King's Bounty Grand Slam Open

[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 (

Evil Beholder (2 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 (
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 125 they are simply to strong for their opponents.

[Zechnophobe]

Originally Posted by 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.

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]

Originally Posted by 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?

I can apologize once again, if you deem it necessary

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

[KongMysen]

Originally Posted by pavned

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?