Tuesday, January 1, 2013

Lotro math - Mastery diminishing returns?



When explaining lotro math, I typically throw in a side comment about the diminishing returns of Mastery (tactical or physical) as it relates to the increased % damage of the attack. (rohan-85-rk-hytbold-and-moors-armor and lotro-stat-math-rk-gear). When I was at 75, the only way to push to much higher Mastery than about 28k, was to have even better gear than I could reasonably obtain or sacrifice another stat (critical, morale, mitigations) and I wasn’t willing to give it up. That same sacrifice is true at level 85.

In this article I will present some more detailed information about what the curve looks like so that you can draw your own conclusions about where you are in your progress.

Here is the curve presented up to 100,000 Tactical Mastery.

Chart 1: Tactical Mastery vs Increase in % Damage

Yowsa! You don’t really need to know what 100k Tactical Mastery looks like. That first chart was just to show that the curve does in fact “curve” and that diminishing returns are real. However, I have never seen my Tactical Mastery above 50k (with Moors buffs). My typical unbuffed build is actually only around 30k or so.

I want to present Chart 1 a different way.  What I really want to know is “how much more Mastery do I need at any given level to achieve +1% greater increase in Damage?” So, Chart 2 says the same thing, just with this emphasis is mind.


What is clear from Chart 2 is that above 32k mastery, the slope increases more rapidly. By 50k mastery, the next +1% increment takes 1000 more mastery. At 100k mastery, the next +1% increment takes 3800.


Chart 2: Amount of Mastery Required to shift % Damage by +1%

You can see that the amount of mastery required to shift % damage by +1% changes for the final time around 27,000 Mastery. By 32k, it is clear that this curve is on its upward trend. Every increment after that requires more mastery to make the shift.


32k Mastery bend?
I haven’t taken a survey, but I think that most characters are probably in the less than 35k range, prior to buffs. You can see from the next curve that up to 32k Mastery, the relationship is fairly linear. Thus, the diminishing returns are nil. Interestingly, at 32k, you are up to 100.3% increased damage. 100% is the magic threshhold. J


Chart 3: Same as Chart 1, zoomed in on Mastery up to 32k

How much Mastery is required to make a +1% shift, when Mastery is <32k?

This next Chart is interesting. I cannot readily explain where the oscillation comes from. However, the answer is that it takes between 270 and 385 mastery to obtain each +1% increase in damage.

Update 02/19/13: Readers Corcaroli and Anonymous in the comments below directed me to a great discussion that shows why the oscillation occurs... it is intrinsic to a tiered formula! ...of course, it is... that is what was driving me bonkers, lol.

See the brilliant writeup by Alad explaining the formula at the link http://forums.lotro.com/showthread.php?424066-Combat-stat-changes-on-Isengard-release.-Mitigation-and-Offence.

All credit is to Alad with insight from Moebius, but the formula looks like 
% = Yo + 1/[1 + K/(R/L - Xo)] 

where K = 300, R = mastery / level, & Xo and Yo are determined based on the table:
R/L K Xo Yo Result Range Segment
0 - 75 300 0 0 0 - 20% 1
75 - 150 300 75 0.2 20% - 40% 2
150 - 225 300 150 0.4 40% - 60% 3
225 - 300 300 225 0.6 60% - 80% 4
>300 300 300 0.8 >80% 5

From this table, you can see that the oscillations occurs at each segment transition. As a reality check, the formula does indeed match exactly with every Chart in this writeup. :D  

Chart 4: Same as Chart 2, focused on Mastery up to 32k


Summarize it, Dana
What would I do?

Let’s look at the 4 pillars of the RK. (1) Morale – has no cap on diminishing return, (2) Mastery – summarized above, limited diminishing return, (3) Critical – caps at 25% (equivalent to 13,401 critical), and (4) Mitigations – caps at 40% (equivalent to 10,602 mitigation).

Once you start approaching a real cap for Critical or a Mitigation, you should optimize and not waste extra effort. As for Mastery… balance it against the other factors. Most likely, I wouldn’t think too hard about it. Just get mastery and get more morale and critical and mitigation.
 
In case you were wondering, I am not as optimized as I would like to be, but I am certainly not hitting any of these hard caps. My current digits look like what you see in the screenie below, hitting no caps, though my Mastery is near 32k.  It will give me something to optimize when replacing all of the remaining level 75 gear. Since I started writing this article, I dropped my mastery slightly to improve my other digits. There is a happy balance for you somewhere in there.

Where did I get this information??
I used to collect my own data. Now, Tomrica has pointed me toward a genius plugin called “Stat Calc”. It can be downloaded from here.

It looks like this screenie when loaded. Stat Calc is on the left side; I also have my character sheet open to see the numbers as the Stat Calc looks at them. You wouldn’t have it open all the time, but when you need to compare some numbers, it is amazingly good to have. You can input shifts into the Stat Calc boxes and it will recalculate everything for you.



