Combat Ratings at level 80 - Page 9

Whitetooth · 09/22/08, 12:28 PM

After hours of work, used up over 40 excel spreadsheets and running multiple regression tools, this is what I got:

$x' = \frac{a}{1+\frac{b}{x}}$

$x'$ is the diminished stat before converting to IEEE754.
$x$ is the stat before diminishing returns.
$a$ is a constant, which also happens to be the cap.
$b$ is a constant.

Further research shows that b = 0.956*a, so we can write:

$\frac{1}{x'} = \frac{1}{a}+\frac{0.956}{x}}$

All floating calculations in wow are done with IEEE754 which has limited precision, it creates a rounding effect on the resulting data, the following formula will convert (x'+Base) to IEEE754 and back.

$k = \lfloor\log_{2}(x'+Base)\rfloor$
$x'' = (round(((x'+Base)/2^k-1)/2^{-23})*2^{-23}+1)*2^k$

$Base$ is the part unaffected by diminishing returns, which is 5 for the following parry from defense data.

Doing a nonlinear regression with my parry data from defense and we have:
$a=47.00351944$
$b=44.93536383$

$x$	Parry Data	$x''$	error
0.00	5.0000000000000	5.0000000000000	0.0000000000000
0.12	5.1251888275146	5.1251888275146	0.0000000000000
0.16	5.1667699813843	5.1667699813843	0.0000000000000
0.20	5.2082781791687	5.2082781791687	0.0000000000000
0.24	5.2497124671936	5.2497124671936	0.0000000000000
0.28	5.2910733222961	5.2910733222961	0.0000000000000
0.32	5.3323612213135	5.3323612213135	0.0000000000000
0.36	5.3735761642456	5.3735761642456	0.0000000000000
0.40	5.4147186279297	5.4147181510925	0.0000004768372
0.44	5.4557881355286	5.4557881355286	0.0000000000000
0.48	5.4967856407166	5.4967851638794	0.0000004768372
0.52	5.5377106666565	5.5377106666565	0.0000000000000
0.56	5.5785636901855	5.5785636901855	0.0000000000000
0.60	5.6193451881409	5.6193451881409	0.0000000000000
0.64	5.6600551605225	5.6600551605225	0.0000000000000
0.68	5.7006936073303	5.7006936073303	0.0000000000000
0.72	5.7412610054016	5.7412610054016	0.0000000000000
0.76	5.7817568778992	5.7817568778992	0.0000000000000
0.80	5.8221826553345	5.8221826553345	0.0000000000000
0.84	5.8625373840332	5.8625373840332	0.0000000000000
0.88	5.9028215408325	5.9028215408325	0.0000000000000
0.92	5.9430356025696	5.9430356025696	0.0000000000000
0.96	5.9831795692444	5.9831795692444	0.0000000000000
1.00	6.0232534408569	6.0232534408569	0.0000000000000
1.04	6.0632576942444	6.0632576942444	0.0000000000000
1.08	6.1031923294067	6.1031923294067	0.0000000000000
1.12	6.1430578231812	6.1430578231812	0.0000000000000
1.16	6.1828536987305	6.1828536987305	0.0000000000000
1.20	6.2225809097290	6.2225809097290	0.0000000000000
1.24	6.2622399330139	6.2622394561768	0.0000004768371
1.28	6.3018293380737	6.3018288612366	0.0000004768371
1.32	6.3413500785828	6.3413500785828	0.0000000000000
1.36	6.3808031082153	6.3808031082153	0.0000000000000
1.40	6.4201874732971	6.4201879501343	-0.0000004768372
1.44	6.4595050811768	6.4595046043396	0.0000004768372
1.48	6.4987540245056	6.4987540245056	0.0000000000000
1.52	6.5379352569580	6.5379352569580	0.0000000000000
1.56	6.5770492553711	6.5770497322083	-0.0000004768372
1.60	6.6160960197449	6.6160964965820	-0.0000004768371
1.64	6.6550760269165	6.6550760269165	0.0000000000000
1.68	6.6939888000488	6.6939888000488	0.0000000000000
1.72	6.7328348159790	6.7328352928162	-0.0000004768372
1.76	6.7716150283813	6.7716145515442	0.0000004768371
1.80	6.8103275299072	6.8103280067444	-0.0000004768372
1.84	6.8489751815796	6.8489751815796	0.0000000000000
1.88	6.8875560760498	6.8875560760498	0.0000000000000
1.92	6.9260706901550	6.9260711669922	-0.0000004768372
1.96	6.9645204544067	6.9645204544067	0.0000000000000
2.00	7.0029044151306	7.0029044151306	0.0000000000000
2.04	7.0412225723267	7.0412225723267	0.0000000000000
2.08	7.0794763565063	7.0794758796692	0.0000004768371
2.12	7.1176638603210	7.1176643371582	-0.0000004768372
