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  1. #1
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    Monster / Avatar / Pet damage

    Our understanding of player pDIF has improved while our understanding of monster pDIF has remained relatively obscure. We do know a few things (like their pDIF cap) and I will show a few more in this post. First, though, I'd like to state my largest assumptions:

    1) Monster pDIF = Avatar pDIF = Pet pDIF (potentially with the exception of the ranged Automaton) - I have seen no evidence to dispute this and they share some common features.

    2) Monsters use similar equations to players. (fSTR, pDIF, cRatio, etc.) - Same as above. It seems reasonable and I see no reason to doubt it. Thus I will focus on determining these relationships.

    fSTR
    I figured that fSTR would be a good one to start with because we can use well known features of the pDIF curve (the 1.0 frequency spike) to determine base damage at any given STR.

    Previous Work
    Much of the original Avatar work (at least on the NA side) was done by Kegsay on Alla. Here is a link to his blog. Now, notable among his conclusions are that Avatar base damage increases every 4 STR even against level -1 monsters outside cities. Furthermore, there are STR values where he finds that Avatars seem to have variable fSTR. Looking back at his data, it becomes apparent that Avatar fSTR is simply uncapped and he's attacking a population that we normally assume to be homogenous (L-1 monsters) but not recognizing that they're actually not (slightly different VIT values). Given the relative lack of Avatar STR sources at the time, it's impressive that he did this. I wouldn't have even considered the test.

    I decided to continue this by going to Abyssea and manipulating Avatar STR using Atma and target VIT with debuffs (like Choke/Wild Oats).

    Test 1, Abyssea vs. EM Bluffalo (118 VIT) with celestial avatars (Garuda and Ramuh)
    <table border="0" cellpadding="0" cellspacing="0" width="384"><colgroup><col style="width:48pt" span="6" width="64"> </colgroup><tbody><tr style="height:15.0pt" height="20"> <td class="xl65" style="height:15.0pt;width:48pt" height="20" width="64">STR Boost</td> <td class="xl65" style="width:48pt" width="64">D</td> <td class="xl65" style="width:48pt" width="64">dSTR</td> <td class="xl65" style="width:48pt" width="64">fSTR</td> <td class="xl65" style="width:48pt" width="64">Same?</td> <td class="xl65" style="width:48pt" width="64">Prediction</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">0</td> <td align="right">47</td> <td align="right">-10</td> <td align="right">0</td> <td>Yes</td> <td align="right">47</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">9</td> <td align="right">48</td> <td align="right">-1</td> <td align="right">1</td> <td>Yes</td> <td align="right">48</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">10</td> <td align="right">49</td> <td align="right">0</td> <td align="right">2</td> <td>Yes</td> <td align="right">49</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">11</td> <td align="right">49</td> <td align="right">1</td> <td align="right">2</td> <td>Yes</td> <td align="right">49</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">20</td> <td align="right">51</td> <td align="right">10</td> <td align="right">4</td> <td>Yes</td> <td align="right">51</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">30</td> <td align="right">53</td> <td align="right">20</td> <td align="right">6</td> <td>Yes</td> <td align="right">53</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">40</td> <td align="right">55</td> <td align="right">30</td> <td align="right">8</td> <td>Yes</td> <td align="right">55</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">50</td> <td align="right">58</td> <td align="right">40</td> <td align="right">11</td> <td>Yes</td> <td align="right">58</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">60</td> <td align="right">60</td> <td align="right">50</td> <td align="right">13</td> <td>Yes</td> <td align="right">60</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">70</td> <td align="right">63</td> <td align="right">60</td> <td align="right">16</td> <td>Yes</td> <td align="right">63</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">80</td> <td align="right">65</td> <td align="right">70</td> <td align="right">18</td> <td>Yes</td> <td align="right">65</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">90</td> <td align="right">68</td> <td align="right">80</td> <td align="right">21</td> <td>Yes</td> <td align="right">68</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20" align="right">100</td> <td align="right">70</td> <td align="right">90</td> <td align="right">23</td> <td>Yes</td> <td align="right">70</td> </tr> </tbody></table>

