updates:

Spoiler
8/25/16: updated for 4.7 relics (including sheets). removed squish summary since no elemental damage is being assumed and the numbers are in the tables.
8/12/16: preliminary 4.7 relic info http://www.swtor.com/community/showp…2&postcount=56
2/25/16: updated for shield added to relics.
10/29/15: updated for new 4 set for sins. fixed inconsistent relic contributions (pt and jugg had crusader relic only giving 460 shield and absorb).
10/28/15: added 198 bmods numbers.
10/27/15b: updated for only 220 b mods being available, and using 1 dps relic for bmod setup
10/27/15a: updated armor rating values, added new force scream bubble values.
10/26/15: updated bulwark/bastion numbers for better regression about p=0.55
10/24/15: updated for new bulwark math and fixed some bad results.
10/22/15: using new format for damage weights where fraction melee varies from 1 to 0.1, the rest is taken as force/tech kinetic energy. updated for corrected 224 gear pool and defense values, and relic contributions.

These are suggested defense, (d), shield (s) and absorb (a) ratings for various gear sets. right now this assumes nothing has changed in defense, shield absorb equations other than the level. new format uses fraction melee damage (m) as tabulating header. high melee/ranged bosses would be closer to m=1, and high force/tech bosses are closer to m=0.1
boss_damage*squish – self _heals*heal_buff – heals_received*healer_buff*heal_buff – self_bubble – relic bubble = damage taken. Squish is the fraction of damage taken, so the lower the better. I have assumed 6,000 dps for these calcs.

Just copy the tabled sections and paste into notepad, it will look alot better.

I optimized the stats for the relics which provide best mitigation. Relic shorthand used:
D: Fortunate Redoubt (defense)
A: Shield Amplification (absorb)
S: Shrouded Crusader (shield and absorb) on Use
W: Reactive Warding (bubble)
E: Eternal Defender (shield and absorb) Proc

reactive warding relic best if boss dps < relic_bubble/((squish_with_relic – squish_without_relic)*cooldown). I have =ward in the tables that shows what the boss dps has to be to make the 2nd best relic for that fight better than the reactive warding relic.

Please find my errors.

BUGS:
need to know if accuracy changes affect boss accuracy
because no internal/elemental damage is being assumed, the squish numbers do not reflect true tank performance

220 BMODS:

Spoiler
sin m=1 m=0.9 m=0.8 m=0.7 m=0.6 m=0.5 m=0.4 m=0.3 m=0.2 m=0.1
d 2506 2506 2506 2506 2506 2506 2506 2506 2506 2506
s 1288 1295 1301 1306 1311 1315 1318 1320 1322 1323
a 1458 1451 1445 1440 1435 1431 1428 1426 1424 1423
base 0.17317 0.19157 0.20988 0.22813 0.24630 0.26442 0.28249 0.30052 0.31852 0.33650
D 0.17000 0.18873 0.20736 0.22593 0.24442 0.26286 0.28125 0.29959 0.31790 0.33619
A 0.17040 0.18848 0.20648 0.22440 0.24225 0.26005 0.27781 0.29552 0.31320 0.33086
S 0.17041 0.18849 0.20649 0.22442 0.24228 0.26008 0.27783 0.29555 0.31323 0.33088
E 0.16961 0.18760 0.20551 0.22335 0.24111 0.25882 0.27648 0.29410 0.31169 0.32925
relic WE WE WE WE WE WE WE WE WE WE
=ward 23372 23968 21724 19860 18290 16951 15797 14793 13914 13138
sigma 0.19118 0.20248 0.21092 0.21687 0.22057 0.22215 0.22169 0.21918 0.21457 0.20773

jugg m=1 m=0.9 m=0.8 m=0.7 m=0.5 m=0.4 m=0.3 m=0.2 m=0.1
d 2971 2506 2506 2506 2506 2506 2506 2506 2506 2506
s 1106 1352 1358 1358 1358 1358 1358 1358 1358 1358
a 1175 1394 1388 1388 1388 1388 1388 1388 1388 1388
base 0.17531 0.19076 0.20518 0.21960 0.23402 0.24844 0.26286 0.27728 0.29170 0.30612
D 0.17244 0.18771 0.20247 0.21722 0.23198 0.24674 0.26150 0.27626 0.29102 0.30578
A 0.17335 0.18863 0.20288 0.21714 0.23140 0.24565 0.25991 0.27417 0.28843 0.30268
S 0.17323 0.18853 0.20278 0.21703 0.23128 0.24553 0.25978 0.27403 0.28828 0.30252
E 0.17263 0.18788 0.20208 0.21629 0.23049 0.24469 0.25889 0.27309 0.28729 0.30149
relic WD WD WE WE WE WE WE WE WE WE
=ward 13451 12615 14191 14974 14051 13236 12510 11859 11273 10742
sigma 0.19797 0.19968 0.20237 0.20331 0.20245 0.19978 0.19522 0.18865 0.17982 0.16840