2.16	7.1557869911194	7.1557874679565	-0.0000004768371
2.20	7.1938462257385	7.1938462257385	0.0000000000000
2.24	7.2318406105042	7.2318406105042	0.0000000000000
2.28	7.2697696685791	7.2697701454163	-0.0000004768372
2.32	7.3076357841492	7.3076357841492	0.0000000000000
2.36	7.3454370498657	7.3454370498657	0.0000000000000
2.40	7.3831744194031	7.3831748962402	-0.0000004768371
2.44	7.4208488464355	7.4208488464355	0.0000000000000
2.48	7.4584589004517	7.4584589004517	0.0000000000000
2.52	7.4960060119629	7.4960060119629	0.0000000000000
2.56	7.5334897041321	7.5334897041321	0.0000000000000
2.60	7.5709104537964	7.5709099769592	0.0000004768372
2.64	7.6082677841187	7.6082677841187	0.0000000000000
2.68	7.6455631256104	7.6455626487732	0.0000004768372
2.72	7.6827950477600	7.6827950477600	0.0000000000000
2.76	7.7199654579163	7.7199649810791	0.0000004768372
2.80	7.7570719718933	7.7570724487305	-0.0000004768372
2.84	7.7941179275513	7.7941179275513	0.0000000000000
2.88	7.8311009407043	7.8311014175415	-0.0000004768372
2.92	7.8680224418640	7.8680229187012	-0.0000004768372
2.96	7.9048829078674	7.9048829078674	0.0000000000000
3.00	7.9416809082031	7.9416813850403	-0.0000004768372
3.04	7.9784183502197	7.9784183502197	0.0000000000000
3.08	8.0150938034058	8.0150938034058	0.0000000000000
3.12	8.0517091751099	8.0517091751099	0.0000000000000
3.16	8.0882635116577	8.0882625579834	0.0000009536743
3.20	8.1247558593750	8.1247558593750	0.0000000000000
3.24	8.1611890792847	8.1611881256104	0.0000009536743
3.28	8.1975612640381	8.1975603103638	0.0000009536743
3.32	8.2338724136353	8.2338724136353	0.0000000000000
3.36	8.2701234817505	8.2701234817505	0.0000000000000
3.40	8.3063154220581	8.3063154220581	0.0000000000000
3.44	8.3424472808838	8.3424472808838	0.0000000000000
3.48	8.3785200119019	8.3785190582275	0.0000009536744
3.52	8.4145326614380	8.4145317077637	0.0000009536743
3.56	8.4504852294922	8.4504852294922	0.0000000000000
3.60	8.4863786697388	8.4863786697388	0.0000000000000
3.64	8.5222139358521	8.5222139358521	0.0000000000000
3.68	8.5579891204834	8.5579891204834	0.0000000000000
3.72	8.5937070846558	8.5937061309814	0.0000009536744
3.76	8.6293649673462	8.6293649673462	0.0000000000000
3.80	8.6649637222290	8.6649646759033	-0.0000009536743
3.84	8.7005052566528	8.7005062103271	-0.0000009536743
3.88	8.7359886169434	8.7359886169434	0.0000000000000
3.92	8.7714138031006	8.7714138031006	0.0000000000000
3.96	8.8067808151245	8.8067808151245	0.0000000000000
4.00	8.8420896530151	8.8420896530151	0.0000000000000
4.04	8.8773412704468	8.8773412704468	0.0000000000000
4.08	8.9125356674194	8.9125356674194	0.0000000000000
4.12	8.9476728439331	8.9476718902588	0.0000009536743
4.16	8.9827518463135	8.9827518463135	0.0000000000000
4.20	9.0177736282349	9.0177736282349	0.0000000000000
4.24	9.0527391433716	9.0527391433716	0.0000000000000
4.28	9.0876474380493	9.0876474380493	0.0000000000000
4.32	9.1224994659424	9.1224994659424	0.0000000000000
4.36	9.1572952270508	9.1572942733765	0.0000009536743
4.40	9.1920328140259	9.1920328140259	0.0000000000000
4.44	9.2267160415649	9.2267160415649	0.0000000000000
4.48	9.2613420486450	9.2613420486450	0.0000000000000
4.52	9.2959117889404	9.2959127426147	-0.0000009536743
4.56	9.3304271697998	9.3304271697998	0.0000000000000
4.60	9.3648853302002	9.3648853302002	0.0000000000000
4.64	9.3992891311646	9.3992881774902	0.0000009536744
4.68	9.4336357116699	9.4336357116699	0.0000000000000
4.72	9.4679279327393	9.4679288864136	-0.0000009536743
4.76	9.5021648406982	9.5021657943726	-0.0000009536744
4.80	9.5363473892212	9.5363473892212	0.0000000000000
4.84	9.5704746246338	9.5704746246338	0.0000000000000
4.88	9.6045475006104	9.6045465469360	0.0000009536744

Although most of the data is correct to the very last place, there are still errors in some of it, I hope someone can come up with a formula that is 100% correct.

Selmarix · 09/22/08, 12:49 PM

Originally Posted by Whitetooth

After hours of work, this is what I got:

$x' = \frac{a}{1-\frac{b}{x}}$

$x'$ is the diminished stat before converting to IEEE754.
$x$ is the stat before diminishing returns.
$a$ is a constant, which also happens to be the cap.
$b$ is a constant.

Something is wrong with that formula. Wouldn't small values of $x$ result in a negative $x'$ ?

Whitetooth · 09/22/08, 12:55 PM

Originally Posted by Selmarix

Something is wrong with that formula. Wouldn't small values of $x$ result in a negative $x'$ ?

Sorry for the typo, should be + instead of - there, fixed now.

Selmarix · 09/22/08, 1:30 PM

That means the diminishing return for additional parry reaches 50% around 20% parry from gear (1% additional parry adds about 0.5% parry then).
On my druid that value for dodge is definitely higher (using the pocket watch at around 33% dodge from gear added slightly more than 8% dodge so the value for half return should be around 38% or so).
So the diminishing returns are probably class specific.

Muphrid · 09/22/08, 1:52 PM

So, Whitetooth, for dodge I get b/a = 0.955999867444231 and 1/a = .0113468848294694, which implies a = 88.1299153934183 and b = 84.2521874339791?

Mijae · 09/22/08, 3:28 PM

Originally Posted by Selmarix

That means the diminishing return for additional parry reaches 50% around 20% parry from gear (1% additional parry adds about 0.5% parry then).
On my druid that value for dodge is definitely higher (using the pocket watch at around 33% dodge from gear added slightly more than 8% dodge so the value for half return should be around 38% or so).
So the diminishing returns are probably class specific.

Is that 38% total, or 38% from dodge rating alone?

Whitetooth · 09/22/08, 3:33 PM

Originally Posted by Muphrid

So, Whitetooth, for dodge I get b/a = 0.955999867444231 and 1/a = .0113468848294694, which implies a = 88.1299153934183 and b = 84.2521874339791?

Yes, your values are about the same as mine

Using the formula:

$\frac{1}{x'} = \frac{1}{a}+\frac{0.956}{x}}$

Doing a nonlinear regression with my dodge data from defense:
$a=88.13154$

Proven by my tests in page 8, these formulas work for not only dodge from defense, but for dodge in general, whether its from agility, dodge rating or defense.

$x$	Dodge Data	$x''$	error
0.00	7.0076994895935	7.0076994895935	0.0000000000000
0.12	7.1330442428589	7.1330437660217	0.0000004768372
0.16	7.1747460365295	7.1747465133667	-0.0000004768372
0.20	7.2164087295532	7.2164092063904	-0.0000004768372
0.24	7.2580323219299	7.2580323219299	0.0000000000000
0.28	7.2996163368225	7.2996163368225	0.0000000000000
0.32	7.3411607742310	7.3411612510681	-0.0000004768371
0.36	7.3826661109924	7.3826665878296	-0.0000004768372
0.40	7.4241323471069	7.4241323471069	0.0000000000000
0.44	7.4655590057373	7.4655594825745	-0.0000004768372
0.48	7.5069470405579	7.5069475173950	-0.0000004768371
0.52	7.5482954978943	7.5482959747314	-0.0000004768371
0.56	7.5896062850952	7.5896058082581	0.0000004768371
0.60	7.6308765411377	7.6308765411377	0.0000000000000
0.64	7.6721086502075	7.6721086502075	0.0000000000000
0.68	7.7133016586304	7.7133016586304	0.0000000000000
0.72	7.7544560432434	7.7544560432434	0.0000000000000
0.76	7.7955713272095	7.7955718040466	-0.0000004768371
0.80	7.8366489410400	7.8366484642029	0.0000004768371
0.84	7.8776865005493	7.8776869773865	-0.0000004768372
0.88	7.9186863899231	7.9186868667603	-0.0000004768372
0.92	7.9596476554871	7.9596476554871	0.0000000000000
0.96	8.0005702972412	8.0005702972412	0.0000000000000
1.00	8.0414552688599	8.0414552688599	0.0000000000000
1.04	8.0823011398315	8.0823011398315	0.0000000000000
1.08	8.1231088638306	8.1231088638306	0.0000000000000
1.12	8.1638784408569	8.1638784408569	0.0000000000000
1.16	8.2046098709106	8.2046098709106	0.0000000000000
1.20	8.2453031539917	8.2453031539917	0.0000000000000
1.24	8.2859573364258	8.2859582901001	-0.0000009536743
1.28	8.3265752792358	8.3265752792358	0.0000000000000
1.32	8.3671541213989	8.3671541213989	0.0000000000000
1.36	8.4076957702637	8.4076957702637	0.0000000000000
1.40	8.4481983184814	8.4481983184814	0.0000000000000
1.44	8.4886636734009	8.4886636734009	0.0000000000000
1.48	8.5290918350220	8.5290918350220	0.0000000000000
1.52	8.5694818496704	8.5694818496704	0.0000000000000
1.56	8.6098346710205	8.6098346710205	0.0000000000000
1.60	8.6501493453979	8.6501493453979	0.0000000000000
1.64	8.6904268264771	8.6904268264771	0.0000000000000
1.68	8.7306661605835	8.7306661605835	0.0000000000000
1.72	8.7708683013916	8.7708683013916	0.0000000000000
1.76	8.8110332489014	8.8110332489014	0.0000000000000
1.80	8.8511610031128	8.8511610031128	0.0000000000000
1.84	8.8912506103516	8.8912515640259	-0.0000009536743
1.88	8.9313049316406	8.9313039779663	0.0000009536743
1.92	8.9713201522827	8.9713201522827	0.0000000000000
1.96	9.0112991333008	9.0112991333008	0.0000000000000
2.00	9.0512399673462	9.0512409210205	-0.0000009536743
2.04	9.0911455154419	9.0911455154419	0.0000000000000
2.08	9.1310129165649	9.1310129165649	0.0000000000000
2.12	9.1708440780640	9.1708431243896	0.0000009536744
2.16	9.2106370925903	9.2106370925903	0.0000000000000
2.20	9.2503938674927	9.2503948211670	-0.0000009536743
2.24	9.2901144027710	9.2901144027710	0.0000000000000
2.28	9.3297977447510	9.3297977447510	0.0000000000000
2.32	9.3694448471069	9.3694448471069	0.0000000000000
2.36	9.4090547561646	9.4090557098389	-0.0000009536743
2.40	9.4486284255981	9.4486293792725	-0.0000009536744
2.44	9.4881658554077	9.4881658554077	0.0000000000000
2.48	9.5276670455933	9.5276670455933	0.0000000000000
2.52	9.5671310424805	9.5671310424805	0.0000000000000
2.56	9.6065587997437	9.6065587997437	0.0000000000000
2.60	9.6459503173828	9.6459503173828	0.0000000000000
2.64	9.6853055953979	9.6853055953979	0.0000000000000
2.68	9.7246246337891	9.7246246337891	0.0000000000000
2.72	9.7639083862305	9.7639083862305	0.0000000000000
2.76	9.8031549453735	9.8031549453735	0.0000000000000
2.80	9.8423662185669	9.8423652648926	0.0000009536743
2.84	9.8815402984619	9.8815402984619	0.0000000000000
2.88	9.9206790924072	9.9206790924072	0.0000000000000
2.92	9.9597816467285	9.9597816467285	0.0000000000000
2.96	9.9988489151001	9.9988489151001	0.0000000000000
3.00	10.0378799438480	10.0378799438476	0.0000000000003
3.04	10.0768756866460	10.0768756866455	0.0000000000005
3.08	10.1158351898190	10.1158351898193	-0.0000000000003
3.12	10.1547594070430	10.1547594070434	-0.0000000000005
3.16	10.1936473846440	10.1936473846435	0.0000000000004
3.20	10.2325000762940	10.2325000762939	0.0000000000001
3.24	10.2713174819950	10.2713174819946	0.0000000000004
3.28	10.3100996017460	10.3100996017456	0.0000000000004
3.32	10.3488464355470	10.3488454818725	0.0000009536744
3.36	10.3875570297240	10.3875570297241	-0.0000000000001
3.40	10.4262323379520	10.4262323379516	0.0000000000003
3.44	10.4648723602290	10.4648723602294	-0.0000000000005
3.48	10.5034780502320	10.5034780502319	0.0000000000001
3.52	10.5420475006100	10.5420475006103	-0.0000000000004
3.56	10.5805826187130	10.5805826187133	-0.0000000000004
3.60	10.6190824508670	10.6190824508666	0.0000000000003
3.64	10.6575469970700	10.6575469970703	-0.0000000000003
3.68	10.6959772109990	10.6959772109985	0.0000000000005
3.72	10.7343721389770	10.7343711853027	0.0000009536743
3.76	10.7727317810060	10.7727317810058	0.0000000000001
3.80	10.8110561370850	10.8110561370849	0.0000000000000
3.84	10.8493471145630	10.8493471145629	0.0000000000000
3.88	10.8876018524170	10.8876018524169	0.0000000000000
3.92	10.9258222579960	10.9258232116699	-0.0000009536739
3.96	10.9640092849730	10.9640092849731	-0.0000000000001
4.00	11.0021610260010	11.0021600723266	0.0000009536743
4.04	11.0402774810790	11.0402774810791	-0.0000000000001
4.08	11.0783596038820	11.0783596038818	0.0000000000002
4.12	11.1164073944090	11.1164073944091	-0.0000000000002
4.16	11.1544218063350	11.1544208526611	0.0000009536739
4.20	11.1923999786380	11.1923999786376	0.0000000000003
4.24	11.2303447723390	11.2303447723388	0.0000000000001
4.28	11.2682552337650	11.2682552337646	0.0000000000004
4.32	11.3061313629150	11.3061313629150	0.0000000000000
4.36	11.3439741134640	11.3439731597900	0.0000009536740
4.40	11.3817815780640	11.3817815780639	0.0000000000000
4.44	11.4195556640630	11.4195556640625	0.0000000000005
4.48	11.4572954177860	11.4572944641113	0.0000009536747
4.52	11.4950008392330	11.4950008392333	-0.0000000000004
4.56	11.5326728820800	11.5326719284057	0.0000009536742
4.60	11.5703105926510	11.5703105926513	-0.0000000000004
4.64	11.6079139709470	11.6079139709472	-0.0000000000003
4.68	11.6454839706420	11.6454839706420	-0.0000000000001
4.72	11.6830205917360	11.6830205917358	0.0000000000002
4.76	11.7205228805540	11.7205228805541	-0.0000000000002
4.80	11.7579917907710	11.7579917907714	-0.0000000000005
4.84	11.7954273223880	11.7954273223876	0.0000000000003
4.88	11.8328294754030	11.8328294754028	0.0000000000002

sp00n · 09/22/08, 4:50 PM

Wow. Amazing.

Now, besides the fact that I understand the desire to not have to fall back to something like the Sunwell Radiance Buff, does it somebody else find quite ironic that, in order to do a little napkin math or a bit theorycrafting ('hm, how high will my avoidance be with this and that gear...'), basically it first requires a degree in mathematics to find out the underlying formula?

// Edit
I would rather like to see a reasonable high avoidance cap on dodge+parry+miss instead of such a complicated formula (block being an exception from that cap).
They already decided to include a cap on armor a long time ago, instead of introducing something fancy like an armor rating with diminishing returns. Seems only reasonable to go down the same road for avoidance.

Malazaar · 09/22/08, 5:01 PM

Originally Posted by sp00n

Wow. Amazing.

Now, besides the fact that I understand the desire to not have to fall back to something like the Sunwell Radiance Buff, does it somebody else find quite ironic that, in order to do a little napkin math or a bit theorycrafting ('hm, how high will my avoidance be with this and that gear...'), basically it first requires a degree in mathematics to find out the underlying formula?

They could just give us the formula, it would save us the trouble and make finding bugs a lot easier. It's not like we wouldn't figure it out eventually.

Would be nice for a change if they'd do something like this: "We implemented diminishing returns on avoidance, you now gain avoidance according to formula X".

Edit:

Originally Posted by sp00n

I would rather like to see a reasonable high avoidance cap on dodge+parry+miss instead of such a complicated formula (block being an exception from that cap).
They already decided to include a cap on armor a long time ago, instead of introducing something fancy like an armor rating with diminishing returns. Seems only reasonable to go down the same road for avoidance.

Those are two very different things. Time to die versus Armor is a linear relationship, so you wouldn't even need an armor cap or armor rating or whatever.

Avoidance is a different matter because time to die versus avoidance has increasing returns. Each percent avoidance you gain is worth more than the last one - that makes (made) stacking avoidance so attractive. It would make sense to implement a hard cap on avoidance but that brings some problems with it.

One thing being that once players reach that cap, there is little way to offer them any improvement with better gear. Another being that avoidance still has increasing returns so until that cap is reached the problem isn't really solved.

So implementing diminishing returns on avoidance is in my opinion the smarter move - it brings it in line with armor and stamina.

Muphrid · 09/22/08, 5:14 PM

Well, Daelo said, more or less, "We'd be wasting our time developing if we told you, and you can figure it out for yourselves."

Yes, we can (and to a good extent, have) figured it out for ourselves, thanks to Whitetooth in particular. And I suppose it's cheaper for them to have us spend hours reverse engineering their mechanics, rather than take 5 minutes and say what the deal is.

I mean, the actual regressing is not hard. We never would've needed exact numbers from the game code, just a general indication of what kind of model to look at. If Whitetooth's model holds, then what we have is this: "the reciprocal of gained avoidance is a linear function of the reciprocal of pre-DR gained avoidance." That one sentence would have saved us hours and hours of trying linear, polynomial, and exponential functions of rating, 1/rating, and God only knows what else.

And there's another issue: how do we know it works "right" if we don't know what model they intended it to follow?

And furthermore, the issue that led to Sunwell Radiance has not been fixed. Avoidance still increases as a function of gear level with no counter. It may increase less quickly, but it still increases. Irony: Sunwell Radiance is the solution to Sunwell Radiance. Or rather, without some way for mobs to mitigate players' avoidance, those mobs are forced to deal spikier damage to keep the same average pressure on healers, which leads to more spike damage deaths. Slowing avoidance growth just slows the progression of the problem, but it is still there.

So implementing diminishing returns on avoidance is in my opinion the smarter move - it brings it in line with armor and stamina.

Sadly, if this was Blizzard's intention, they haven't done that. It was this possibility that drove my first regression, and that model was bad. I'm still waiting for a more thorough and complete understanding of how all the stats interact to determine whether avoidance will increase average TTL faster or slower than linear, but I'm reasonably certain that it will not increase TTL linearly.

• Aldriana · 09/22/08, 5:21 PM

True, although the counterargument is that slowing down the problem is enough. The issues that led to Sunwell Radiance didn't really become severe until, well, Sunwell. So if they can postpone the problem for one tier, that's good enough for most practical purposes.

Selmarix · 09/22/08, 5:25 PM

What base value did you use for your dodge regression? Does the dodge from base agility diminish or not?

Whitetooth · 09/22/08, 5:31 PM

Originally Posted by Selmarix

What base value did you use for your dodge regression? Does the dodge from base agility diminish or not?

Dodge from base agility does not diminish, initially I thought base agility also diminishes, but that assumption failed and wasted an hour of my time.

Muphrid · 09/22/08, 5:35 PM

Originally Posted by Aldriana

True, although the counterargument is that slowing down the problem is enough. The issues that led to Sunwell Radiance didn't really become severe until, well, Sunwell. So if they can postpone the problem for one tier, that's good enough for most practical purposes.

True, we didn't have Sunwell Radiance until, well, Sunwell, obviously. That said, it begs the question: how do we know when mob damage has become too spiky? I mean, we know that as avoidance increases, spikiness of mob damage must increase (again, to keep the same healing pressure on the tank, since they don't get hit as often). Do we evaluate this qualitatively--say that only in Sunwell was it so serious a problem that it needed to be addressed?

I don't know how much I buy that school of thought. I view it as a continuum: that the damage is at some level of spikiness at some base gear level, and it get spikier and spikier. And I feel this has subtle implications for class balance and viability: does it begin to select against healers who can't deal with spike damage and tanks who have less powerful "oh-$#!%" buttons? To me, this is plausible, but difficult to prove (and, I think, difficult to disprove).

So, faced with questions that are simply difficult to answer, I say punt. We already have ??-bosses that are fixed at +3 levels above us. Why not ???-bosses that are +6 and ????-bosses that are +9? Counter increasing avoidance with increasing boss hit rates. To keep avoidance valuable, punish people who don't keep their avoidance above a minimum level (if a boss has, say, a 110% chance to hit you, they not only hit you, but they deal 10% more damage--something like that).

And then you make avoidance linearly increase average TTL. Or, you know, if you subscribe to the school of thought that varying stat equivalences are bad, you put all the stats on exponential curves, balance the game once, and then you're done.

Selmarix · 09/22/08, 6:50 PM

I tried to apply that dodge formula on my level 70 night elf druid in beta on some data points, but I can't really get it to fit. The dodge values are only approximates written down from the ingame UI, but the higher values are not even close to what you would expect with the dodge formula from above.

Agility	Defense	Dodge Rating	Dodge Percent
79	350	0	8.91 (That is without items)
132	350	0	11.56
169	350	54	15.99
173	350	82	17.49
177	358	82	17.94
256	358	82	21.28
327	364	82	24.30
390	368	97	27.37
403	375	122	28.98
465	384	139	31.95

sp00n · 09/22/08, 6:57 PM

Originally Posted by Muphrid

So, faced with questions that are simply difficult to answer, I say punt. We already have ??-bosses that are fixed at +3 levels above us. Why not ???-bosses that are +6 and ????-bosses that are +9? Counter increasing avoidance with increasing boss hit rates. To keep avoidance valuable, punish people who don't keep their avoidance above a minimum level (if a boss has, say, a 110% chance to hit you, they not only hit you, but they deal 10% more damage--something like that).

Increasing boss level to 4+ would not only increase their chance to hit, but also bring back crushing blows and completely destroy DPS on such bosses (due to resist rates, glancing blows and increased misses).
Of course you could only increase their weapon skill, but that's really no different than simply giving them a buff like Sunwell Radiance; and would possibly still have the effect of crushing blows, which I currently don't know if they depend on weapon skill or pure level difference (the former I suspect).