    The above table only matches our known fSTR curve for a D47 weapon used by a 108 STR character, but it matches it perfectly:
    Spoiler: show


    Anyway, there are any number of potential curves that would fit the points I made, but this is at least enough information to make me comfortable with the idea that Avatars do use player fSTR equations. Also, it gives us a value to use for level 99 Celestial avatar base damage and STR.


    pDIF
    Avatars do not hit for the same damage every time. Therefore there is at least one randomization function in play, which we might as well call pDIF. Furthermore, there's a secondary randomizer of 1~1.05 damage. Again I'm going to have to cite Kegsay as the previous work, though I know the idea was around on several forums already. What we know:
    1) Monster pre-randomizer pDIF caps at 4 (unlike 3 for players) - This was apparent before they added the secondary randomizer after the 2-hander changes. It's also a pattern followed by every type of pet.
    2) There is a secondary randomizer of 1~1.05, just like for player melee hits.
    3) Critical Hits increase Ratio or pDIF but do not bypass the pDIF cap. - These appear higher on some monsters/pets/avatars due to Critical Attack Bonus II, which many of them seem to possess.
    4) Monsters appear to receive a ratio boost when attacking players of lower level than themselves. - This has been proposed as +0.05 Ratio/level difference and we have no reason to reject it.
    5) 2 STR = 1 Attack for monsters. - This can be confirmed with the Harle Automaton, but it's also apparent from some tests I've done in Abyssea. +50 Attack gives the same Ratio range as +100 STR.

    Recent Work:
    Xilk shows that Gorefang Hobs (99) caps pDIF on level 61 Sand Lizards with +0 Attack. He also shows that Gorefang Hobs fails to cap pDIF on level 62 Sand Lizards with almost all of the pet attack in the game (>+100) despite the 6 defense difference between the two lizards.

    This indicates that the actual attack/defense comparison is irrelevant in this case. Gorefang Hobs appears to be capping due to the Ratio bonus from level correction alone. It's a 38 level gap so we'd estimate it as +1.9, but we don't really know because we don't have any mapping between Ratio and pDIF.

    This also clarifies why Kegsay could not detect attack bonuses from equipment in his tests despite later work showing an effect. He was capping purely because he was fighting Bees that were 38+ levels below him. That's why his only uncapped pDIF samples are when he uses Avatar's Favor, which gives a Ratio penalty that is applied at some point but perhaps isn't involved in either the cap.

    Overall, I'd propose:
    : Avatar cRatio = (Avatar Attack/Target Defense) + Level Correction (positive) - Penalties
    * (Avatar Attack/Target Defense) probably has a cap of 2 given the recent statements by SE.
    * Level Correction (positive) seems to cap at 38 levels different.
    * Penalties could be uniquely applied, or it could be folded into another term. Given the testing that has been done, it is not possible to say.

    Future:
    The next (and most laborious step) is going to be to determine the pDIF curves for monsters. This is probably easiest done with Automatons because you can actually see their Attack. My preliminary tests using Avatars against Level 0 Bluffalo seem to indicate that the Monster pDIF function is fundamentally different from player pDIF functions. Mapping from one to the other just doesn't work, and monsters have higher variability than we would expect at every point.

  2. #2
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    Avatar Physical BPs / (Monster TP moves)
    I'm less confident claiming that Avatar physical BPs work just like Monster TP moves, but they probably do. Thus, I decided to whip out Garuda and abuse the SMN 2-hour on the test server.

    Previous Work:
    At some point (in 2005ish?) SE adjusted Avatar BP damage and added a Ratio cap to it (or perhaps removed the level correction component). This means that Avatar BPs cannot reach the 4.0 pDIF cap even on crits, which means they're incredibly variable and difficult to test. Kegsay took a stab at quantifying physical BP damage, but due to the lack of available ways to manipulate the BPs and the stupidly long BP recast timer he reached some conclusions that were probably not right. Specifically, the formula he uses is wrong and the assumption that the entire BP worth of damage is calculated at once (instead of on a hit-by-hit basis) is also wrong. Still, his link does give you a pretty good idea of how BPs stack up against each other.

