Damage Calculation

[Zack]

@The_Seeker

Very interesting! Is this formula applied to all heroes?

As far as I can tell: yes. This formula is for the attacking team. It also works for the defending team when the damage gets increased by a factor of approx. 1.2

@The_Seeker

Are the 25.5; 0385; 0.93 and the others constant?

It looks like it. The calculated damage numbers are close to the actual damage or at least not far off. The exact numbers still need some tweaking as you can see with our efforts in this thread a little bit above, but it takes too much effort to get accurate data for that

@Harbinger1777

QA=1213 and TD=246

Expected damage
[25.5 x 1213 x 320% / 246 + 0.0385 x (1213 x 320% – 0.93 x 246)] x 3 x 11/12 ±5% = 1416 (min=1345; max=1487)

[25.5 x 1213 x 520% / 246 + 0.0385 x (1213 x 520% – 0.93 x 246)] x 3 x 11/12 ±5% = 2317 (min=2201; max=2433)

actual damage from the screenshots:
with 320%: 1358 and 1375 versus 1345|1416|1487 (min|avg|max)
with 520%: 2319 and 2398 versus 2201|2317|2433 (min|avg|max)

formula seems to work

@Harbinger1777

Sorry been busy with work. Found something more to do with power being a variable in skill damage:

Now you can test?

Did 5 runs on S4 10-1 with the biome effect: +100% power for Special Skill attacks of green heroes.
I put Vela and Gobbler next to Ludwig to get them charged several times.

Vela with troop bonus: 847 ATK and 150% damage = 1270 attack power
Gobbler with troop bonus: 743 ATK and 170% damage = 1263 attack power
Gobbler with 270% damage: 2006 attack power

The defense of the Fungal Soldiers and Stompsharks ranged from 660 to 680. I didn’t get enough data (yet) because of the 5% variance, but here is what I got (so far):

Vela:

attack power	defense	actual min	actual max	avg	calc avg	calc min	calc max	5% variation
1270	660	200	216	208	204	194	214	10
1270	665	200	215	207,5	202	192	212	10
1270	670	196	213	204,5	201	191	211	10
1270	675	198	211	204,5	199	189	209	10
1270	680	193	210	201,5	198	188	208	10

Gobbler with 270% special attack %:

attack power	defense	actual min	actual max	avg	calc avg	calc min	calc max	5% variation
2006	660	351	383	367	360	342	378	18
2006	665	357	383	370	358	340	376	18
2006	670	344	383	363,5	356	338	374	18
2006	675	346	374	360	354	336	372	18
2006	680	341	374	357,5	352	334	370	18

The calculation for Vela is ok imho.
Gobbler does slightly more damage than what I expect with just 100% more special attack %

Still, it looks like the biome effect is simply added to the special attack %.

[The_Seeker]

Thank you so much for the answer! It’s really useful and clear information and I am really grateful that you are doing this.

Imo this should be the main aim of the forum and not the usual buff this, nerf that, SG is , shut up, it’s their business and they can do whatever they want.

So thanks again for driving forward the quality of forum posts. And if you need any additional support with collecting data, let me know.

[SaGa]

guys,
I have a doubt about special skill calculation. Example:
if I have a Milena, lets say, 4^lv80 with 800 attack
If I choose to limit break and a full attack emblem path and the new attack is 950:

Milena’s 2nd charge skill uses its 950 attack or its 800 attack to calculate the special skill damage?

thanks in advance. An amazing math discussion!

[OAlexisO]

When Quenell first came out, there was data collected as @Radar1 pointed out, but I believe the data concluded what I posted above. After hearing others results I tested my own Quenell at the time, and did find that to be true (she was doing around 2x the damage). However, I did not record any data of my own and did not do continuous runs of my own. When, after a few of my runs seemed to confirm what others where saying, that was good enough for me. After seeing your image, that seemed a bit too far off to be within the range of what 2x damage could result in. I did 100 manual runs total of the same level during this AR to record the damage, 50 with base damage & 50 with 200% power, and took screenshots of the damage. In the few days after AR ends I’ll try to collage images together to post, because I am not going to post 100 screenshots here and clutter the messages up . What I saw is that Quenell does NOT do 2x the damage anymore. I know that 50 of each type of hit isn’t a ton of data, but when none of the 200% power hits fall inside the the range of the base damage hits to be 2x the damage, that is a pretty good indication to me that something is different. I was incredibly lucky to get Quenell the very 1st CoK portal, so it has been some time since I compared these two hits, and she does crazy amounts of damage at 200% power as it currently stands (in ideal circumstances she follows up EDD & DD for me). What alarms me, is that this does appear different to when she was first released, without anything having ever been said about any adjustment to her skill/how the damage is determined. After reading what @Radar1 said, and having gathered these 100 screenshots, it has me questioning my sanity a little bit . I honestly hope that it was just me misunderstanding/being confused (and not realizing it) from when she was 1st released (but then how would my own runs from back then fit in)…because as I said above, if there was a change to this at some point without mention, that would be alarming.

PS: I hope that this all makes sense above, as I am very sick and struggle to get my words out

[Harbinger1777]

No worries heroes get nerfed all the time

[Zack]

@SaGa

if I have a Milena, lets say, 4^lv80 with 800 attack
If I choose to limit break and a full attack emblem path and the new attack is 950:

Milena’s 2nd charge skill uses its 950 attack or its 800 attack to calculate the special skill damage?

The special skill damage then uses the 950 attack for the damage calculation.