Muphrid · 09/22/08, 7:07 PM

Originally Posted by sp00n

Increasing boss level to 4+ would not only increase their chance to hit, but also bring back crushing blows and completely destroy DPS on such bosses (due to resist rates, glancing blows and increased misses).
Of course you could only increase their weapon skill, but that's really no different than simply giving them a buff like Sunwell Radiance; and would possibly still have the effect of crushing blows, which I currently don't know if they depend on weapon skill or pure level difference (the former I suspect).

Crushing and glancing blows: I mean, they bumped it up to +4 just so +3 level bosses wouldn't be a problem. I would just get rid of them.
Resist rates, miss rates: you mean there's a scaling cap? Blasphemy! It means the stat point distribution of items will actually become less complicated as the designers no longer have to account for caps.

To Selmarix: I don't think we're at the point yet where we can pin down the combined effects of multiple stats put together. It seems like they should all follow the same general curves (just independent of each other), but we haven't even established the a and b values for pure dodge rating and agility.

• Aldriana · 09/22/08, 7:30 PM

Glancing and crushing blows have an important role in terms of game balance outside of raids - I've previously enumerated the reasons behind this in this post. Basically, Crushing and Glancing need to exist - the shift from +3 to +4 on crushings was done because it was making tanks hard to balance, not because they don't like the mechanic.

That said, it's perfectly reasonable to add bosses that have hit or expertise bonuses to address the issues of avoidance scaling, and they may well do that in addition to the diminishing returns. In point of fact, I suspect the diminishing returns is in not so much to address the "healing spikiness" issue as the "100% avoidance tanking" issue. The fact that it also postpones the other problems that led to Sunwell Radiance is just an added bonus.

Muphrid · 09/22/08, 7:46 PM

Originally Posted by Aldriana

Glancing and crushing blows have an important role in terms of game balance outside of raids - I've previously enumerated the reasons behind this in this post. Basically, Crushing and Glancing need to exist - the shift from +3 to +4 on crushings was done because it was making tanks hard to balance, not because they don't like the mechanic.

I understand the notion that crushes and glances are desirable to drive how leveling players level. I have no objection to that principle, but as you aptly note, Blizzard has effectively made crushes and glances a non-issue with respect to raiding, and all I was saying is that I have no intention of suggesting that they revert that.

That said, it's perfectly reasonable to add bosses that have hit or expertise bonuses to address the issues of avoidance scaling, and they may well do that in addition to the diminishing returns. In point of fact, I suspect the diminishing returns is in not so much to address the "healing spikiness" issue as the "100% avoidance tanking" issue. The fact that it also postpones the other problems that led to Sunwell Radiance is just an added bonus.

To be honest, I see 100% avoidance tanking and healing spikiness as related. I mean, how do you make a mob that's threatening if they only have 1 or 2% chance to hit? Obvious answer: you basically allow them to come within an inch of one-shotting. But that's lame and we all know it's lame. It makes healing a game of "watch the full health bar until something interesting happens...you'll be here for a while." And tanking a game of "keep your finger on the emergency red button because sometime or other you'll take a massive smacking, but nobody knows when."

• Aldriana · 09/22/08, 8:04 PM

As far as I know, Glancing Blows still apply to +3 mobs; it's only Crushings that were pushed to +4. Or at least, that's the testing I saw in the rogue thread a couple weeks back.

As for avoidance tanking versus spikiness: they're certainly related, but my point is that I think Blizzard isn't necessarily worried about "late expansion bosses will be tricky to heal as their damage is very spiky". They're late expansion bosses, they're *supposed* to be tricky to heal. Admittedly, it does get to the point where you can't make the boss hit hard enough to be an issue and have the fight be theoretically doable, which is where Sunwell Radiance came in - as original Patchwerk showed us, intermittent damage doing 80% of the tank's HP is totally healable, and you can't really hit any harder than that and have the fight be even theoretically possible.

I think Blizzard's concern is not so much "I have high avoidance and will take a significant amount of damage from the few things that hit me", as the possibility - realized in BC - of "I am theoretically unhittable, which is a good thing as there is no possible way for me to survive getting hit even once". This was demonstrated via, for instance, rogue tanking on various fights, and creates some surprising degeneracies that Blizzard doesn't want to have to anticipate. A truly unhittable tank eliminates or greatly reduces the notion of "MT healing", and in some cases, "OT healing" as well. Shahraz when your tank only needs healing for the shadow damage and you don't need OTs at all is a very different fight than they intended.

