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| Units, artifacts and armor-bearers Discussion, questions and solutions about units, artifacts and armor-bearers. |
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#1
03-02-2010, 03:26 PM
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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. 
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#2
03-03-2010, 10:48 AM
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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. Last edited by Lord Ludwig; 03-03-2010 at 12:26 PM.
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#3
03-03-2010, 02:13 PM
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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/showthr...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)."
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#5
03-03-2010, 04:46 PM
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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.
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#6
03-03-2010, 06:56 PM
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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. Last edited by KongMysen; 03-03-2010 at 06:58 PM.
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#7
03-03-2010, 07:45 PM
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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.
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#8
03-05-2010, 06:29 PM
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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. Last edited by KongMysen; 03-05-2010 at 06:31 PM.
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#9
03-04-2010, 01:57 AM
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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  .
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#10
03-04-2010, 09:13 AM
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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. Last edited by MaroonMaurader; 03-04-2010 at 09:16 AM. Reason: correct typo
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