Monday, 11 May 2009

The numbers behind LIs - or how Turbine made our life hell.

There are many threads about the tediuos grind for T8 relics, but virtually none about the actual chance for decent legacies on legendary items (LIs). It has been shown that one T8 relic on average equals the deconstruction of less then 100 lvl2 items, and thus can be earned within a few days.

However, I've come to the conclusion that for some classes, the chance for getting a really good LI within a lifetime approaches zero. The LI system, promoted as character customization, is in essence a lottery with the delusion of customization, and with similar low chances like you favorite RL national lottery.

(Sidenote: Other classes automatically get their dream legacy (DPS), and don't need to care that much about other stuff. I guess for them it's at least 100-10k times easier to find a satisfying weapon...)

First, the basic numbers, taken from experience:
On identification of a LI, 2-4 legacies are completely randomly chosen from 15 possible legacies and 6 qualities (bronze-gold), giving a total of 90 possibilities. When reaching lvl 10, 30, and 50 you can "choose" one additional out of 2 random legacies. (I won't discuss upgrading one of two random legacies on lvl 20 and 40 by 2 tiers here; it doesn't matter much compared to other aspects.)

So what's up with this "customization" upon reforging? If you've been very, very lucky (see below) and got your nearly perfect LI with 4 initial legacies, you probably only need one special, additional legacy. The chances to get this are
up to lvl 10: 1-(10/11)*(9/10) = 2/11 = 18%
up to lvl 30: 4/11 = 36%
up to lvl 50: 6/11 = 54%.

However, we forgot quality. If you intend to max out this legacy and thus want it golden (5 or 6), chances are only
lvl 10: 1-(32/33)*(29/30) = approx. 2/33 = 6%
lvl 30: approx 13%
lvl 50: approx 22% (...and some 12% when heading for pure t6-gold)

Anyone having fun with spending 3 million xp on a blue or yellow item for a 20% chance of NOT being forced to throw it away in the end? I did it twice, failed twice, and lost 50 gold and 2 million xp twice.

That's why we need all of the crucial legacies right from the start. Let's calculate the chances of finding one (the maths are identical to a lottery):

3 legacies of random quality out of 15: 3!/(15*14*13) = 1/455 = 0.2% chance
(That's 500 tablets on average already; but of course we don't want bronze quality!)

3 T4/5/6 = 3 out of 30: 1/4060 = 0.02%
3 golden = 3 out of 45: 1/14190 = 0.007%
3 T6 = 3 out of 90....: 1/117480 = 8.5e-6

4 T4/5/6: 1/27405 = 0.004%
4 golden: 1/148,995 = 6.7e-6
4 T6....: 1/2,555,190 = 3.9e-7

Now for the Jackpot: On the US forum there's a screenie of a 2nd age runestone with exactly those 6 legacies everyone wants for dps, 5 of which are T6. Probability for this is approx.
3.9e-7 * 6% * 9% = 2e-9 = 1 to 475 million.
That's worse than the chance for the jackpot in most lotteries.

How many blue or yellow runestones are found each day per server? 10? 100?
If it's 100 per day, chances are 50% that no other one of similar quality will be found within the next 13000 years :P

Keep in mind that that jackpot-stone *could* have been better. And keep in mind that runekeepers also need a different stone for healing, and at least 2 different satchels.

Good luck people!

1. Chances are somewhat better due to upgrading legacies, maybe by a factor 5.
2. On lvl50 one of the proposed legacies is always T6.
3. First age items tend to have primarily golden legacies.
4. I'm no pro, so correct me if I'm wrong somewhere...

Article by cthun
posted on LotRO Europe forums

I must say I was afraid to do the math alone, and - as it comes out - on good grounds. The numbers are horrendous.
Now, adding to all that depressing number, please keep in mind that the Devs are planning to give us a lvl cap rise this year already!
This means that even if you win the 1/145 million lottery now, your dream item will be less that useless within half a year (as their plan goes).
Muahaha. No, not funny. Makes me want to quit.

Someone on the forums suggested that maybe this insane grind is aimed to attract grinder asian gamer community... Even though a joke, it might hold a seed of truth... Why would Turbine care if they lost couple of thousands of Western players, if they could attract million of Asians?


  1. More proof that math ruins everything it touches (hence the feminine gender in French)!

    I've been pleasantly surprised with how easy it is to find a legendary with most of the legacies I want at a decent quality. I suppose I could make myself crazy because they are not the exact top 6-7 legacies I want at rank 6 quality, but why? I'm as hardcore as they come, but I don't see the problem here. It doesn't grieve me if someone else has something better than I do because they're lucky- in fact, I wish them well. My concern is that noone ever has something I do not because they are more skillful than I, something that will always be entirely within my control.

  2. I guess such approach would preserve my sanity too, but unfortunately it's beyond me.
    I know how much my efficiency could be improved if I had the 'right' satchel+runestone sets. It's really hard to settle for less for me if I'm being given a promise that I could get more... Maybe it's the little Asian inside me?

    The main problem as I see it is Dev's approach to character builds. I've read on US forums multiple times their answers concerning skill boosts being "You can get a LI that will do just that!"
    Well getting LIs that will do it all is impossible, and - as the math above shows - getting ones that will do exactly what you want is not impossible either.
    I think it might be even harder for a Rune-keeper, we do actively use 3 of our roles (solo DPS is most efficient if Lightning-based, Raid dps reaches it's peaks while Fire based, and there's Healing too): this would mean 3 sets of 2 LIs, which would fill up all out LI slots, making us unable to lvl items for decon... It'd be far too difficult to get relics. And while you can perfectly imagine a LI set for both DPS roles, it's like, not possible to get. Because one guy on US already has the Rune-stone that has ALL desired DPS legacies, math tells us noone else will ever gonna get one like that. Well, maybe in a century...

    I should just chill and that's what I'm trying to do. I just need a better Satchel ;)

    But I won't stop moaning - maybe, just maybe Devs will come to their senses finally and realize that some things may sound great on sketch, but they could come out terribly wrong...

  3. My hope is that the level cap increase is also opened for legendaries... meaning that they will truly "grow with us" as originally claimed. Open up more levels for already maxed LIs, give them access to better buffs, etc.

    Guess we'll see.

    Absolutely wonderful site, by the way.

    - Tony

  4. It all depends on what you define as 'good'. I think there's this assumption that you should be able to get the best possible combination and that anything less is well, less than great.

    All you need is two decent things to start spending points on when you get any given Legendary. If you treat it as an upgrade system, you're leveling a bunch of items as potential replacements for your current.

    That all said, I think Turbine has made a bit of a mistake, because they should have known people would obsessively theorycraft the numbers and work out their exact / slim chances at getting the 'perfect' min-maxed item of choice.

  5. I was just reading that forum thread and got a bit blah about it all! I think we all know there are problems with the LI system, which once seemed so interesting, I'm sure they'll be tweaking it sometime!

  6. I really did try to read all of this, but there were numbers and percentage signs, and I cam out in a cold sweat.

    But seriously, I'm hoping Turbine consider reworking the LI system in the near future. I seem to remember the spin... sorry previews of the LI systme used terms like mobile quest hub, and deeds for using the weapon in a particular way or place. This sounded cool... +3% sprint duration (whatever tier) on a champ axe does not sound cool.


  7. Tbh it seems that most minstrel 2nd age are crap below 58...ive been lucky in that @56 i paid 7g for a 58 2nd age book with has great legacies and wierdly got a dropped lvl 60 mace with the legacies id choose to start and then next 2 forgings had great ones id say its luck :)
    On another point where is the 1st age minstrel stuff :P