I have no idea how it was built though I assume deep magic was involved. It is a work of brilliance from the author, Polymnie. Mebbe, he or she will enlighten me someday (autograph book at the ready just in case). Heyhey! See Update above as the deep magic was revealed to me through the formula and link!

Good luck out there and happy flying!


28 comments:

Lothirieth said...

Hmmm... math... :o *brain melts*

I went from around 32.5k mastery at 75 to 35.8k now.. I dunno how much that's improved. I also have a nice set bonus on my LM set that made a bump in damage noticeable. I just try to go after the best stuff, knowing it's likely small changes, but well.. at least I know I can't do any better. :P

Joshua said...

I suspect that the oscillation you see there is an artifact of the calculation. The actual mastery formula should produce a continuous curve.

Asciel said...

LOTRO math! You wrote this post just for me, did you :D

Danania said...

Lothirieth!

Lol. yeah... at 32.5k mastery and level 85, you are at 101.5% damage increase. At 35.8k mastery and level 85, you are at 106.7%. The question would be in the optimized tradeoff. What could you have gotten instead of an extra 5.2% damage?

The answer might be that the decision is absolutely the best thing for you. I mention it because I was discussing numbers with a mini friend (who was at 37k mastery) who noted that he could either have an extra 3% mastery OR 1000 morale.

It is a question and balance that you are most keen to decide for yourself, when you have the data in front of you. :D

Danania said...

Joshua,

Very interesting take on the oscillation. I do not know that answer. I can see it and it shows up in "statcalc" and I can reproduce it on my character.

I supposed that the lack of linearity is that the formula might have a tiered effect (kinda like the US IRS tax or something). Would be fun to know the formula behind it as I have never seen it.

Danania said...

Asciel...lol!

You know I wrote it just for you. It was my new-year's resolution... Be more like Asciel is 2013. :D

Lothirieth said...

Hehe, thanks Dana. :P My mind sees these numbers and graphs and just goes "wut?" and shuts off. :P Oh how it celebrated when I took my last math class in Uni and has promptly forgotten nearly everything it learned... except the quadratic equation, but only because my teacher in high school taught us to remember it by singing it to the tune of "Pop Goes the Weasel" and music is something I'm good at. :D *ahem* aaaaanyway... :P

What you describe is what I try to do. Sure I could go more glass cannon, but I like having healthy morale. I could get more dps, but I'm happy with my stats right now. :) I feel I've kept a good balance!

Danania said...

Oh Lothirieth... the joys of learning math... :) My geometry teacher used to remind us that Pie R round and cornbread R square. Of course, that ties back to PI R squared = the area of a circle (and circles are round, hence the pi formula)... confusing? lol.

I try not to question anyone else's build (especially one that I know has beaten Saruman T2, hehe). As you know, my point was that mastery diminishing returns are real, it isn't a huge impact or any impact for where most people operate, and you optimize to what makes sense for you (which is what you do!) :D

Iaksones said...

Good stuff. I'd kinda assumed after the 100% mark there would be another section of straight graph to 120%, then 140%, and so on. I don't really stack mastery too high. So it seems, not only do you see diminishing returns when the relationship from rating to % shift from almost-linear to non-linear after the +100% mastery mark as you point out, but the application of mastery buffs also gets diminshing returns as well (not just at the +100% mark, but always).

Like, if your character were to be naked and statless, her attacks would be at 100% capacity. Mastery converted to % stacks additively with that with the +80%, +100%, +120%, etc total bonus you might have from your gear & stuff.

Now for example say you had +100% outgoing damage modifier from your stats (~32k mastery rating, right): you'd have a total outgoing damage multiplier of 200%. If you get buffed +10% more damage from FB To Arms, you get a multiplier of 210%. However, 210% is only 5% bigger than 200%; rather than do 10% more damage as most people would expect, you do 5% more dmage. The higher your outgoing melee/range/tact damage multiplier is, the less each successive % point means for you. Thus another layer of diminishing returns on stacking mastery. Crit, on the other hand, doesn't suffer from diminishing-returns-on-application.

Easily tested on training dummies, as long as you're mindful of what skill-specific damage legacies you have that could interfere.

Danania said...

Iaksones... you rock.

Zaianya said...

I...am a level 85 minstrel, with full Hytbold armor, and am stuck at around 26k tactical mastery. Erm...am I doing something wrong? :)

Danania said...

Oh Zaianya, I would never suggest that you would be doing something wrong... the game is for you to enjoy! :D

You do pose an interesting question, 85 Mini 26k mastery. My everyday RK gear is slightly more than 30k, not that it is a contest. I am no Mini but I would think that Mini stats run similar to RK, so I will breakdown where my mastery comes from and see if it helps you. I don't promise that my build has the most mastery; it is just one that works well for me.