    Predator Claws:
    So I took my level 99 SMN/RDM, put on AF2+2 body/head/hands (Avatar Crit rate +6%), and headed to East Ron to fight some rabbits on the test server. The new SMN 2-hour (which refills your MP and reduces BP recasts to 0) is still set to a 10 second recast on the test server, so I can spam it to spam BPs. First I verified that Tunnel Worms/Wild Rabbits were giving my Avatar the same base damage because we know its fSTR is uncapped. They were, and that base damage was 73. This is a reasonable base damage using the above fSTR equations for a 108 STR / 47 damage weapon with no cap. Next, I spammed the shit out of Pred Claws.
    Spoiler: show
    Garuda
    Melee
    + 299: 1
    + 301: 1
    +^ 302: 1
    + 305: 1
    Melee Crits
    + 317: 1
    +^ 327: 1
    + 329: 1
    Ability
    Predator Claws
    236: 1
    258: 1
    270: 1
    280: 1
    281: 1
    289: 1
    292: 1
    303: 1
    427: 1
    430: 1
    1834: 1
    1852: 1
    1856: 1
    1867: 1
    1872: 1
    1876: 1
    1893: 1
    1898: 1
    1906: 1
    1911: 1
    1913: 1
    1914: 1
    1917: 1
    1918: 1
    1925: 1
    1926: 1
    1929: 2
    1939: 1
    1943: 1
    1956: 1
    1959: 1
    1971: 1
    1978: 1
    1983: 1
    1991: 1
    1998: 1
    1999: 1
    2004: 1
    2014: 2
    2016: 1
    2019: 1
    2022: 1
    2023: 1
    2027: 1
    2032: 1
    2038: 1
    2046: 1
    2057: 1
    2058: 1
    2062: 1
    2063: 1
    2067: 2
    2075: 1
    2081: 1
    2102: 1
    2107: 1
    2111: 1
    2113: 1
    2118: 1
    2120: 1
    2124: 1
    2125: 1
    2130: 1
    2131: 2
    2135: 1
    2139: 1
    2140: 1
    2142: 1
    2145: 1
    2147: 1
    2156: 1
    2160: 1
    2161: 1
    2165: 1
    2166: 1
    2184: 1
    2193: 1
    2197: 1
    2200: 1
    2206: 1
    2207: 1
    2212: 1
    2215: 1
    2217: 1
    2221: 1
    2223: 1
    2225: 1
    2231: 1
    2232: 1
    2237: 2
    2242: 1
    2244: 1
    2249: 1
    2254: 1
    2256: 1
    2268: 1
    2269: 1
    2274: 1
    2276: 1
    2284: 1
    2286: 1
    2292: 1
    2294: 1
    2297: 2
    2301: 1
    2302: 1
    ^ 2304: 1
    2308: 1
    2309: 1
    2319: 1
    2322: 2
    2325: 1
    2334: 1
    2336: 1
    2351: 1
    2352: 2
    + 2357: 4
    2364: 1
    2366: 1
    2367: 2
    2369: 1
    2371: 1
    2375: 1
    2376: 1
    2377: 1
    2381: 1
    2384: 1
    2385: 1
    2386: 2
    2387: 1
    2388: 1
    2395: 2
    2399: 1
    2404: 2
    2405: 1
    2415: 1
    2419: 1
    2421: 1
    2425: 1
    2429: 1
    2435: 2
    2448: 1
    2451: 1
    2454: 1
    2457: 1
    2459: 1
    2469: 1
    2476: 1
    2507: 1
    2511: 1
    2898: 1
    2916: 1
    2934: 1
    2950: 1
    2961: 2
    2974: 1
    2980: 1
    2992: 1
    3020: 1
    3022: 1
    3026: 1
    3046: 1
    3056: 1
    3084: 1
    3087: 1
    3095: 1
    3110: 1
    3122: 1
    3171: 1
    3173: 1
    3175: 1
    3183: 1
    3194: 1
    3207: 1
    3211: 1
    3224: 2
    3244: 1
    3263: 1
    3284: 1
    3289: 1
    3300: 1
    3308: 1
    3328: 1
    3350: 1
    3384: 1
    3387: 1
    3389: 1
    3397: 1
    3413: 1
    3419: 1
    3422: 1
    3424: 1
    3431: 2
    3460: 1
    3477: 1
    3483: 1
    3493: 2
    3508: 1
    3515: 1
    3534: 1
    3557: 1
    3561: 1
    3597: 1
    3608: 1