Expected damage for that example:
attacking team:
[25.5 x 950 x troop_attack_bonus x 420% / target’s_defense_during_battle + 0.0385 x (950 x troop_attack_bonus x 420% – 0.93 x target’s_defense_during_battle)] x 3 x 11/12 ±5%

defending team:
[25.5 x 950 x troop_attack_bonus x 420% / target’s_defense_during_battle + 0.0385 x (950 x troop_attack_bonus x 420% – 0.93 x target’s_defense_during_battle)] x 3 x 11/10 ±5%

[milkyjoe001]

@Harbinger1777

No worries heroes get nerfed all the time

Does this mean Quenelle has been nerfed? I still don’t understand ??

[SaGa]

thanks bro, for the clear explanation!

[Harbinger1777]

I don’t actually remember if Quenell was nerfed, I simply assumed that had it been the case of what whoever said the post above mine (the one you quoted) sorry no time to check—late for work—then she was probably nerfed (again I do not know).

[Harbinger1777]

@Zack

This would give you another set of test points for troop dmg vs weak colors:

s5 amulets:

This scarab amulet is earned upon completing s5:16-10 normal for the first time.

Cheers!

[Zack]

I currently have a few videos of hard mode of provinces 34 and 35 where I used this scarab amulet.

According to the amulet description it increases the elemental bonus damage for troops (= tiles) against the weaker element by 200%.

From the various previous tests we know that elemental bonus damage is applied in the damage modifier for the tile damage:
If the target’s defense is smaller than 0.93% of the total attack, then
tile damage = [25.5 x total_attack / defense + 0.0385 x (total_attack – 0.93 x defense] x damage_modifier ±5%

with damage_modifier = (1+ elemental_bonus_damage% + critical_damage% + combo%) x (1 + TieBreaker%)

My team:
Rigard
Sekhmet with 1470 attack (= 992 x 1.24 x 1.2) with her +20% S5 bonus
Ludwig
Zenobia with 1194 attack (= 963 x 1.24)
Kullervo with 1182 attack (= 954*1.24)

test mission: S5 35-10 hard
Enemy mob has around 747 defense
Boss monsters have 1401 defense

test 1 with mob monsters:
active buffs/debuffs:
Zenobia’s +64%attack for red tiles

total_attack = (1470 + 1194) x (1 +64%) = 4378 attack
defense = 747 defense < 0.93 x 4378 => normal formula
damage_modifier = (1 + 100% + 200%) = 4

expected damage range:
[25.5 x 4378 / 747 + 0.0385 x (4378 – 0.93 x 747] x 4 ±5% = 1106|1165|1224 (avg|min|max)
versus actual damage 1103, 1116 and 1153

If I apply the 200% damage bonus from the amulet as a multiplicative bonus the calculated damage would be too high for the mob monsters:
damage_modifier = (1 + 100%) x (1 + 200%) = 6
[25.5 x 4378 / 747 + 0.0385 x (4378 – 0.93 x 747] x 6 ±5% = 1659|1747|1835 (avg|min|max)

test 2 with boss monster:
active buffs/debuffs:
+20% combo%

total_attack = 1182 attack
defense = 1401 defense > 0.93 x 1182 => reduced formula
damage_modifier = (1 + 100% + 200% + 20%) = 4.2

Since the target’s defense is higher than 93% of the attack, the formula is reduced to the first term.
=> expected damage range:
[25.5 x 1182 / 1401] x 4.2 ±5% = 85|90|94 (avg|min|max)
versus actual damage: 90 and 92

Result:
The amulet’s bonus damage against the weaker element is simply added to the strong elemental bonus damage, which doubles the already doubled tile damage

[sleepyhead]

thanks @Zack for your analyses! I was just searching for threads on minion damage calcs, and found some of your old posts - they were very helpful!

[Harbinger1777]

@Zack of all ppl I think you ought to be able to see if this actually works

Balance Overhaul Proposal - Mitigate Out of Control Damage via Adjustments to Defensive Stats

TL;DR Version and Examples As many of you may already be aware, Small Giant has released a large balance update to beta for testing. Being a beta-tester myself, I have had the opportunity to experience this balance change first-hand, and I have found that it fundamentally fails to address the very real problems with balance in the game, and instead actually exacerbates them. See below for the crux of SG’s approach to the balance change. Continuing the discussion from On the upcoming Big Ba…

Yk the dmg calculation better than all of us, long read but…?

-YouShouldBeHigher (aka Harbiner1777)

[Wolfx1131]

I need a TL;DR. What’s the current damage formula? I don’t want to obtain a PhD in statistics to decipher this thread.

[Rayy]

@SolemnWolf

Damage ≈ 100 x ( θ x Att / Def ) ^ 1.35

@SolemnWolf

The random parameter ±50% follows a Gaussian law with an average of 0% and a variance of 1%.

Since e(0) = 1 → θ = 1 on average.

So TL;DR the average/expected damage output is calculated as

Damage ≈ 100 x ( Att / Def ) ^ 1.35

[gingerhuny]

Here is what I had calculated once upon a time (could be wrong or outdated)