pt m=1 m=0.9 m=0.8 m=0.7 m=0.5 m=0.4 m=0.3 m=0.2 m=0.1
d 2506 2506 2506 2506 2506 2506 2506 2506 2506 2506
s 1589 1589 1589 1589 1589 1589 1589 1589 1589 1589
a 1157 1157 1157 1157 1157 1157 1157 1157 1157 1157
base 0.17436 0.18524 0.19611 0.20698 0.21785 0.22872 0.23960 0.25047 0.26134 0.27221
D 0.17169 0.18283 0.19397 0.20511 0.21625 0.22739 0.23853 0.24967 0.26081 0.27195
A 0.17170 0.18241 0.19311 0.20382 0.21452 0.22523 0.23594 0.24664 0.25735 0.26805
S 0.17160 0.18230 0.19300 0.20370 0.21440 0.22510 0.23580 0.24650 0.25720 0.26790
E 0.17080 0.18145 0.19210 0.20275 0.21340 0.22405 0.23470 0.24535 0.25600 0.26665
relic WE WE WE WE WE WE WE WE WE WE
=ward 13965 13146 12417 11765 11177 10646 10163 9722 9317 8945
sigma 0.16989 0.17715 0.18289 0.18723 0.19028 0.19210 0.19271 0.19214 0.19038 0.18738

224 UNLETTERED:

Spoiler
sin m=1 m=0.9 m=0.8 m=0.7 m=0.6 m=0.5 m=0.4 m=0.3 m=0.2 m=0.1
d 2931 2931 2931 2931 2931 2931 2931 2931 2931 2931
s 1309 1316 1323 1329 1334 1338 1341 1344 1346 1347
a 1481 1474 1467 1461 1456 1452 1449 1446 1444 1443
base 0.16691 0.18580 0.20460 0.22331 0.24196 0.26054 0.27907 0.29755 0.31600 0.33443
D 0.16429 0.18345 0.20251 0.22149 0.24040 0.25924 0.27803 0.29678 0.31549 0.33417
A 0.16425 0.18281 0.20128 0.21967 0.23799 0.25624 0.27444 0.29260 0.31073 0.32883
S 0.16426 0.18283 0.20130 0.21969 0.23801 0.25627 0.27447 0.29263 0.31075 0.32885
E 0.16349 0.18196 0.20035 0.21864 0.23687 0.25503 0.27314 0.29120 0.30923 0.32723
relic WE WE WE WE WE WE WE WE WE WE
=ward 27817 24784 22340 20329 18649 17227 16008 14955 14036 13228
sigma 0.19013 0.20208 0.21100 0.21729 0.22123 0.22296 0.22257 0.22006 0.21537 0.20837

jugg m=1 m=0.9 m=0.8 m=0.7 m=0.6 m=0.5 m=0.4 m=0.3 m=0.2 m=0.1
d 2980 2931 2931 2931 2931 2931 2931 2931 2931 2931
s 1349 1381 1381 1381 1381 1381 1381 1381 1381 1381
a 1392 1409 1409 1409 1409 1409 1409 1409 1409 1409
base 0.16964 0.18468 0.19967 0.21465 0.22964 0.24462 0.25961 0.27459 0.28958 0.30457
D 0.16687 0.18215 0.19741 0.21268 0.22795 0.24322 0.25848 0.27375 0.28902 0.30428
A 0.16775 0.18261 0.19743 0.21225 0.22706 0.24188 0.25670 0.27152 0.28634 0.30115
S 0.16765 0.18252 0.19733 0.21214 0.22695 0.24176 0.25657 0.27138 0.28619 0.30100
E 0.16708 0.18190 0.19666 0.21142 0.22618 0.24094 0.25569 0.27045 0.28521 0.29997
relic WD WE WE WE WE WE WE WE WE WE
=ward 13944 15221 16497 15346 14344 13466 12688 11996 11375 10815
sigma 0.19427 0.19923 0.20250 0.20384 0.20328 0.20081 0.19637 0.18980 0.18089 0.16925