    Looking at the above data, you can see there are clearly 3-4 ranges for BP damage. Those ranges are:
    * 236~303 - Missed first hit, non-crit (N=8 )
    * 427~430 - Missed first hit, crit (N=2)
    * 1834~2511 - First hit landed, non-crit (N=158 )
    * 2898~3608 - First hit landed, crit (N=58 )
    Together this makes my crit rate 60/226, or 26.5%. This is about what we'd predict for a dDEX capped Avatar with Crit rate +6%, so good deal.

    So now, what can we say from the data?

    1) There are no obvious plateaus/frequency changes, which indicate that it doesn't include 4.0 or 1.0 pDIF even on the critical BPs.

    2) Because there are so very obviously these ranges, it's very safe to say that avatar BP damage is calculated on a hit-by-hit basis just like normal melee WSs.

    3) The ratio of max non-crit first hit BP to min non-crit first hit BP is 1.304 (once you remove the secondary randomizer), while the ratio of max non-crit off hit BP to min non-crit off hit BP is 1.222. This has a few implications:
    * First, it means that the minimum non-crit BP is 303/1.304/1.05 = 221 and that the maximum non-crit BP is 323
    * Second, it means that my 427~430 range really are crits, because of the above.

    4) Avatars are not using their normal melee base damage for two reasons.
    * First, the range of damages generated by one-hit Pred Claws is much larger than normal at the cap, which indicates a larger pDIF range. If we're getting about the same damage (on off-hits) with a larger pDIF range, it means that there's higher base damage.
    * Second, you can see a clear benefit from critical hits which indicates that we're uncapped yet still doing about the same damage. Because we know they aren't hitting 1.0 or 4.0, we can predict that the base damage is between 76 (303/4) and 221 (min possible hit). If we assume that crits add 1 pDIF and still aren't capped, then we can increase the lower limit to 101. This range is huge, but reasonable for a level 75 cap WS. If it had a 75% STR mod like Gekko, it would have 141 base damage.

    5) Assuming off-hits have a multiplier of 1 and that we saw the whole range of first-hit damages (which we probably didn't), the first-hit multiplier is between 7.77 and 8.26.

    6) If I take a Ratio of the max and min first-hit non-crit to crits, I end up with 1.33 for the max and 1.4635 for the mins. If we assume Crits are pDIF +1 (they're probably actually Ratio +1, but more about that later) then we get pDIF values of about 2.15 non-crit and 3.15 crit for the low end of the range and 3 non-crit to 4 crit for the upper end of the range. With a M of 8, this would indicate a base damage of about 104-106. That's right in the range I'd expect for a mid-to-low mod WS.

  3. #3
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    I just got a "Token has Expired" error and lost about half an hour of writing, so this is the short version:

    First off, it seems that Magical Avatar BP damage follows a similar formula to Magic WSs. It is something like:
    Code:
    Damage = ( (D) * fTP + dSTAT ) * Magic Multipliers
    
    D = Constant + Stat Modifiers
    dSTAT:
    I have heard that Holy Mist relies on MND, but Tier 2/4s and Merit BPs from Celestial Avatars rely on INT and have an M of 1.5:

    If there is an inflection point, I didn't hit it. I did not check M at negative dINTs because I couldn't find anything with more INT than Avatars. Related, but Celestial Avatars at 99 have 130 INT, as determined by letting myself and the avatar get nuked. I have a similar plot for Merit BPs and it has the same slope.

    It is worth noting that despite its seemingly high correlation, my dSTAT term correction is not perfect. I don't know why, but I still get up to 2 base damage variance at constant stats even after I subtract dSTAT. It is possible that I messed something up when recording the monster INTs.

    I also made sure that the impact of dSTAT did not vary with TP. It did not, and granted a constant boost to the Tier 2 nukes regardless of the TP.

    Avatar TP Anchor Points:
    They're at 0, 150, and 300TP:

    This is for Tier 2 nuke BPs (Aero II, Fire II, etc.), which are all the same. The damage values have dSTAT and MAB removed.

    Modifiers:
    They do exist and the equation we assumed is correct, observe:
    <table border="0" cellpadding="0" cellspacing="0" width="256"><colgroup><col style="width:48pt" span="4" width="64"> </colgroup><tbody><tr style="height:15.0pt" height="20"> <td style="height:15.0pt;width:48pt" height="20" width="64">
    </td> <td style="width:48pt" align="right" width="64">130INT</td> <td style="width:48pt" align="right" width="64">250INT</td> <td style="width:48pt" align="right" width="64">1.92x</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">0TP</td> <td align="right">166</td> <td align="right">202</td> <td align="right">1.21x</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">300TP</td> <td align="right">374</td> <td align="right">458</td> <td align="right">1.22x</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20">
    </td> <td align="right">2.253x</td> <td align="right">2.267x</td> <td>Ratios
    </td> </tr> </tbody></table>The above table shows Damages (without MAB or my imperfect dSTAT correction) in each of the four conditions for Tier 2 nukes.

    You can see that base damage still increases substantially with INT even after removing dSTAT, and it increases a constant amount. You can also see that removing the damage added by INT is not going to bring us back to 0 damage. This supports the idea of some kind of constant added on (like Level + 2 in the Magic WS equations).

    You can also see that increasing TP increases damage by a constant amount regardless of the base damage, indicating the two terms are multiplied by each other (fTP and D, as proposed).

    Still, we have not disentangled fTP from the above damages so we cannot guess what they are.

    The Constant:
    If the constant is Level + 2 (101 in this case), then we expect that the 0TP fTP would be 1.25 (166-((202-166)*130/120) = 127 ~= 1.25*101). If the 0TP fTP is 1.25 and the 300TP fTP is 2.25ish times that, then it is approximately 2+13/16. The 150 TP Anchor in this case would be 2.5. That would make Tier 2 BPs:
    0TP fTP = 1.25
    150TP fTP = 2.5
    300TP fTP = ~2.8125
    These are approximately what we observe.



    I'll have to come back to this tomorrow. I'm just pissed that it ate my post.

  4. #4
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    Do we have player abilities/spells that use the 0/150/300 TP anchor aside from BLU? Seems to be a consistent finding that player at 100/200/300 and monsters at 0/150/300. BLU's exception is self-explanatory.

  5. #5
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    Quote Originally Posted by Byrthnoth View Post
    Related, but Celestial Avatars at 99 have 130 INT, as determined by letting myself and the avatar get nuked.
    Did you take into account the DT-7% of Stout Servant? With 107 INT and MDT-7% I take the same amount of damage than a Celestial Avatar.

  6. #6
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    Looks like I back-calculated my own INT <_<; Time to look at that again.

    Ramuh gets Quake'd for 798 by a 124 INT worm, so he would take 852 damage without Stout Servant (-16/256 damage) and 609 damage without the worm's 40 MAB. Quake's M is 2 and D is 577, so that works out to dINT=16 in favor of the 124INT worm. That puts him at 108 INT.

    Well, this doesn't actually affect any of the conclusions about the equation's form above (just messes up the constant calculation that I said probably wasn't right) and luckily gives us some negative dINT points. dINT does appear to drop by 0.5 when it goes negative (same as for spells) and becomes 1.