Formula used -

Defense Attack	600	618	636	654	672	690	708	726	744	762	780	798	816	834	852	870	888	906	924	942	960	978	996	1014	1032	1050
600	76	72	68	65	61	58	55	51	48	45	42	39	36	33	30	27	24	22	19	16	14	11	9	6	3	1
615	79	76	72	68	65	61	58	54	51	48	45	42	39	36	33	30	27	25	22	19	16	14	11	9	6	4
630	83	79	75	71	68	64	61	57	54	51	48	45	42	39	36	33	30	27	25	22	19	17	14	11	9	6
645	86	82	78	75	71	67	64	61	57	54	51	48	45	42	39	36	33	30	27	25	22	19	17	14	12	9
660	90	86	82	78	74	71	67	64	60	57	54	51	48	45	42	39	36	33	30	27	25	22	19	17	14	12
675	93	89	85	81	77	74	70	67	63	60	57	54	51	48	45	42	39	36	33	30	27	25	22	19	17	14
690	96	92	88	84	81	77	73	70	66	63	60	57	53	50	47	44	41	39	36	33	30	27	25	22	20	17
705	100	96	92	88	84	80	76	73	69	66	63	60	56	53	50	47	44	41	39	36	33	30	27	25	22	20
720	103	99	95	91	87	83	80	76	73	69	66	63	59	56	53	50	47	44	41	39	36	33	30	28	25	22
735	107	102	98	94	90	86	83	79	76	72	69	66	62	59	56	53	50	47	44	41	38	36	33	30	28	25
750	110	106	101	97	93	90	86	82	79	75	72	68	65	62	59	56	53	50	47	44	41	38	36	33	30	28
765	113	109	105	101	97	93	89	85	82	78	75	71	68	65	62	59	56	53	50	47	44	41	38	36	33	30
780	117	112	108	104	100	96	92	88	85	81	78	74	71	68	65	62	58	55	52	50	47	44	41	38	36	33
795	120	116	111	107	103	99	95	92	88	84	81	77	74	71	68	64	61	58	55	52	49	47	44	41	38	35
810	124	119	115	110	106	102	98	95	91	87	84	80	77	74	70	67	64	61	58	55	52	49	46	44	41	38
825	127	122	118	114	109	105	102	98	94	90	87	83	80	77	73	70	67	64	61	58	55	52	49	46	44	41
840	130	126	121	117	113	109	105	101	97	93	90	86	83	80	76	73	70	67	64	61	58	55	52	49	46	43
855	134	129	125	120	116	112	108	104	100	96	93	89	86	82	79	76	73	70	66	63	60	57	55	52	49	46
870	137	132	128	123	119	115	111	107	103	99	96	92	89	85	82	79	75	72	69	66	63	60	57	54	52	49
885	141	136	131	127	122	118	114	110	106	102	99	95	92	88	85	82	78	75	72	69	66	63	60	57	54	51
900	144	139	134	130	126	121	117	113	109	105	102	98	95	91	88	84	81	78	75	72	69	66	63	60	57	54
915	147	142	138	133	129	124	120	116	112	109	105	101	98	94	91	87	84	81	78	74	71	68	65	62	60	57
930	151	146	141	136	132	128	123	119	115	112	108	104	100	97	94	90	87	84	80	77	74	71	68	65	62	59
945	154	149	144	140	135	131	127	122	118	115	111	107	103	100	96	93	90	86	83	80	77	74	71	68	65	62
960	158	153	148	143	138	134	130	126	122	118	114	110	106	103	99	96	92	89	86	83	80	77	73	70	68	65
975	161	156	151	146	142	137	133	129	125	121	117	113	109	106	102	99	95	92	89	86	82	79	76	73	70	67
990	164	159	154	149	145	140	136	132	128	124	120	116	112	109	105	102	98	95	92	88	85	82	79	76	73	70
1005	168	163	158	153	148	144	139	135	131	127	123	119	115	112	108	104	101	98	94	91	88	85	82	79	76	73
1020	171	166	161	156	151	147	142	138	134	130	126	122	118	114	111	107	104	100	97	94	91	87	84	81	78	75
1035	175	169	164	159	154	150	145	141	137	133	129	125	121	117	114	110	107	103	100	97	93	90	87	84	81	78
1050	178	173	167	162	158	153	149	144	140	136	132	128	124	120	117	113	109	106	103	99	96	93	90	87	84	81
1065	181	176	171	166	161	156	152	147	143	139	135	131	127	123	119	116	112	109	105	102	99	96	92	89	86	83
1080	185	179	174	169	164	159	155	150	146	142	138	134	130	126	122	119	115	112	108	105	102	98	95	92	89	86
1095	188	183	177	172	167	163	158	153	149	145	141	137	133	129	125	122	118	114	111	108	104	101	98	95	92	88
1110	192	186	181	176	171	166	161	157	152	148	144	140	136	132	128	124	121	117	114	110	107	104	101	97	94	91
1125	195	189	184	179	174	169	164	160	155	151	147	143	139	135	131	127	124	120	117	113	110	106	103	100	97	94
1140	198	193	187	182	177	172	167	163	158	154	150	146	142	138	134	130	126	123	119	116	113	109	106	103	100	96
1155	202	196	191	185	180	175	170	166	161	157	153	149	145	141	137	133	129	126	122	119	115	112	109	105	102	99
1170	205	199	194	189	183	178	174	169	164	160	156	152	147	144	140	136	132	128	125	121	118	115	111	108	105	102
1185	209	203	197	192	187	182	177	172	167	163	159	154	150	146	143	139	135	131	128	124	121	117	114	111	108	104
1200	212	206	200	195	190	185	180	175	171	166	162	157	153	149	145	142	138	134	131	127	124	120	117	113	110	107
1215	215	209	204	198	193	188	183	178	174	169	165	160	156	152	148	144	141	137	133	130	126	123	119	116	113	110
1230	219	213	207	202	196	191	186	181	177	172	168	163	159	155	151	147	143	140	136	133	129	126	122	119	116	112
1245	222	216	210	205	199	194	189	184	180	175	171	166	162	158	154	150	146	143	139	135	132	128	125	121	118	115
1260	226	220	214	208	203	197	192	187	183	178	174	169	165	161	157	153	149	145	142	138	134	131	128	124	121	118
1275	229	223	217	211	206	201	196	191	186	181	177	172	168	164	160	156	152	148	144	141	137	134	130	127	124	120
1290	232	226	220	215	209	204	199	194	189	184	180	175	171	167	163	159	155	151	147	144	140	136	133	130	126	123
1305	236	230	224	218	212	207	202	197	192	187	183	178	174	170	166	162	158	154	150	146	143	139	136	132	129	126
1320	239	233	227	221	216	210	205	200	195	190	186	181	177	173	168	164	160	157	153	149	145	142	138	135	132	128
1335	243	236	230	224	219	213	208	203	198	193	189	184	180	176	171	167	163	159	156	152	148	145	141	138	134	131
1350	246	240	233	228	222	216	211	206	201	196	192	187	183	178	174	170	166	162	158	155	151	147	144	140	137	134
1365	249	243	237	231	225	220	214	209	204	199	195	190	186	181	177	173	169	165	161	157	154	150	146	143	140	136
1380	253	246	240	234	228	223	217	212	207	202	198	193	189	184	180	176	172	168	164	160	156	153	149	146	142	139
1395	256	250	243	237	232	226	221	215	210	205	201	196	192	187	183	179	175	171	167	163	159	155	152	148	145	141
1410	260	253	247	241	235	229	224	218	213	208	204	199	194	190	186	182	177	173	170	166	162	158	155	151	148	144
1425	263	256	250	244	238	232	227	222	216	211	207	202	197	193	189	184	180	176	172	168	165	161	157	154	150	147
1440	266	260	253	247	241	235	230	225	219	214	210	205	200	196	192	187	183	179	175	171	167	164	160	156	153	149
1455	270	263	257	250	244	239	233	228	223	218	213	208	203	199	194	190	186	182	178	174	170	166	163	159	156	152
1470	273	266	260	254	248	242	236	231	226	221	216	211	206	202	197	193	189	185	181	177	173	169	165	162	158	155
1485	277	270	263	257	251	245	239	234	229	224	219	214	209	205	200	196	192	187	183	180	176	172	168	164	161	157
1500	280	273	266	260	254	248	243	237	232	227	222	217	212	207	203	199	194	190	186	182	178	175	171	167	164	160
1515	283	276	270	263	257	251	246	240	235	230	225	220	215	210	206	202	197	193	189	185	181	177	174	170	166	163
1530	287	280	273	267	260	255	249	243	238	233	228	223	218	213	209	204	200	196	192	188	184	180	176	173	169	165
1545	290	283	276	270	264	258	252	246	241	236	231	226	221	216	212	207	203	199	195	191	187	183	179	175	172	168
1560	294	286	280	273	267	261	255	249	244	239	234	229	224	219	215	210	206	202	197	193	189	185	182	178	174	171
1575	297	290	283	276	270	264	258	253	247	242	237	232	227	222	217	213	209	204	200	196	192	188	184	181	177	173
1590	300	293	286	280	273	267	261	256	250	245	240	235	230	225	220	216	211	207	203	199	195	191	187	183	180	176
1605	304	297	290	283	277	270	264	259	253	248	243	238	233	228	223	219	214	210	206	202	198	194	190	186	182	179
1620	307	300	293	286	280	274	268	262	256	251	246	241	236	231	226	222	217	213	209	204	200	196	192	189	185	181
1635	311	303	296	289	283	277	271	265	259	254	249	243	239	234	229	224	220	216	211	207	203	199	195	191	188	184
1650	314	307	300	293	286	280	274	268	262	257	252	246	241	237	232	227	223	218	214	210	206	202	198	194	190	187
1665	317	310	303	296	289	283	277	271	265	260	255	249	244	239	235	230	226	221	217	213	209	205	201	197	193	189
1680	321	313	306	299	293	286	280	274	268	263	258	252	247	242	238	233	228	224	220	215	211	207	203	199	196	192
1695	324	317	309	302	296	289	283	277	272	266	261	255	250	245	241	236	231	227	222	218	214	210	206	202	198	194
1710	328	320	313	306	299	293	286	280	275	269	264	258	253	248	243	239	234	230	225	221	217	213	209	205	201	197
1725	331	323	316	309	302	296	290	283	278	272	267	261	256	251	246	242	237	232	228	224	220	215	211	207	204	200
1740	334	327	319	312	305	299	293	287	281	275	270	264	259	254	249	244	240	235	231	226	222	218	214	210	206	202
1755	338	330	323	315	309	302	296	290	284	278	273	267	262	257	252	247	243	238	234	229	225	221	217	213	209	205
1770	341	333	326	319	312	305	299	293	287	281	276	270	265	260	255	250	245	241	236	232	228	224	219	215	212	208
1785	345	337	329	322	315	308	302	296	290	284	279	273	268	263	258	253	248	244	239	235	231	226	222	218	214	210
1800	348	340	333	325	318	312	305	299	293	287	282	276	271	266	261	256	251	246	242	238	233	229	225	221	217	213
1815	351	343	336	329	322	315	308	302	296	290	285	279	274	269	264	259	254	249	245	240	236	232	228	224	220	216
1830	355	347	339	332	325	318	311	305	299	293	288	282	277	271	266	262	257	252	248	243	239	234	230	226	222	218
1845	358	350	342	335	328	321	315	308	302	296	291	285	280	274	269	264	260	255	250	246	241	237	233	229	225	221
1860	362	353	346	338	331	324	318	311	305	299	294	288	283	277	272	267	262	258	253	249	244	240	236	232	228	224
1875	365	357	349	342	334	327	321	314	308	302	297	291	285	280	275	270	265	261	256	251	247	243	238	234	230	226
1890	368	360	352	345	338	331	324	318	311	305	300	294	288	283	278	273	268	263	259	254	250	245	241	237	233	229
1905	372	364	356	348	341	334	327	321	314	308	303	297	291	286	281	276	271	266	261	257	252	248	244	240	236	232
1920	375	367	359	351	344	337	330	324	317	311	306	300	294	289	284	279	274	269	264	260	255	251	247	242	238	234
1935	379	370	362	355	347	340	333	327	321	314	309	303	297	292	287	282	277	272	267	262	258	254	249	245	241	237
1950	382	374	366	358	350	343	336	330	324	317	312	306	300	295	290	284	279	275	270	265	261	256	252	248	244	240
1965	385	377	369	361	354	346	340	333	327	320	314	309	303	298	292	287	282	277	273	268	263	259	255	250	246	242
1980	389	380	372	364	357	350	343	336	330	323	317	312	306	301	295	290	285	280	275	271	266	262	257	253	249	245
1995	392	384	375	368	360	353	346	339	333	327	320	315	309	303	298	293	288	283	278	273	269	264	260	256	252	247
2010	396	387	379	371	363	356	349	342	336	330	323	318	312	306	301	296	291	286	281	276	272	267	263	258	254	250
