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Tests

Multiple-Target Damage Reduction

In this test, I set out to confirm the damage reduction from area of effect Elemental Magic spells hitting multiple targets, as well as this term's place in the overall magic damage calculation. The test subjects were Huge Hornets in North Gustaberg. These are known to possess an INT value of 5, although I have personally verified this as well.

Initial Results

In the first phase of this test, I cast Thundaga 3 eleven times, on increasing numbers of total targets per cast. As a Hume BLM/RDM with 5 merits in INT and 5 merits in Lighting Magic Potency, I equipped myself with INT+28, MAB+8 with no staff, to bring my total INT to 105 and MAB to 1.5. This kept the dINT value at 100 throughout this phase of the test. Testing was done on a neutral day of the week, and no weather was present. For reference, the applicable subformula of the magic damage formula (using "[ ]" as shorthand for the floor function throughout) is:

[[(dINT * M) + V] * MAB] = [[(100 * 1.5) + 697] * 1.5] = [847 * 1.5] = [1270.5] = 1270

Targets	Damage	Possible Multiplier	Possible V
1	1270	1	697
2	1015	.8	527
3	952	.75	485
4	888	.7	442
5	825	.65	400
6	762	.6	358
7	697	.55	315
8	634	.5	273
9	571	.45	231
10	507	.4	188
11	507	.4	188

This suggests, as I have indicated in the third and fourth column of the table, that for two or more targets there is either a fractional decrease in total damage from an additional multiplier, or that there is a preprogrammed alternate V value for multiple targets. It also suggests that for 10 or more targets the decreased damage per target remains the same. Furthermore, if it is in fact an additional multiplier, it is calculated prior to MAB, since:

[[847 * 1.5] * .8] = [1270 * .8] = 1016

while

[[847 * .8] * 1.5] = [677 * 1.5] = 1015

the value achieved in the test.

Determining the Type of Reduction

In this phase of the test, I equipped myself with a total of 104 INT (dINT = 99) and 1.5 MAB, and cast Thundaga 3 on two hornets. If the reduced damage results from an additional multiplier, then the resulting value should be:

[[[(99 * 1.5) + 697] * .8] * 1.5] = [[845 * .8] * 1.5] = [676 * 1.5] = 1014

Whereas, if the reduced value results from a different V value for multiple targets, then by the above result, the calculation for the damage equation gives:

[[(99 * 1.5) + 527] * 1.5] = [675 * 1.5] = 1012

The result was 1014, confirming that the decrease results from an additional multiplier in the damage calculation.

Determining the Placement of the Term with Respect to the Overall Formula

The parts of the of damage formula ordering which have so far been confirmed are that the calculation of D precedes the resist term, which precedes the staff bonus term, which precedes the Day/Weather term, which precedes the MAB term, and that the Magic Burst term also precedes the MAB term. I next checked the placement of the AoE reduction term with respect to the staff bonus term, however as you will see that its relationship to the staff bonus term is implied by its relationship to the resist term, I will omit the results of my staff bonus tests in the interests of brevity. For this next test, I forced my INT to 109 (dINT = 104) and MAB again to 1.5. I then continued to gather pairs of bees and cast Thundaga 3 on them until one resisted the spell. For a 1/2 resist, the outcome if the resist term was calculated prior to the AoE reduction term would be:

[[[[(104 * 1.5) + 697] * .5] * .8] * 1.5] = [[[853 * .5] * .8] * 1.5] = [[426 * .8] * 1.5] = [340 * 1.5] = 510

while the outcome were the AoE term calculated first would be:

[[[[(104 * 1.5) + 697] * .8] * .5] * 1.5] = [[[853 * .8] * .5] * 1.5] = [[682 * .5] * 1.5] = [341 * 1.5] = 511

The result was 511, confirming that the multiple-target damage reduction is calculated prior to the resist term.

Comments

Please feel free to ask any questions or make any comments regarding this test in this subsection.

M and V data

The goal for this test was to confirm the values for M and V for all of the Black Magic damage spells. Over three separate tests I confirmed the values for every spell in this family except for the Ancient Magic series II spells. While I used the data to determine the values independently from previous figures, I will present it here simply in a collection of tables, and anyone concerned with the accuracy of the results can verify the values in the table with the formula and the screenshots of the damage in the chat log. The MAB I used was 1.5 throughout, as that would ensure that the damage would increase by at least one point per change in dINT after flooring. The relevant portion of the magic damage formula for the entire series of tests is [[dINT*M + V] * 1.5], where "[]" indicates flooring.