    Re-working the table with new dINT removal values:
    <table border="0" cellpadding="0" cellspacing="0" width="256"><colgroup><col style="width:48pt" span="4" width="64"> </colgroup><tbody><tr style="height:15.0pt" height="20"> <td style="height:15.0pt;width:48pt" height="20" width="64">
    </td> <td style="width:48pt" align="right" width="64">108INT</td> <td style="width:48pt" align="right" width="64">228INT</td> <td style="width:48pt" align="right" width="64">2.111111</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">0TP</td> <td align="right">191</td> <td align="right">235</td> <td align="right">1.230366</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">300TP</td> <td align="right">399</td> <td align="right">491</td> <td align="right">1.230576</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20">
    </td> <td align="right">2.089005</td> <td align="right">2.089362</td> <td>Ratios
    </td> </tr> </tbody></table>
    The calculated values I get for 108 INT and 300 TP without dINT are either 399 or 398. The 0 TP values for 108 INT without dINT are 190-192.

    If adding 120 INT got us 44 D*fTP at 0TP, then we'd expect removing the other 108 INT would remove approximately 40 more D*fTP and bring us down to 151. If this is a multiple of 101, then the multiple is 1.5 at 0 TP. That would make the TP points:
    0TP: 1.5
    150TP: 2.75
    300TP: ~50/16

    This is much better and the numbers pass my checks, lol. I still don't know why I'm getting 1-2 variance in the base damage after I remove dINT.

    Overall, the equation using a ".245" INT mod, 101 base damage from level, M of 1.5 (1 at negative dINTs) and the above anchor points is within 4 damage of all the results I have recorded. If I bump the mod up to .25, I am 0~2 damage high on the different INTs (which is consistent with the randomness in my dSTAT.)

  7. #7
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    I know BST pets when summoned, without relic+2 hands, have level variances. I remember being told avatars also had level differences they can spawn at. I'm probably wrong since this was something I had heard when I was just starting out...in '04.

  8. #8
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    As far as I know, Avatars are always "EM" to you when summoned. I desummoned my avatars and re-called them to make sure the different avatar BPs did the same damage and they all did, so that indicates there's at least no stat variation between them.

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    Level 90 Avatars have 97 INT
    Spoiler: show
    A worm that I can Fire II for 159 damage on SMN/SCH with 0 MAB and 132 INT (106 INT worm) 2-target Stonega III's my level 90 avatar for 462 damage (485 before Stout Servant).
    159-133 = 26 dINT
    132-26=106

    CEILING(462*256/244,1) = 485
    FLOOR(FLOOR(FLOOR(1.5*dINT+434,1)*0.8,1)*1.36,1) = 485 @ dINT=9
    106-9 = 97 INT for the Avatar


    Using the formula established above:
    FLOOR( ( ( Level+2+FLOOR(97 INT*.249,1) )*1.5 + 1*dINT ) * 1.5 MAB,1 ) = Damage at level 90 with negative dINT = 247 with the outlined values
    Observed value: 247

    :3

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    Level 75 Avatars seem to have 82 INT:
    Spoiler: show
    A worm that I can Water II for 113 damage on SMN/SCH with 0 MAB and 119 INT (101 INT worm) Stone IVs my level 75 avatar for 553 damage (no Stout Servant). The worm has +32 MAB (checked with Byrth).
    113-95 = 18 dINT
    119-18=101

    FLOOR(FLOOR(2*dINT+381,1)*1.32,1) = 553 @ dINT=19
    101-19 = 82 INT for the Avatar


    Thunder II with 0 TP does:
    FLOOR( ( ( Level+2+FLOOR(82 INT*.249,1) )*1.5 + 1*dINT ) * 1.42 MAB,1 ) = Damage at level 75 with negative dINT = 179 with the outlined values
    Observed: 178

    That's as close as any of my predictions.

    Also, I compared my damage with Atma of the Savior to my damage with Atma of the Clawed Butterfly and they were the same, so there are not other mods.

    I guess the next step is to nail it down for merit BPs!

  11. #11
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    Looks like LV+7 until you hit LV99 so far. Did you have SMN gear when doing the LV99 test that the LV90/75 didn't have?