2025	399	390	382	374	366	359	352	345	339	333	326	321	315	309	304	299	294	289	284	279	274	270	265	261	257	253
2040	402	394	385	377	370	362	355	348	342	336	329	324	318	312	307	302	296	291	287	282	277	273	268	264	260	255
2055	406	397	389	381	373	366	358	352	345	339	332	327	321	315	310	304	299	294	289	285	280	275	271	267	262	258
2070	409	400	392	384	376	369	362	355	348	342	335	329	324	318	313	307	302	297	292	287	283	278	274	269	265	261
2085	413	404	395	387	379	372	365	358	351	345	338	332	327	321	315	310	305	300	295	290	285	281	276	272	268	263
2100	416	407	399	390	383	375	368	361	354	348	341	335	330	324	318	313	308	303	298	293	288	284	279	275	270	266
2115	419	410	402	394	386	378	371	364	357	351	344	338	332	327	321	316	311	305	300	296	291	286	282	277	273	269
2130	423	414	405	397	389	381	374	367	360	354	347	341	335	330	324	319	313	308	303	298	294	289	284	280	276	271
2145	426	417	408	400	392	385	377	370	363	357	350	344	338	333	327	322	316	311	306	301	296	292	287	283	278	274
2160	430	420	412	403	395	388	380	373	366	360	353	347	341	335	330	324	319	314	309	304	299	294	290	285	281	277
2175	433	424	415	407	399	391	383	376	369	363	356	350	344	338	333	327	322	317	312	307	302	297	293	288	284	279
2190	436	427	418	410	402	394	387	379	373	366	359	353	347	341	336	330	325	320	314	309	305	300	295	291	286	282
2205	440	431	422	413	405	397	390	383	376	369	362	356	350	344	339	333	328	322	317	312	307	303	298	293	289	285
2220	443	434	425	416	408	400	393	386	379	372	365	359	353	347	341	336	330	325	320	315	310	305	301	296	292	287
2235	447	437	428	420	411	404	396	389	382	375	368	362	356	350	344	339	333	328	323	318	313	308	303	299	294	290
2250	450	441	432	423	415	407	399	392	385	378	371	365	359	353	347	342	336	331	326	320	316	311	306	301	297	293
2265	453	444	435	426	418	410	402	395	388	381	374	368	362	356	350	344	339	334	328	323	318	313	309	304	300	295
2280	457	447	438	429	421	413	405	398	391	384	377	371	365	359	353	347	342	336	331	326	321	316	311	307	302	298
2295	460	451	441	433	424	416	409	401	394	387	380	374	368	362	356	350	345	339	334	329	324	319	314	309	305	300
2310	464	454	445	436	428	419	412	404	397	390	383	377	371	365	359	353	347	342	337	332	327	322	317	312	308	303
2325	467	457	448	439	431	423	415	407	400	393	386	380	374	367	362	356	350	345	339	334	329	324	320	315	310	306
2340	470	461	451	442	434	426	418	410	403	396	389	383	377	370	364	359	353	348	342	337	332	327	322	318	313	308
2355	474	464	455	446	437	429	421	414	406	399	392	386	379	373	367	362	356	350	345	340	335	330	325	320	316	311
2370	477	467	458	449	440	432	424	417	409	402	395	389	382	376	370	364	359	353	348	343	338	333	328	323	318	314
2385	481	471	461	452	444	435	427	420	412	405	398	392	385	379	373	367	362	356	351	345	340	335	330	326	321	316
2400	484	474	465	455	447	438	430	423	415	408	401	395	388	382	376	370	364	359	353	348	343	338	333	328	324	319
2415	487	477	468	459	450	442	434	426	418	411	404	398	391	385	379	373	367	362	356	351	346	341	336	331	326	322
2430	491	481	471	462	453	445	437	429	422	414	407	401	394	388	382	376	370	364	359	354	348	343	338	334	329	324
2445	494	484	474	465	456	448	440	432	425	417	410	404	397	391	385	379	373	367	362	356	351	346	341	336	332	327
2460	498	487	478	469	460	451	443	435	428	420	413	407	400	394	388	382	376	370	365	359	354	349	344	339	334	330
2475	501	491	481	472	463	454	446	438	431	423	416	410	403	397	390	384	379	373	367	362	357	352	347	342	337	332
2490	504	494	484	475	466	458	449	441	434	426	419	413	406	399	393	387	381	376	370	365	359	354	349	344	340	335
2505	508	497	488	478	469	461	452	444	437	429	422	415	409	402	396	390	384	378	373	367	362	357	352	347	342	338
2520	511	501	491	482	473	464	456	448	440	432	425	418	412	405	399	393	387	381	376	370	365	360	355	350	345	340
2535	515	504	494	485	476	467	459	451	443	436	428	421	415	408	402	396	390	384	378	373	368	362	357	352	348	343
2550	518	508	498	488	479	470	462	454	446	439	431	424	418	411	405	399	393	387	381	376	370	365	360	355	350	346
2565	521	511	501	491	482	473	465	457	449	442	434	427	421	414	408	402	396	390	384	379	373	368	363	358	353	348
2580	525	514	504	495	485	477	468	460	452	445	437	430	424	417	411	404	398	393	387	381	376	371	366	361	356	351
2595	528	518	507	498	489	480	471	463	455	448	440	433	426	420	413	407	401	395	390	384	379	373	368	363	358	353
2610	532	521	511	501	492	483	474	466	458	451	443	436	429	423	416	410	404	398	392	387	381	376	371	366	361	356
2625	535	524	514	504	495	486	477	469	461	454	446	439	432	426	419	413	407	401	395	390	384	379	374	369	364	359
2640	538	528	517	508	498	489	481	472	464	457	449	442	435	429	422	416	410	404	398	392	387	382	376	371	366	361
2655	542	531	521	511	501	492	484	475	467	460	452	445	438	431	425	419	413	407	401	395	390	384	379	374	369	364
2670	545	534	524	514	505	496	487	479	471	463	455	448	441	434	428	422	415	409	404	398	392	387	382	377	372	367
2685	549	538	527	517	508	499	490	482	474	466	458	451	444	437	431	424	418	412	406	401	395	390	384	379	374	369