Now, these problems are of course related, as the fact that tanks in regular gear get up to 80% avoidance is related to the fact that someone who stacks avoidance can make 100; and they do have a common solution in approaches like Sunwell Radiance. My point is that even if the diminishing returns on avoidance only mitigates the first part without solving it completely, the fact that it completely and totally cures the second part makes it worthwhile from Blizzard's perspective.

Selmarix · 09/22/08, 9:11 PM

Originally Posted by Muphrid

To Selmarix: I don't think we're at the point yet where we can pin down the combined effects of multiple stats put together. It seems like they should all follow the same general curves (just independent of each other), but we haven't even established the a and b values for pure dodge rating and agility.

Whitetooth's tests from page 8 show that dodge does not diminish independent between dodge rating and defense but rather that dodge diminishes in total no matter the source of the dodge.
So I tried to fit it under that assumption with first the computation of the dodge percentage and then diminishing it as a whole. But yes, it did not work out. That might have been either druids using another formula or other values or one of my assumptions being wrong.

Whitetooth · 09/23/08, 12:50 AM

Originally Posted by Selmarix

Whitetooth's tests from page 8 show that dodge does not diminish independent between dodge rating and defense but rather that dodge diminishes in total no matter the source of the dodge.
So I tried to fit it under that assumption with first the computation of the dodge percentage and then diminishing it as a whole. But yes, it did not work out. That might have been either druids using another formula or other values or one of my assumptions being wrong.

It didn't work because most likely your calculations for increased dodge before DR was wrong, how much dodge before DR per agility is something that needs to be calculated.

Or it could be because the cap is different for different classes and levels, but its easy to test this with just a few data points now.

Whitetooth · 09/23/08, 1:56 AM

Dodge from agility tests were impossible before because we don't know the exact dodge per agi. But now I got the correct formula for diminishing returns, the tests can be done and dodge per agi can be calculated using my DR formula.

So I copied over a premade druid and did some tests on agi, results show that the formula still holds, but the cap value $a$ is different.

Build: 8970
Name: Whitetooth
Level: 80
Class: Druild
Base Defense: 400

agi	increased agi	dodge%	$y$ = dodge% - base	$x$	dodge per agi
87	0	7.0390000343323	0.0000000000000
137	50	8.2606649398804	1.2216649055481	1.180246784	0.0236049356862
187	100	9.4570579528809	2.4180579185486	2.360493569	0.0236049356862
237	150	10.6289548873900	3.5899548530577	3.540740011	0.0236049334061
299	212	12.0492029190060	5.0102028846737	5.004246902	0.0236049382172

Take the data points from 137 and 187 agi:

$y_1=1.2216649055481$
$y_2=2.4180579185486$

$\begin{cases}\frac{1}{y_1}=\frac{1}{a}+\frac{0.956}{x}\\\frac{1}{y_2}=\frac{1}{a}+ \frac{0.956}{2x}\\\end{cases}$

$x=\frac{0.956}{2(\frac{1}{y_1}-\frac{1}{y_2})}=1.180246784$
$a=\frac{1}{\frac{1}{y_1}-\frac{0.956}{x}}=116.8909884$

Now that we have $a$ for level 80 durids, we can calculate the original dodge before DR with the formula:
$x=\frac{0.956}{\frac{1}{y}-\frac{1}{a}}$

This is the formula used in the above table for $x$ , using the dodge before DR we can calculate the correct dodge per agi which is 0.023604935.

This test shows that the cap value $a$ is different from my level 60 warrior, more tests need to be done to see if its because of class or level or both.

Prinsesa · 09/23/08, 2:50 AM

Moving toward the practical side of things, do these changes mean that a Parry gem ([Flashing Living Ruby]) can potentially add more avoidance than a Dodge gem ([Subtle Living Ruby]) if a lot of Dodge Rating on existing gear has already diminished the value?

Selmarix · 09/23/08, 4:49 AM

Originally Posted by Prinsesa

Moving toward the practical side of things, do these changes mean that a Parry gem ([Flashing Living Ruby]) can potentially add more avoidance than a Dodge gem ([Subtle Living Ruby]) if a lot of Dodge Rating on existing gear has already diminished the value?

Yes, but parry rating diminishes faster so you need considerably more dodge than parry before that is the case.

Originally Posted by Whitetooth

This is the formula used in the above table for $x$ , using the dodge before DR we can calculate the correct dodge per agi which is 0.023604935.

This test shows that the cap value $a$ is different from my level 60 warrior, more tests need to be done to see if its because of class or level or both.

Ah, my mistake was that I only left one variable variable at a time, but both my Agi/dodge and my $a$ was wrong.
The values on my level 70 druid seem to fit

$a=116.8909884$

and dodge per agi is approximately 0.049 .

That seems to fit a higher dodge cap due to lack of parry and that the caps do not change with level (you want to have the caps regardless of level).