With the current set of gear that I like everyday: 30601 total = 12290 jewelry + 11874 armor + 4896 LIs & chisel + 1541 baseline.

My armor is a hytbold 5 piece, some good shoes, and draigoch cloak. You have hytbold, so the difference probably isn't there, although I do see that RK hytbold sets vary by around +1k mastery.

My LIs don't spend a lot of effort on mastery, though they do have some Will. Depending on your LIs, legacies, passives, relics, there might be a small amount there.

That leaves Jewelry. I have a hodge-podge of pieces including four pieces from LLG. Surprisingly, 5 of my 8 pieces are level 75 pieces, one is a quest reward, one is a Rohan-barter-build-a-ring, and the last was taken off the neck of the great goblin in the new instance. I would think that jewelry choices could shift mastery by a few thousand mastery.

Best of luck. What do you think?

Zaianya said...

I think you might be right; I have never put a lot of effort into the Jewelry.

I did find that by switching to a different Hytbold mini set, and opting for a four/two split (four from one set and two from another) I got more total Will out of the whole business than if I had chosen six pieces from a single set. So now, I'm working on getting a full set of crafted 85 jewelry (all of which I calculate to be an improvement). So far I'm already up to 27.5k mastery!

Danania said...

Oh yay Zaianya!
I'm glad I could help; it sounds like you are already doing quite well! go you!

Corcaroli said...

Danania, this is really good work and shows a lot of dedication and understanding for this game but as Iaksonen has already written about mastery only applying to the base damage I will not do so as well.
As for those oscillations: The conversion of TM into % is not linear as you can see here (you have to scroll down a bit):
http://forums.lotro.com/showthread.php?424066-Combat-stat-changes-on-Isengard-release.-Mitigation-and-Offence.&p=5735823#post5735823

Anonymous said...

About the "oscillation": mastery-to-% conversion curve is built up of five segments (0-20%, 20-40%, 40-60%, 60-80%, and >80%). Your chart 4 correctly shows the first four segments.

http://forums.lotro.com/showthread.php?424066-Combat-stat-changes-on-Isengard-release.-Mitigation-and-Offence.

Anonymous said...

Doesn't Tactical Offense cap at 50% like the wiki says at http://lotro-wiki.com/index.php/Character_Stats

Danania said...

Hello Anonymous,
That would be a negative... Tactical Offense does not cap at 50%. You can see the percentages as they relate to tactical offense in this post. That Wiki page needs to be corrected (it is noted at the top of the wiki page that it is being worked on).

Fatalix said...

Fatalix here
Hiya Danania this gona open my eyes on balance on my RK as I went for top damage and ended up getting nuked by creeps hehe. Good to see at what amount to focus mastery and if I pass that amount, it only makes me unbalanced with more importent stats being missed and not gaining anymore than needed.

Do have to say that I got here a bit late and have to start play around with the new content since U11 out now. But this gives me focus to work on :) thanks

Danania Darzil said...

Fatalix, so glad it helped. :)

I've seen that often actually. I think I could pull in about 15% or more tactical damage, but at the expense of key survivability stats.

Balancing Mastery, Critical, Mitigation, and Morale works very well for me. Best of luck and ask quesitons if I can assist. :)

Hmm said...

Very helpful post. Thank you.

Danania Darzil said...

Very welcome Hmm. I'm glad it continues to be helpful. :)

R. Michael Duttera said...

Hi,
Was wondering if I was wasting time upgrading relics with ever greater mastery or whether I should diversify and change LI relics with the new Wildemore relics to having skills I've not yet incorporated to date in my LIs that are harder to see if/how they help RKs. Since Im still under 20K Tac mastery and things don't begin to level off till ca. 32K I guess you answered my Q; ever more mastery is still the ticket apparently, looks like to me! Tx for doin' this.

Danania Darzil said...

Great question RMichael!

Someday my articles might get more organized... however, check this one out...
http://www.danania.net/2013/04/update-10-t9-and-eastemnet-relics.html

My short answer to you is one of need and balance. You need more morale and mastery. I use my relics primarily for morale and use my gear primarily for mastery/will. Of course, there is cross-over, but the relics are a great source of morale.

My intent is to start consolidating some of my RK intell onto the page... http://www.danania.net/p/danania-85.html

I hope it helps. Feel free to ask more questions anytime. :)

Justalittleperil said...

So this is an awesome post, I targeted 100% increased damage throughout RoR. Now all it needs is an update for HD! Great work and well presented.

Danania Darzil said...

Thanks justalittleperil!

I was just recently thinking about this article and how it applies to math for mitigations and how shift to level 95 has walked out on this curve.

I will hopefully write an updated version soon enough. Thanks for the comment! :)

Jeffery Legere said...

Any word on the u pdated version?

Danania Darzil said...

Ha Jeffrey. You are right; I do need an update. I had tried to track the changes but it seemed the game calcs were changing faster than I could see them! It is on my list though. :)

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