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    Level 75 didn't have AF3+2 head, which gives MAB+4. Also, Avatar MAB trait level is changing throughout the tests. I don't know where you're getting Level + 7 from.

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    INT Levels:
    75+7 = 82
    90+7 = 97

    LV99 is the exception.

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    Ah! Okay!

    I assume that avatars follow the monster stat equations, but haven't bothered to figure out what their rating is. Celestials are probably BLMs.

    Merit BPs

    Similar table to the last one for level 99:
    <table border="0" cellpadding="0" cellspacing="0" width="256"><colgroup><col style="width:48pt" span="4" width="64"> </colgroup><tbody><tr style="height:15.0pt" height="20"> <td style="height:15.0pt;width:48pt" height="20" width="64">
    </td> <td style="width:48pt" align="right" width="64">108</td> <td style="width:48pt" align="right" width="64">228</td> <td style="width:48pt" width="64">
    </td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">0</td> <td align="right">683</td> <td align="right">844</td> <td align="right">1.235725</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" align="right" height="20">300</td> <td align="right">1368</td> <td align="right">1690</td> <td align="right">1.23538</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20">
    </td> <td align="right">2.002928</td> <td align="right">2.00237</td> <td>Ratio
    </td> </tr> </tbody></table>

    These are post-dINT and MAB removal but still involve fTP. It comes out at about 4/3 damage per INT at 0 TP, so we can take off another 144 damage from the 683 damage case and get back to 538 damage. Considering dINT removal is somewhat messy, etc., I would say that 538/101 ~= 5.375. If that's 5.375 fTP, then 300 TP is 10.75. Unlike Tier 2 nukes, Merit BPs don't have an inflection point, so 150 TP is 8.0625. If those things are true, then the INT mod is 0.249 again.

    Spoiler: show

    TP vs. damage



    These stats work for Merit BPs:
    0TP = 5.375 fTP
    150 TP = 8 + 1/16 fTP
    300 TP = 10 + 12/16 fTP
    INT Modifier = .249

    This equation is slightly more off than the previous one (up to 6 damage away after dINT and MAB (which is less than 1 base damage). I could correct for this by fine tuning the fTPs, but I feel it's probably indicative of the same problem that causes my random variance after dINT removal so I'd prefer to just leave it.

    As a check for level, I did Thunderstorm @ 0 TP vs. a 101 INT worm as a level 75 Avatar.
    1107 damage predicted, 1101 damage observed. Close enough.

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    Tier 4 Nukes:

    Same deal as before!
    <table border="0" cellpadding="0" cellspacing="0" width="256"><colgroup><col style="width:48pt" span="4" width="64"> </colgroup><tbody><tr style="height:15.0pt" height="20"> <td style="height:15.0pt;width:48pt" height="20" width="64">
    </td> <td style="width:48pt" align="right" width="64">108</td> <td style="width:48pt" align="right" width="64">228</td> <td style="width:48pt" width="64">
    </td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20">0 TP</td> <td align="right">462</td> <td align="right">571</td> <td align="right">1.235</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20">300 TP</td> <td align="right">782</td> <td align="right">966</td> <td align="right">1.235</td> </tr> <tr style="height:15.0pt" height="20"> <td style="height:15.0pt" height="20">
    </td> <td align="right">1.69</td> <td align="right">1.69</td> <td>Ratio</td> </tr> </tbody></table>
    These are modeled by:
    0 TP - 3.625
    150 TP - 5.3125
    300TP - 6.125

    INT Mod = .249


    Magic BPs that remain:
    Meteorite
    Holy Mist
    Lunar Bay
    Night Terror
    Nether Blast? <-- unaffected by TP, as far as I can tell, but it is affected by MAB IIRC?

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    Nether Blast:
    No Stat modifier, no dINT
    0 TP - 5
    150 TP - 5
    300 TP - 5

    Something probably varies with TP for this, but it's not clear what. Perhaps range?


    Night Terror:
    It's on record as doing 40% more damage to slept monsters, but I don't think this is correct.