pt m=1 m=0.9 m=0.8 m=0.7 m=0.6 m=0.5 m=0.4 m=0.3 m=0.2 m=0.1
d 2931 2931 2931 2931 2931 2931 2931 2931 2931 2931
s 1613 1613 1613 1613 1613 1613 1613 1613 1613 1613
a 1177 1177 1177 1177 1177 1177 1177 1177 1177 1177
base 0.16884 0.18014 0.19145 0.20276 0.21406 0.22537 0.23668 0.24798 0.25929 0.27060
D 0.16662 0.17815 0.18968 0.20121 0.21274 0.22426 0.23579 0.24732 0.25885 0.27037
A 0.16626 0.17739 0.18853 0.19966 0.21079 0.22193 0.23306 0.24420 0.25533 0.26646
S 0.16617 0.17729 0.18842 0.19955 0.21068 0.22180 0.23293 0.24406 0.25519 0.26632
E 0.16539 0.17647 0.18754 0.19862 0.20970 0.22077 0.23185 0.24292 0.25400 0.26507
relic WE WE WE WE WE WE WE WE WE WE
=ward 14442 13535 12736 12025 11390 10819 10302 9832 9404 9011
sigma 0.16974 0.17742 0.18347 0.18804 0.19124 0.19315 0.19379 0.19318 0.19131 0.18813

198 BMODS

Spoiler
sin m=1 m=0.9 m=0.8 m=0.7 m=0.6 m=0.5 m=0.4 m=0.3 m=0.2 m=0.1
d 1700 1318 1318 1318 1318 1318 1318 1318 1318 1318
s 1544 1758 1773 1776 1779 1781 1782 1783 1784 1783
a 1684 1852 1837 1834 1831 1829 1828 1827 1826 1827
base 0.17811 0.19380 0.20842 0.22300 0.23753 0.25202 0.26649 0.28093 0.29536 0.30978
D 0.17384 0.18945 0.20457 0.21963 0.23465 0.24963 0.26458 0.27950 0.29441 0.30931
A 0.17528 0.19073 0.20508 0.21941 0.23369 0.24793 0.26215 0.27635 0.29053 0.30471
S 0.17529 0.19076 0.20513 0.21946 0.23374 0.24799 0.26221 0.27640 0.29059 0.30476
E 0.17447 0.18987 0.20417 0.21842 0.23263 0.24681 0.26095 0.27508 0.28918 0.30329
relic WD WD WE WE WE WE WE WE WE WE
=ward 17324 17010 19188 20624 19282 18108 17072 16153 15333 14598
sigma 0.18722 0.19319 0.20037 0.20597 0.20997 0.21250 0.21360 0.21332 0.21166 0.20858

jugg m=1 m=0.9 m=0.8 m=0.7 m=0.5 m=0.4 m=0.3 m=0.2 m=0.1
d 2340 2340 1952 1472 1318 1318 1318 1318 1318 1318
s 1268 1268 1472 1728 1816 1816 1816 1816 1816 1816
a 1320 1320 1504 1728 1794 1794 1794 1794 1794 1794
base 0.18105 0.19536 0.20971 0.22282 0.23438 0.24565 0.25692 0.26819 0.27946 0.29073
D 0.17736 0.19203 0.20631 0.21927 0.23116 0.24296 0.25477 0.26658 0.27839 0.29020
A 0.17903 0.19317 0.20738 0.22039 0.23183 0.24298 0.25413 0.26528 0.27642 0.28757
S 0.17892 0.19305 0.20727 0.22030 0.23175 0.24290 0.25404 0.26519 0.27633 0.28748
E 0.17831 0.19239 0.20657 0.21957 0.23099 0.24209 0.25320 0.26431 0.27542 0.28653
relic WD WD WD WD WE WE WE WE WE WE
=ward 10447 11608 11337 10868 11983 14017 13402 12838 12321 11843
sigma 0.19650 0.20080 0.20011 0.19672 0.19459 0.19261 0.18936 0.18478 0.17876 0.17114

pt m=1 m=0.9 m=0.8 m=0.7 m=0.5 m=0.4 m=0.3 m=0.2 m=0.1
d 1506 1318 1318 1318 1318 1318 1318 1318 1318 1318
s 1942 2042 2049 2049 2049 2049 2049 2049 2049 2049
a 1480 1568 1561 1561 1561 1561 1561 1561 1561 1561
base 0.17817 0.18678 0.19502 0.20326 0.21150 0.21975 0.22799 0.23623 0.24447 0.25271
D 0.17430 0.18306 0.19172 0.20037 0.20903 0.21768 0.22634 0.23499 0.24364 0.25230
A 0.17550 0.18400 0.19211 0.20023 0.20835 0.21647 0.22459 0.23270 0.24082 0.24894
S 0.17542 0.18393 0.19204 0.20016 0.20827 0.21639 0.22450 0.23262 0.24073 0.24885
E 0.17462 0.18309 0.19117 0.19925 0.20733 0.21540 0.22348 0.23156 0.23964 0.24772
relic WD WD WE WE WE WE WE WE WE WE
=ward 9964 10382 11680 12418 11934 11486 11071 10685 10324 9988
sigma 0.16680 0.17260 0.17800 0.18255 0.18621 0.18905 0.19108 0.19235 0.19287 0.19263

Assumptions and Math

Spoiler
no cooldowns, just perfect execution. using new set bonuses
assuming 75% bland melee/ranged kinetic/energy damage.

unlettered assumptions: 116 defense from enhancements, 168 absorb/shield from enhancements, 128 defense from mod, 77 defense from each relic, 81 defense from stim, 1022 def/shield/absorb from augments. assuming implant/ear is equivalent to a mod+enhancement gives defense min of 2931 (mod,enhancement, relic, stim), and a pool of 5633.

220 lettered assumptions: 116 defense from enhancements, 168 absorb/shield from enhancements, 99 defense from mod, 77 defense from one relic, 81 defense from stim, 1022 def/shield/absorb from augments. assuming implant/ear is equivalent to a mod+enhancement gives defense min of 2506 (mod,enhancement, relic, stim), and a pool of 5208.

198 lettered assumptions: 116 defense from enhancements, 168 absorb/shield from enhancements, 72 defense/absorb from mod, 77 defense from one relic, 81 defense from stim, 1022 def/shield/absorb from augments. assuming implant/ear is equivalent to a mod+enhancement gives defense min of 1318 (mod,enhancement, relic, stim), and a pool of 4884.

heavy armor: 7450
light armor: 3987

definitions:
defense d, absorb a, shield s, (http://www.swtor.com/community/showthread.php?t=779094)
fraction m/r+k/e kw (w for weapon), fraction f/tr+k/e kf, fraction m/r i/e ew, fraction f/t +i/e ef,
fraction named fn, fraction bland fb,
damage reduction of k/e dr_k, damage reduction of i/e dr_e, damage reduction of m/r dr_w, damage reduction of f/t dr_f, overall damage reduction dr
rdd is dynamic relic buff to defense rating, rda is dynamic relic buff to absorb rating, rds is dynamic relic buff to shield rating. rsd is static relic buff to defense
parentheses without a * means a function of. like f(x,a,b)=a*x+b

kw_squish(d,s,a)= (0*d+[(1-d)*(1-s)+(1-d)*s*(1-a)]*(1-(dr_k+dr_w+dr)))
ew_squish(d,s,a)=(0*d+[(1-d)*(1-s)+(1-d)*s*(1-a)]*(1-(dr_e+dr_w+dr)))
kf_squish(d,s,a)=(0*r+[(1-r)*(1-s)+(1-r)*s*(1-a)]*(1-(dr_f+dr_k+dr)))
ef_squish(d,s,a)=(0*r+(1-r)*(1-(dr_e+dr_f+dr)))

squish(d,s,a)= kw*(fn*kw_squish(d)+fb*kw_squish(d+0.1)) + ew*ew_squish + kf*kf_squish + ef*ef_squish
def_relic_squish=6/22*squish(d+rdd+rsd,s,a) + ((22-6)/22)*squish(d+rsd,s,a)
two relics: 6/22*6/22*both_on+6/22*16/22*one_on+6/22*16/22*other_on+16/22*16/22*both_off
similar for other relics.

sigma= sqrt(sum(probability[ij]*(squish[ij] – squish)^2)
where i runs over kw_named, kw_bland, kf and ef (i thought there was ew damage, but i guess not)
and j runs over defended, resisted, shielded and full hit. note that squish[ij] differs from the squish previously calculated as it is independent of defense, shield and resistance. see the spreadsheet for more detail.

SHADOW

m/r dr:
0.05 slow time active

i/e dr:
0.10 willpower buff passive
0.10 technique mastery passive
0.02 old 4 set

overall dr:
0.02 elusiveness passive tree
0.02 mental fortitude passive tree
0.04 harnessed shadows active utility
0.006 224 2 set active .02*(3/10)
0.0114 198 4 set passive
0.02 186 4 set passive

endurance
0.01 companion passive
0.02 mental fortitude passive tree
0.03 shadows training passive
0.05 aim buff passive

heals:
0.01 companion passive

armor scalar
0.2 elusivness passive
1.3 stance passive

resistance:
0.02 shadow sight passive tree

defense
0.05 psych passive tree
0.04 double saber tactics passive tree
0.02 shadow sight passive tree
0.05 being a consular passive

shield
0.18 kinetic ward active 3% more in 4.0
0.05 shield passive
0.15 stance passive
0.05 186 2 set

absorb:
A(bulwark) active
0.04 shadowsight passive
0.20 shield passive

Bulwark math with set bonus. swing timer T, effective absorb contribution A. calcs use swing timer of 0.85 seconds

m(T):=floor((23.75)/(T)):
with(SumTools);
p(d,s,r,kw,kf,fb,fn):=1/(kw+kf)*(kf*s*(1-r)+kw*s*(fb*(1-(d+0.1))+fn*(1-d))):
E(n,p):=Summation(piecewise(i<11,(n!)/(i!*(n-i)!)*p^(i)*(1-p)^(n-i)*i,i<19,(n!)/(i!*(n-i)!)*p^(i)*(1-p)^(n-i)*10,19<=i,0),i=1..n):
P(m,p):=piecewise(m>=19,(m!)/(19!*(m-19)!)*p^(19)*(1-p)^(m-19),0):
A(T,p):=piecewise(m(T)<19,1/(m(T))*Summation(E(n,p),n=1..m(T)),Summation((Summ ation(E(n,p),n=1..19+i)* P(19+i,p))/(19+i),i=0..m(T)-19)+((1- Summation(P(n,p),n=19..m(T)))*Summation(E(n,p),n=1 ..m(T)))/(m(T))):

this assumes 23.75 second ward duration, 19 charges, 10 stacks of bulwark.

the regression for absorb% = ( -24.526*p^2 + 32.038*p – 3.61) (only for 0.85 timer) R^2=0.99
p is chance of ward proc, taking shield, resist, defense, damage weights into account.

GUARDIAN

f/t dr:
0.05 guardian slash active

i/e dr:
0.05 inner peace passive tree
0.10 willpower buff passive

overall dr:
0.03 warding strike active
0.06 stance passive
0.0075 new 2 set (.02 * 4/12) active

endurance:
0.01 companion passive
0.05 aim buff passive

heals:
0.01 companion passive

self heals: active
1 * BonusHealing + 0.05 * 27510
setting to 2771 every 12 seconds for bmods and 2826 for unlettered
replace with 1.2*(BonusHealing + 0.05 * 27510) if using old 4 piece

armor scalar:
0.15 exp protector passive tree
0.60 stance passive

defense:
0.05 dust storm active
0.05 blade barricade (riposte) active
0.03 stance passive
0.03 single saber mastery passive
2% per tick of ravage, lasts for 6 seconds in 4.0. ataking 2 ticks at timer=0 and last tick at 2.7 sec we get
(4*(2.7-0)+6*(8.7-2.7)+0*(18-8.7))/18=2.6% defense

shield:
0.04 shield specialist passive tree
0.05 shield passive
0.15 stance passive

absorb:
0.03 warding power active
0.20 shield passive

POWERTECH

m/r dr:
0.05 combust active

f/t dr:
0.05 firestorm active

i/e dr:
0.10 willpower buff passive

overall dr:
0.02 power armor passive tree
0.02 ion screen passive (stance)
0.05 stance passive
0.0083 new 2 set (0.02*5/12) active

enduance:
0.01 companion passive
0.05 aim buff passive

heals:
0.01 companion passive

self heals:
20% health every 90 seconds from shield cannon
2.5% health every aoe, 3 sec cooldown, passive – conditional

armor scalar:
0.15 power armor passive tree
0.60 stance passive

resist:
0.02 old 4 set passive

defense:
0.04 deflective plating passive tree
0.02 old 4 set passive

shield:
0.02 shield vents passive tree
0.03 shield enhancers passive tree
0.05 shield passive
0.15 stance passive

absorb:
0.1475 heat screen and heat blast active
0.04 ablative upgrade passive tree
0.20 shield passive

heat screen: 3% +5% for 6 seconds after heat blast. 5% for 4.0
heat blast: during heat blast: (25+0)*1.5+(25+1)*1.5+(25+2)*1.5*1+(25+3)1.5
taking time averaged for both gives ((3+5)*6+25*1.5+26*1.5+27*1.5+28*1.5)*(1/12) = 17.25% absorb.

sheets link: https://drive.google.com/open?id=0B_…UN4dlFnaFF6Y3M