2700	552	541	531	521	511	502	493	485	477	469	461	454	447	440	434	427	421	415	409	403	398	392	387	382	377	372
2715	555	544	534	524	514	505	496	488	480	472	464	457	450	443	437	430	424	418	412	406	401	395	390	385	380	375
2730	559	548	537	527	517	508	499	491	483	475	467	460	453	446	439	433	427	421	415	409	403	398	393	387	382	377
2745	562	551	540	530	521	511	503	494	486	478	470	463	456	449	442	436	430	423	418	412	406	401	395	390	385	380
2760	566	554	544	534	524	515	506	497	489	481	473	466	459	452	445	439	432	426	420	414	409	403	398	393	388	383
2775	569	558	547	537	527	518	509	500	492	484	476	469	462	455	448	442	435	429	423	417	412	406	401	395	390	385
2790	572	561	550	540	530	521	512	503	495	487	479	472	465	458	451	444	438	432	426	420	414	409	403	398	393	388
2805	576	564	554	543	534	524	515	506	498	490	482	475	468	461	454	447	441	435	429	423	417	412	406	401	396	391
2820	579	568	557	547	537	527	518	510	501	493	485	478	471	463	457	450	444	437	431	426	420	414	409	403	398	393
2835	583	571	560	550	540	530	521	513	504	496	488	481	473	466	460	453	447	440	434	428	423	417	411	406	401	396
2850	586	575	564	553	543	534	524	516	507	499	491	484	476	469	462	456	449	443	437	431	425	420	414	409	404	399
2865	589	578	567	556	546	537	528	519	510	502	494	487	479	472	465	459	452	446	440	434	428	422	417	412	406	401
2880	593	581	570	560	550	540	531	522	513	505	497	490	482	475	468	462	455	449	443	437	431	425	420	414	409	404
2895	596	585	573	563	553	543	534	525	516	508	500	493	485	478	471	464	458	452	445	439	434	428	422	417	412	406
2910	600	588	577	566	556	546	537	528	519	511	503	496	488	481	474	467	461	454	448	442	436	431	425	420	414	409
2925	603	591	580	569	559	549	540	531	523	514	506	499	491	484	477	470	464	457	451	445	439	433	428	422	417	412
2940	606	595	583	573	562	553	543	534	526	517	509	501	494	487	480	473	466	460	454	448	442	436	430	425	420	414
2955	610	598	587	576	566	556	546	537	529	520	512	504	497	490	483	476	469	463	457	450	445	439	433	428	422	417
2970	613	601	590	579	569	559	550	540	532	523	515	507	500	493	486	479	472	466	459	453	447	441	436	430	425	420
2985	617	605	593	582	572	562	553	544	535	526	518	510	503	495	488	482	475	468	462	456	450	444	439	433	428	422
3000	620	608	597	586	575	565	556	547	538	529	521	513	506	498	491	484	478	471	465	459	453	447	441	436	430	425
3015	623	611	600	589	579	569	559	550	541	532	524	516	509	501	494	487	481	474	468	461	455	450	444	438	433	428
3030	627	615	603	592	582	572	562	553	544	535	527	519	512	504	497	490	483	477	470	464	458	452	447	441	436	430
3045	630	618	606	595	585	575	565	556	547	538	530	522	515	507	500	493	486	480	473	467	461	455	449	444	438	433
3060	634	621	610	599	588	578	568	559	550	542	533	525	518	510	503	496	489	482	476	470	464	458	452	446	441	436
3075	637	625	613	602	591	581	571	562	553	545	536	528	520	513	506	499	492	485	479	473	466	461	455	449	444	438
3090	640	628	616	605	595	584	575	565	556	548	539	531	523	516	509	502	495	488	482	475	469	463	457	452	446	441
3105	644	631	620	608	598	588	578	568	559	551	542	534	526	519	511	504	498	491	484	478	472	466	460	454	449	444
3120	647	635	623	612	601	591	581	571	562	554	545	537	529	522	514	507	500	494	487	481	475	469	463	457	452	446
3135	651	638	626	615	604	594	584	575	565	557	548	540	532	525	517	510	503	496	490	484	477	471	466	460	454	449
3150	654	641	630	618	607	597	587	578	568	560	551	543	535	527	520	513	506	499	493	486	480	474	468	463	457	452
3165	657	645	633	622	611	600	590	581	572	563	554	546	538	530	523	516	509	502	496	489	483	477	471	465	460	454
3180	661	648	636	625	614	603	593	584	575	566	557	549	541	533	526	519	512	505	498	492	486	480	474	468	462	457
3195	664	652	640	628	617	607	597	587	578	569	560	552	544	536	529	522	515	508	501	495	488	482	476	471	465	459
3210	668	655	643	631	620	610	600	590	581	572	563	555	547	539	532	524	517	511	504	497	491	485	479	473	468	462
3225	671	658	646	635	623	613	603	593	584	575	566	558	550	542	535	527	520	513	507	500	494	488	482	476	470	465
3240	674	662	649	638	627	616	606	596	587	578	569	561	553	545	537	530	523	516	509	503	497	491	485	479	473	467
3255	678	665	653	641	630	619	609	599	590	581	572	564	556	548	540	533	526	519	512	506	499	493	487	481	476	470
3270	681	668	656	644	633	622	612	602	593	584	575	567	559	551	543	536	529	522	515	508	502	496	490	484	478	473
3285	685	672	659	648	636	626	615	605	596	587	578	570	562	554	546	539	532	525	518	511	505	499	493	487	481	475
3300	688	675	663	651	640	629	618	609	599	590	581	573	564	557	549	542	534	527	521	514	508	501	495	489	484	478
3315	691	678	666	654	643	632	622	612	602	593	584	576	567	559	552	544	537	530	523	517	510	504	498	492	486	481
3330	695	682	669	657	646	635	625	615	605	596	587	579	570	562	555	547	540	533	526	520	513	507	501	495	489	483
3345	698	685	673	661	649	638	628	618	608	599	590	582	573	565	558	550	543	536	529	522	516	510	503	497	492	486
3360	702	688	676	664	652	641	631	621	611	602	593	585	576	568	560	553	546	539	532	525	519	512	506	500	494	489
3375	705	692	679	667	656	645	634	624	614	605	596	588	579	571	563	556	548	541	535	528	521	515	509	503	497	491
