (26), 855 total dam (3)

Bye
Giant (5) 6 units, 5400 total HP (900 for 1), 540 total dam (90 for 1)

I need your inputs and help to determine the Swordman vs Bowman confrontation, I really wonder what are the effect of the fire arrow and ice arrow!

As for the other match-ups, they were pretty easy to settle, except for the Elf vs Robber. The Robber, even with the Attk and Def stats accounting for is doing 1,5 more dmaage. But the fact that he's so slow (only 2 of speed) and lower initiative mean that the elf can it the robber 3 times before getting hit. In the process the Robber lost 124 units and is dealing about the same amount of damage then the elf. The elf having better HP he's losing less units with every hit.

The other one is the Fire Spider vs Orc. The Fire SPider surprisingly good stats and the fact that they are giving the 1st blow means they'll end up winning the match-up against the orc.

The inquisitor bonus attack against undead is a clear winner vs the Skeleton Archer.

The Royal Snake prove to be way too strong for the goblin. I wonder how they'll fair in the next round dealing 2 time the amount of damages of the Goblin

As for the Black Unicorn (2032 damages vs 1125), Guard Droid (1760 vs 1201 and giving the 1st blow) and Veteran orc (1887 vs 1258) they are simply to strong for their opponents.

[Zechnophobe]

It's certainly possible that I am mistaken. I did not know about Zechnophobe's formula, I just interpreted what the game states when you read about the effects of DE and AT. I always understood it as being based upon the ratio between AT and DE rather than upon plain difference. It makes more senso to me that AT 12 vs DE 4 should be equal to AT 90 vs DE 30 rather than AT 90 vs DE 82, but if Zech says so I suppose it's all another bad translation or just a misinterpretation on my part.

It DOES make sense to me to operate on ratio rather than absolute difference... 30 people fighting 60 are more comparable to 30,000 fighting 60,000 than to 59,970 fighting 60,000. But if the game mechanics are different than I imagined them and would like them to be than that's just the way it is. Means I have to check back on those old semifinals of mine as well :-(

I certainly apologize for thinking you were not careful when it seems I am the one who erred. I'll look again at the data considering this different interpretation of the AT and DE effects.

I was going to mention something in the other thread, but hadn't realized you completely had not known about this. The ratio is irrelevant, and only the absolute difference matters. That is why things like MORALE (which increases the ABSOLUTE attack and defense of a unit by a PERCENTAGE of the base) are not equally effective across troops. Black Dragons with +2 Morale get +14 attack and defense, which is a massive boost. Most level 1 and two units only get a point or two, which is minimal.

I am a horrible math geek (I am a software developer by trade, and I love analyzing complex systems) so I try to make it a point to understand these things :).

[MaroonMaurader]

If you decide to add hero defense to unit defense, you pretty much have to do damage as a difference rather than ratio. Suppose Amelie has 25 defense. Then if things are done as a ratio, she cuts damage to a Black Dragon stack in her army by 26%, but cuts damage to a peasant stack in her army by an astonishing 96%.* Now suppose you balance peasants and black dragons so roughly equivalent leadership, on their own, are roughly equally dangerous. This means that when a 25-defense Amelie has roughly equal leadership of them in her army, the peasants are *vastly* more dangerous than the black dragons, because they're practically invincible compared to the dragons.
On the other hand, if the damage is done by difference, then for both the Black Dragons and the Peasants Amelie is changing the difference between attacking unit's Attack and the defender's Defense by the same amount, and thus changing damage by roughly the same factor - so units that are balanced to work on their own remain balanced when working with a hero boosting their attack and defense.

*A quick example in case it wasn't clear where those numbers came from...
If damage is done as a ratio, then the damage formula is something like...
Damage = BaseDamage * (Attack/Defense).
Damage (with Hero defending) = BaseDamage * (Attack / (Defense + Hero Defense)).
The ratio of the two, Damage (with Hero) / Damage, is then...
Base Damage * (Attack/ (Defense + Hero Defense)) / [BaseDamage * (Attack / Defense)]
This simplifies out, giving...
Damage (with Hero) / Damage = Defense / (Defense + Hero Defense).
When Defense is 1 and Hero Defense is 25, that ratio is 0.04. When Defense is 70 and Hero Defense is 25, that ratio is 0.74.