Test I

This was done in North Gustaberg against Huge Hornets. I varied my dINT to 100, 101, and 102 for each spell in this test. I actually tested the series II single-target spells here as well, to compare with the second test and ensure that I didn't hit the inflection point for adding INT, but they agree with the values in Test 2 below until Stone II, so I will omit them here.

TABLE I
Spell	V	M	100	101	102
Stone III	210	1.5	540	541	544
Water III	236	1.5	579	583	540
Aero III	265	1.5	622	624	627
Fire III	295	1.5	667	669	672
Blizzard III	320	1.5	705	706	709
Thunder III	345	1.5	742	744	747
Spell	V	M	100	101	102
Stone IV	381	2	871	874	877
Water IV	410	2	915	918	921
Aero IV	440	2	960	963	966
Fire IV	472	2	1008	1011	1014
Blizzard IV	506	2	1059	1062	1065
Thunder IV	541	2	1111	1114	1117

Test II

These tests were performed with Nivlakian's help against Aht Urhgan Attercops. He cast Blizzard IV or Thunder IV with fixed INT and MAB, which we used to calculate the individual spider's INT, then I adjusted my INT to achieve a dINT of 0 and 5 for each spell. Please note, the tests for single-target Aero I/II and Stone I/II were done on Windsday, so when referencing the screenshots use the lower Aero damage and the higher Stone damage.

TABLE II
Spell	V	M	0	5
Stone	10	1	15	22
Water	16	1	24	31
Aero	25	1	37	45
Fire	35	1	52	60
Blizzard	46	1	69	76
Thunder	60	1	90	97
Spell	V	M	0	5
Stone II	78	1	117	124
Water II	95	1	142	150
Aero II	113	1	169	177
Fire II	133	1	199	207
Blizzard II	155	1	232	240
Thunder II	178	1	267	274
Spell	V	M	0	5
Stonega	56	1	84	91
Waterga	74	1	111	118
Aeroga	93	1	139	147
Firaga	120	1	180	187
Blizzaga	145	1	217	225
Thundaga	172	1	258	265
Spell	V	M	0	5
Stonega II	201	1	301	309
Waterga II	232	1	348	355
Aeroga II	266	1	399	406
Firaga II	312	1	468	475
Blizzaga II	350	1	525	532
Thundaga II	392	1.5	588	598
Spell	V	M	0	5
Stonega III	434	1.5	651	661
Waterga III	480	1.5	720	730
Aeroga III	527	1.5	790	801
Firaga III	589	1.5	883	894
Blizzaga III	642	1.5	963	973
Thundaga III	697	1.5	1045	1056
Spell	V	M	0	5
Freeze	526	2	789	804
Tornado	552	2	828	843
Flood	630	2	945	960
Flare	657	2	985	1000

Test III

When analyzing the data, I noticed a problem with the recorded images for Quake and Burst, so I returned to North Gustaberg to retest those spells. I used dINT of 80 and 100 for this test.

TABLE III
Spell	V	M	80	100
Quake	577	2	1105	1165
Burst	603	2	1144	1204

Image Record

Aero4 Stone4:

Aero1/2 Stone1/2 dINT0:

Aero1/2 Stone1/2 dINT5:

Aeroga 1/2/3 dINT0 dINT5:

Freeze dINT0 dINT5:

Blizzaga 1/2/3 dINT0 dINT5:

Fire3 Aero3:

Fire4 Water4:

Fire1/2 Water1/2 dINT0:

Fire1/2 Water1/2 dINT5:

Firaga1/2/3 dINT0 dINT5:

Quake Burst dINT80 dINT100:

Stonega 1/2/3 Waterga1/2/3 dINT0:

Stonega 1/2/3 Waterga1/2/3 dINT5:

Thunder3 Blizzard3:

Thunder4 Blizzard4:

Thunder1/2 Blizzard1/2 dINT0:

Thunder1/2 Blizzard1/2 dINT5:

Thundaga1/2/3 dINT0 dINT5:

Water3 Stone3:

Flood Tornado Flare dINT0 dINT5: