I've been playing with the Zodiac and Excelsis rings while waiting for placeholders camping Drooling Daisy for a Magian trial sequence I'll probably never finish, so I can shed a little light on them.
Zodiac Ring seems to give approximately a 3% boost to the damage of spells of the current day's element, rounded down. How and where it's built into the magic damage calculation, I'm not entirely sure, obviously, heh.
Data supporting this inside the spoiler block, not particularly cleaned up but hopefully comprehensible:
FIRESDAY
fire1, ochu:
128 ring
128 ring
125
125
128 ring
3/125 = .0240 (next value up (4/125) = .032)
fire1, poison leech
134 ring
134 ring
134 ring
131
131
3/131 = .0229 (next value up = .0305)
fire1, poison leech:
129
129
129
132 ring
146 ring <-- day bonus proc
3/128 = .0234 (next value up = .0313)
fire1 poison leech
134 ring
134 ring
134 ring
131
131
3/131 = .0229 (next value up = .0305)
fire2, poison leech:
292 ring
284
320 ring <-- day bonus proc
8/284 = .0282 (next value up = .0317)
fire3, poison leech:
569 ring
553
16/553 = .0289 (next value up = .0307)
fire3, ochu
541
557 ring
16/541 = .0296 (next value up = .0314)
fire3, poison leech:
553
624 ring
probable day bonus proc
fire3, ochu
613 ring
544
probable day bonus proc
fire2, poison leech
315 ring
285
probable day bonus proc
fire2, ochu
276
284 ring
302 <-- day bonus proc
310 ring <-- day bonus proc
276
8/276 = .0290 (next value up = .0326)
8/302 = .0265 (next value up = .0298 )
fire3, poison leech
608 <-- day bonus proc
569 ring
fire2, poison leech
321 ring
313
8/313 = .0256 (next value up = .0288 )
fire3, ochu
544
560 ring
16/544 = .0294 (next value up = .0313)
EARTHDAY
stone3, ochu
460 ring
407
probable day bonus proc
stone1, clipper
29 <-- resist
55 ring
54
55 ring
54
55 ring
54
55 ring
59 <-- day bonus proc
55 ring
55 ring
1/54 = .0185 (next value up = .0385)
stone2, ochu
192
197 ring
5/192 = .0260 (next value up = .0313)
WINDSDAY
aero2, ochu
243 ring
260 <-- day bonus proc
267 ring <-- day bonus proc
237
267 ring <-- day bonus proc
237
6/237 = .0253 (next value up = .0295)
7/260 = .0269 (next value up = .0308 )
aero1, poison leech
103
105 ring
103
105 ring
103
105 ring
2/103 = .0194 (next value up = .0231) ***
aero3, poison leech
504 ring
490
14/490 = .0286 (next value up = .0306)
(*** upper bound is abnormally low.)
Intersection of all lower/upper bounds ignoring ***:
empty set, .0296 to .0288...
Excelsis is much more of a pain to test, naturally. I gave it a shot by spamming aspir on crabs, alternating with and without ring, until they were empty, throwing out the last aspir amount before 0, and throwing out the last full result if it led to an uneven number of ring/no ring uses on a particular crab, and then checked the stats for with and without ring. Eleven crabs total, before I got my 3 kills and was entirely sick of it, which isn't really an adequate sample size, but I may as well post it anyway. Results were:
With ring:
(max, min) = (98,24)
quartiles (third, median, first) = (85, 70, 59)
average = 69.4
Without ring:
(max, min) = (94, 10)
quartiles (third, median, first) = (75.5, 69, 56.5)
average = 66.2
So a very small improvement in damage alleged, on the general order of 5% (just comparing averages). Again, though, the sample size is too small, your mileage may vary, caveat emptor, etc.
Here's the data for this testing:
clipper #1
72 aspir
98 aspir (ring)
55 aspir
76 aspir (ring)
74 aspir
69 aspir (ring)
74 aspir
93 aspir (ring)
63 aspir (ring)
69 aspir
89 aspir (ring)
1 aspir <-- crab empty, throwing out previous line too, to even out
0
clipper #2
91 aspir (ring)
78 aspir
54 aspir
30 aspir (ring)
57 aspir
77 aspir (ring)
82 aspir
62 aspir (ring)
47 aspir
59 aspir (ring)
47 aspir
60 aspir (ring) <-- crab empty, throw out previous to even out
0
clipper #3
61 aspir
97 aspir (ring)
72 aspir
59 aspir (ring)
51 aspir
90 aspir (ring)
80 aspir
59 aspir (ring)
75 aspir
73 aspir (ring)
88 aspir
28 aspir (ring) <-- crab empty, throw out previous to even out
0
clipper #4
94 aspir (ring)
48 aspir
69 aspir (ring)
78 aspir
81 aspir (ring)
71 aspir
50 aspir (ring)
94 aspir
61 aspir (ring)
72 aspir
84 aspir (ring) <-- crab empty
0
clipper #5
72 aspir
92 aspir (ring)
59 aspir
24 aspir (ring)
10 aspir
89 aspir (ring)
71 aspir (ring)
58 aspir
39 aspir (ring)
27 aspir
82 aspir (ring)
34 aspir <-- crab empty, throw out previous to even out
0
clipper #6
56 aspir (ring)
71 aspir
59 aspir (ring)
80 aspir
92 aspir (ring)
77 aspir
87 aspir (ring)
56 aspir
82 aspir (ring)
36 aspir <-- crab empty, throw out previous to even out
0
clipper #7
77 aspir (ring)
58 aspir
65 aspir (ring)
56 aspir
60 aspir (ring)
87 aspir
73 aspir (ring)
55 aspir
91 aspir (ring)
88 aspir
90 aspir (ring)
33 aspir <-- crab empty, throw out previous to even out
0
clipper #8
67 aspir
70 aspir (ring)
50 aspir
77 aspir (ring)
74 aspir
29 aspir (ring)
68 aspir
58 aspir (ring)
74 aspir
80 aspir (ring)
43 aspir <-- crab empty
0
clipper #9
81 aspir (ring)
67 aspir
64 aspir (ring)
47 aspir
79 aspir (ring)
81 aspir
56 aspir (ring)
70 aspir
50 aspir (ring)
52 aspir
49 aspir (ring)
76 aspir
61 aspir (ring) <-- crab empty
0
clipper #10
78 aspir
87 aspir (ring)
75 aspir
62 aspir (ring)
88 aspir
51 aspir (ring)
62 aspir
70 aspir (ring)
66 aspir
43 aspir (ring)
87 aspir
33 aspir (ring) <-- crab empty, throw out previous to even out
0
clipper #11
67 aspir
54 aspir (ring)
84 aspir
94 aspir (ring)
52 aspir
66 aspir (ring)
66 aspir
88 aspir (ring)
57 aspir
83 aspir (ring)
64 aspir
27 aspir (ring) <-- crab empty, throw out previous to even out
0
Testing the Griffon Ring seems a little above my pay grade. I'm tempted to put it in my idle set since I seem to get critted every other round when I pull hate, but composing and running a decent test is daunting.
(Just for clarity's sake- all mobs listed in the data are in Rolanberry Field around the lake at the back door of Crawler's Nest. All tests were done on rdm80/blm40 without elemental staves (magian sword, heh), and with a fairly random mix of gear on I could list, but I don't think is relevant so not bothering with it right now.)