3390	708	695	682	670	659	648	637	627	617	608	599	590	582	574	566	559	551	544	537	531	524	518	512	506	500	494
3405	712	698	686	674	662	651	640	630	621	611	602	593	585	577	569	562	554	547	540	533	527	520	514	508	502	497
3420	715	702	689	677	665	654	644	633	624	614	605	596	588	580	572	564	557	550	543	536	530	523	517	511	505	499
3435	719	705	692	680	668	657	647	636	627	617	608	599	591	583	575	567	560	553	546	539	532	526	520	514	508	502
3450	722	708	696	683	672	661	650	640	630	620	611	602	594	586	578	570	563	555	548	542	535	529	522	516	510	505
3465	725	712	699	687	675	664	653	643	633	623	614	605	597	589	581	573	565	558	551	544	538	531	525	519	513	507
3480	729	715	702	690	678	667	656	646	636	626	617	608	600	591	584	576	568	561	554	547	541	534	528	522	516	510
3495	732	719	706	693	681	670	659	649	639	629	620	611	603	594	586	579	571	564	557	550	543	537	530	524	518	512
3510	736	722	709	696	685	673	662	652	642	632	623	614	606	597	589	582	574	567	560	553	546	540	533	527	521	515
3525	739	725	712	700	688	676	665	655	645	635	626	617	609	600	592	584	577	570	562	555	549	542	536	530	524	518
3540	742	729	715	703	691	680	669	658	648	638	629	620	611	603	595	587	580	572	565	558	552	545	539	532	526	520
3555	746	732	719	706	694	683	672	661	651	641	632	623	614	606	598	590	582	575	568	561	554	548	541	535	529	523
3570	749	735	722	709	697	686	675	664	654	644	635	626	617	609	601	593	585	578	571	564	557	550	544	538	532	526
3585	753	739	725	713	701	689	678	667	657	647	638	629	620	612	604	596	588	581	574	567	560	553	547	540	534	528
3600	756	742	729	716	704	692	681	671	660	651	641	632	623	615	607	599	591	584	576	569	563	556	549	543	537	531
3615	759	745	732	719	707	695	684	674	663	654	644	635	626	618	609	602	594	586	579	572	565	559	552	546	540	534
3630	763	749	735	722	710	699	687	677	666	657	647	638	629	621	612	604	597	589	582	575	568	561	555	548	542	536
3645	766	752	739	726	713	702	691	680	669	660	650	641	632	623	615	607	599	592	585	578	571	564	558	551	545	539
3660	770	755	742	729	717	705	694	683	673	663	653	644	635	626	618	610	602	595	587	580	573	567	560	554	548	542
3675	773	759	745	732	720	708	697	686	676	666	656	647	638	629	621	613	605	598	590	583	576	569	563	557	550	544
3690	776	762	748	735	723	711	700	689	679	669	659	650	641	632	624	616	608	600	593	586	579	572	566	559	553	547
3705	780	765	752	739	726	714	703	692	682	672	662	653	644	635	627	619	611	603	596	589	582	575	568	562	556	550
3720	783	769	755	742	730	718	706	695	685	675	665	656	647	638	630	622	614	606	599	591	584	578	571	565	558	552
3735	787	772	758	745	733	721	709	698	688	678	668	659	650	641	633	624	616	609	601	594	587	580	574	567	561	555
3750	790	775	762	748	736	724	712	701	691	681	671	662	653	644	635	627	619	612	604	597	590	583	576	570	564	558
3765	793	779	765	752	739	727	716	705	694	684	674	665	656	647	638	630	622	614	607	600	593	586	579	573	566	560
3780	797	782	768	755	742	730	719	708	697	687	677	668	658	650	641	633	625	617	610	602	595	589	582	575	569	563
3795	800	786	772	758	746	733	722	711	700	690	680	671	661	653	644	636	628	620	613	605	598	591	585	578	572	565
3810	804	789	775	761	749	737	725	714	703	693	683	674	664	655	647	639	631	623	615	608	601	594	587	581	574	568
3825	807	792	778	765	752	740	728	717	706	696	686	676	667	658	650	642	633	626	618	611	604	597	590	583	577	571
3840	810	796	781	768	755	743	731	720	709	699	689	679	670	661	653	644	636	628	621	614	606	599	593	586	580	573
3855	814	799	785	771	758	746	734	723	712	702	692	682	673	664	656	647	639	631	624	616	609	602	595	589	582	576
3870	817	802	788	775	762	749	738	726	715	705	695	685	676	667	658	650	642	634	626	619	612	605	598	591	585	579
3885	821	806	791	778	765	752	741	729	718	708	698	688	679	670	661	653	645	637	629	622	615	608	601	594	588	581
3900	824	809	795	781	768	756	744	732	722	711	701	691	682	673	664	656	648	640	632	625	617	610	603	597	590	584
3915	827	812	798	784	771	759	747	736	725	714	704	694	685	676	667	659	650	643	635	627	620	613	606	600	593	587
3930	831	816	801	788	774	762	750	739	728	717	707	697	688	679	670	662	653	645	638	630	623	616	609	602	596	589
3945	834	819	805	791	778	765	753	742	731	720	710	700	691	682	673	664	656	648	640	633	626	619	612	605	598	592
3960	838	822	808	794	781	768	756	745	734	723	713	703	694	685	676	667	659	651	643	636	628	621	614	608	601	595
3975	841	826	811	797	784	772	759	748	737	726	716	706	697	687	679	670	662	654	646	638	631	624	617	610	604	597
3990	844	829	814	801	787	775	763	751	740	729	719	709	700	690	682	673	665	657	649	641	634	627	620	613	606	600
4005	848	832	818	804	791	778	766	754	743	732	722	712	703	693	684	676	667	659	652	644	637	629	622	616	609	603
4020	851	836	821	807	794	781	769	757	746	735	725	715	705	696	687	679	670	662	654	647	639	632	625	618	612	605
4035	855	839	824	810	797	784	772	760	749	738	728	718	708	699	690	682	673	665	657	649	642	635	628	621	614	608
4050	858	842	828	814	800	787	775	763	752	741	731	721	711	702	693	684	676	668	660	652	645	638	631	624	617	611