    Preliminarily:
    * It uses dINT*1.5 for its dSTAT term
    * With a level 99 Diabolos, it gains 292 damage (pre-MAB) regardless of target INT when being used on a slept monster at 0 TP. This bonus increases to 420 damage at 300TP, which indicates that it is a boost to base damage rather than fTP or being a flat multiplier. It is not clear yet whether it is a boost to the INT modifier or just a flat boost to base damage.


    Random observations:
    Assuming monsters and players use the same TP calculations and Avatars don't get Store TP, Diabolos has 280~283 delay (7.4 TP/hit) compared to Celestial Avatar's 318~321 delay (8.3 TP/hit). He has the same base damage against Wild Rabbits and is also a BLM, so his stats/D are probably the same. He also gets Critical Attack Bonus II like the Celestials.

    Mana Cede will only consume enough MP to get your Avatar within 1 TP of 300 TP. So if you're at 218.4 TP and you use Mana Cede, it will give your Avatar 299.4 TP.

    Pavor Nocturnus is incredibly inaccurate at 0 TP with an unslept monster. I managed to land it on a slept Wild Rabbit after spamming it with the new SMN 2-hour, but it wasn't easy.

  17. #17
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    I know it seems insignificant but would be any small feat to test Wyvern base damage? On TW it seems to do pretty good damage ~200-250ish but of course the damage drops down to like 40-60 in Legion. Hard to calculate wyvern fSTR like any pet I suppose though I guess it would help somewhat to know that Wyverns have Dragoon as their main job which would provide a ballpark for their STR growth and their Attack Bonus II. Also somewhat wondering if Wyrm Mail +2 not only gives subjob traits but also gives the wyvern attributes (STR/DEX/VIT/AGI/MND/INT/CHR) as if they have a subjob too. Almost every single AF2+2 that enhances a job trait/job ability gives an extra enhanced version than the AF2 NQ and since the NQ mail already gave traits up to the current level of your SJ, can't think of what +2 does(unless as someone proposed NQ gave up to /37 JTs and +2 gives up to /49 JTs but I kinda doubt it since many subs don't have traits from 37 to 49)

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    Yeah, look at fSTR section of the OP and repeat it with a wyvern.

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    I'm still certain that a Celestial Avatar has 107 INT at 99 but I used a more basic method to verify this.
    First I checked if wearing Twilight Torque + Lieutenant's Sash gives a damage reduction similar to the Stout Servant Trait. For this, I used the Blood Pacts Somnolence and Nether Blast in Ballista since they ignore target's INT but not MDT/MDB, both Garuda and me have took the same damage (Nether Blast has the reputation of ignoring MDT but this is in fact false, it only bypass Shell). Then I adjusted my own INT as necessary and redid all the work on a Boulder Worm just to be sure (I know players take less damage in Ballista but this also applies to Avatars so it should not change anything for these tests).
    With a similar method and spells like Holy II or Eyes On Me I was able to determine that a level 99 Avatar has 64 MND and 76 CHR, that's awfully low.

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    Okay, I went back and re-worked it with 107 INT. Now:

    Tier 2:
    Alpha: 0.85
    Mod%: INT 30%
    dSTAT: ( pINT - mINT)*1.5
    Avatar Level 99 INT: 107

    0 TP: 1.5
    150 TP: 2.75
    300 TP: 3.0

    The exact formula I am using is:
    FLOOR( FLOOR( Level + 2 +FLOOR(INT*Mod%,1)*Alpha,1)*IF(TP<150, 1.5+TP*(2.75-1.5)/150, 2.75+(TP-150)*(3.125-2.75)/150) + FLOOR( dINT * IF( dINT >0, 1.5, 1 ), 1), 1)

    Simplified in a way that doesn't suck to read:
    floor( Level + 2 + floor(Stat*Mod%)*alpha)*fTP + dSTAT

    That all gets multiplied by the typical MAB, Day/weather, etc. Also, these constants are a perfect match for the observed Avatar damage. It is exactly the same as the magic WS damage.

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