[Zechnophobe]

You don't do damage as a ratio, because that is not how damage is computed, I don't think there is anything else that needs to be said, is there?

[Lord Ludwig]

You don't do damage as a ratio, because that is not how damage is computed, I don't think there is anything else that needs to be said, is there?

I can apologize once again, if you deem it necessary :oops:

Funny how I completed a no-loss game on impossible while completely misunderstanding one of the fundamental game mechanics...

[KongMysen]

I need your inputs and help to determine the Swordman vs Bowman confrontation, I really wonder what are the effect of the fire arrow and ice arrow!

With a higher initiative the Bowmen go first. Ice Arrow will reduce the speed of the swordsmen to 2 for 3 rounds. This will make the swordsmen need 4 rounds to reach the bowmen on a medium grid. Objects and/or a larger grid could give the Bowmen an even bigger advance.
Burning does 5-10% dmg so I'm going with the average on 7,5%. It also reduce defence from 16 to 10 for 3 rounds.

Here goes:

Bowman - Ice Arrow 700dmg kills 20 - Swordsmen 9275hp (266 units)
Bowmen - Fire Arrow 900dmg kills 26 - Swordsmen 8375hp (240 units)
Burning 628dmg - Swordsmen 7747hp (222 units)
Bowmen - shoots 840dmg kills 24 - Swordsmen 6907hp (198 units)
Burning 518dmg - Swordsmen 6389hp (183 units)
Bowmen - shoots 840dmg kills 24 - Swordsmen 5549hp (159 units)
Burning 416dmg - Swordsmen 5133hp (147 units)

Swordsmen - Smashing blow 1176dmg. Kills 34. Bowmen retaliates doing 349dmg killing 10. Swordmen 4784hp (137) - Bowmen 5624hp (166)

Bowmen - steps away and shoots 581dmg kills 16. Swordmen 4203 (121) - Bowmen 5624hp (166)

Swordsmen - attacks 545 dmg kills 17. Bowmen retaliates doing 261dmg killing 8. Swordmen 3942 (113) - Bowmen 5079hp (149)

Bowmen - steps away and shoots 522 dmg kills 15. Swordsmen 3420hp (98 ) - Bowmen 5079hp (149)

Swordsmen - attacks 441dmg kills 12. Bowmen retaliates doing 240dmg killing 7. Swordmen 3180hp (91) . Bowmen 4638hp (137)

Not even with Smashing blow as the next move from the swordsmen, will they be able to close the gap. Burning and the 4 free shots from the bowmen should determine the outcome.
bowmen comes out victorious.

[Zechnophobe]

30% dodge chance though, after 30% of their health is gone. That's a pretty decent effect right there.

I also just had a weird question (not relavent to this battle) but some races of units gets +1 morale if they are the only race in your army. This would be true in all such battles in this competition, and for certain units will add a significant boost to their stats and crit chance.

Oh, and is anyone figuring in crit damage when computing average damage?

[Zechnophobe]

Let me elucidate on crit % real quick, in case it wasn't obvious. Each unit, when doing a retaliation or normal attack has a chance to get a critical hit for additional damage. This total damage of a crit is equal to 150% of the upper number on the units damage range. For instance, a fire spider that does 4-5 damage will crit for 7.5 damage.

Just like how you can take an average on the base damage (4-5 averages to 4.5) you can also factor into that average the potential crit damage. A firespider has a crit rate of 15% (If I remember correctly). So it has a 15% chance to go from 4.5, to 7.5 damage. Or, to state it better, a 15% chance to do 3 more damage on average. So we'll simply add that into the average, and say it does .15*3+4.5 damage, or 4.95 damage on average.

That is the number you should use before doing your attack vs defense calculations. Since some untis (dryads) do crits very rarely (5% of the time) and others(bears) very often (25% of the time) it is a non trivial calculation.

Note that I quoted the exact damage and crit rates above off the top of my head, and could be wrong on the particulars, though I am sure of the process.

[KongMysen]

30% dodge chance though, after 30% of their health is gone. That's a pretty decent effect right there.


Shit, I totally forgot about the dodge chance. I still think that even with a 30% dmg reduction the Bowmen would win. With a no-retaliation shot + the retaliation blow, the archers already did approx 1.5 dmg each round. Removing 30% dmg would even the odds. But at the time Swordsmen reaches 70% troops the Bowmen would be in the lead hp-wise. In this particular battle where the luck factor is so great Swordsmen will win occasionally. But mostly not.

I didn't make accurate calculations on crit dmg. Mostly because I'm not a math student and because I was lazy.
Bowmen have 10% cance of increasing dmg with 2,5 points on every shot except the first 2, and by 1.25 on every retaliation blow. Swordmen have 8% chance of increasing dmg with 3 points on 2 out of 3 attacks. Numbers seems pretty close.

I do however agree that it can be a mayor factor in some battles. The Royal snake for instance will increase dmg from 8 to 15, 25% of the times. Average dmg goes from 8 to 10.25 for the Royal Snakes. The strike only do 9,5 dmg, so its simply better to use normal attacks unless poisoning is dying out and you need the 100% certainty to reactivate it. This Gran Slam will properly show, why they are so commonly used by a lot of players.
Polar bears and furious goblins are also going to gain a lot from their high crit chance and large dmg intervals. (Polar Bears average 17 - crit 33, 30% of the times- Furious Goblins Average 5 - crit 10,5, 20% of the times)

[pavned]

Let me elucidate on crit % real quick, in case it wasn't obvious. Each unit, when doing a retaliation or normal attack has a chance to get a critical hit for additional damage. This total damage of a crit is equal to 150% of the upper number on the units damage range. For instance, a fire spider that does 4-5 damage will crit for 7.5 damage.

Just like how you can take an average on the base damage (4-5 averages to 4.5) you can also factor into that average the potential crit damage. A firespider has a crit rate of 15% (If I remember correctly). So it has a 15% chance to go from 4.5, to 7.5 damage. Or, to state it better, a 15% chance to do 3 more damage on average. So we'll simply add that into the average, and say it does .15*3+4.5 damage, or 4.95 damage on average.

That is the number you should use before doing your attack vs defense calculations. Since some untis (dryads) do crits very rarely (5% of the time) and others(bears) very often (25% of the time) it is a non trivial calculation.

Note that I quoted the exact damage and crit rates above off the top of my head, and could be wrong on the particulars, though I am sure of the process.

I haven't consider crit chance, is there any match-up you think they'll be ending differently if crit factor would be consider?

I can calculate the outcome if so.

About further calculations, what is the % of creatures summoned for the "summon2" spell used by the units with summoning ability? Cause for the second half of the table there's some summoner and I'm stuck!

[KongMysen]

The Demonologists will summon troops worth 52-105 for each units.
That means an average of 75% and 7500 leadership for the first cast. Still there is such a huge difference between the units summoned.

Druids will summon troops with a total healt of 20-25 HP pr. unit.
That equals 2000-2500HP for 10.000 leadership of druids summoning

Dryads summons thorns worth 8-10 leadership. pr. unit which equals 40-50% of total leadership. 4000-5000 leadership when cast with an unharmed troop.

1 Royal thorn may summon troops woth 150-300 leadership. On average it's 225 leadership which equals 59%.
10.000 Leadership Royal Thorns will summon 5900 leadership smaller thorns

Hayterants lays an egg with 50% leadership
Choshas summons 80 leadership Gobots. That equals 36,4%. 10.000 leadership means 3636 leadershop Gobots.

Royal Griffins summons 150 leadership Angelic Guards each. That's 50% and 10.000 leadership Griffins will summon 5000 leadership Guards.

Demons summon troops worth 90 leadership each. That equals 30% or 3000 leadership for a full stack. Like the Demonologists its really a matter of luck what you get.

I hope that includes everyone. Note that i wrote HP on the druid summon. That's not a mistake ;)