[gingerhuny]

1. Risk and Reward for Low Defense: Characters with low defense stats are at a higher risk due to the division by defense in the formula. However, if such characters also have high attack stats, they can potentially deal massive damage before getting hit. This creates a risk-reward scenario, making gameplay more dynamic and strategic.
2. Scaling for Various Scenarios: The formula scales well for both ‘David vs. Goliath’ and ‘Equal Power’ scenarios. In an ‘Equal Power’ situation where both attack and defense are similar, the damage done is moderate, making battles longer and more tactical. In ‘David vs. Goliath’ scenarios, where there’s a significant difference between attack and defense, the formula allows for potential upsets, making the game more exciting.
3. Avoiding Snowballing: In many games, a slight lead in stats can snowball into an insurmountable advantage. The division by defense in this formula can act as a counterbalance. Even if a character is significantly stronger, if they have low defense, they can still be defeated, thus preventing a runaway leader scenario.
4. Diverse Character Builds: The formula’s sensitivity to both high attack and low defense encourages diverse character builds. Players may opt for a balanced approach, maximizing both attack and defense, or may specialize, maximizing one stat at the expense of the other, which can still be effective but requires different strategies.
5. Complex Decision-making: The formula isn’t straightforward, meaning players will need to think critically about how they allocate their stats. This adds an extra layer of strategy to the game, as players must consider not just raw numbers but also how those numbers interact.
6. Tactical Gameplay: Because the formula incorporates both attack and defense in a non-linear manner, it encourages players to think tactically. For instance, using a special move that temporarily boosts attack could be far more effective when the enemy’s defense is lowered, adding a layer of depth to combat.
7. Late-Game Viability: As characters level up and both attack and defense stats increase, the formula ensures that both stats remain relevant. This ensures that early-game characters and strategies do not become obsolete, maintaining game balance throughout different stages of gameplay.
8. Check and Balance: The linear terms in the formula act as a check and balance for the ratio term. While the ratio term can potentially cause very high or low damage, the linear terms ensure that the damage remains within a reasonable range.

[gingerhuny]

Using the formula… Here is a chart for complete space constructed in same format as the very original post, for various attack (600-15,000) and defense (600-3000) numbers and respective damage…
Hope one can see, that fitting a single curve done by original author, while seems reasonable (and even effective to some extent), doesn’t cover the entire space

[yelnats_24]

Anyone know whose defense is used to calculate damage received in Musketeer’s Cover? Is it the defense of the hero protected by Cover or the defense of the hero providing Cover?