Analysis of LFR Loot System

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01/16/2013 10:21 AMPosted by Terrawatt
...I enjoy LFR...

Simple minds find the most mundane things fun .. like rep grinding or endless dailies.

I'm as simple mided as they get, and I enjoy LFR. It's fast, doesn't require a lot of brainpower, and is almost impossible to wipe in, unless someone does it intentionally.

I'm also not concerned about whether or not I get gear; I'm not a raider so why do I need raid gear?

For us with simple minds, LFR is great! :)
So let's say there are only two people in the raid, and everybody rolls on everything. The probability of winning an item is NOT 0.7 * 0.5.
Actually it is.

0.5 * 0.41 (1 item)
+ 0.5 * 0.23 (1st of 2 items)
+ 0.5 * 0.23 (2nd of 2 items)
+ etc.

No, because the (1st of 2 items) probability was already counted when you did the (1 item) calculation. This is what I'm getting at. You can't just mix and match averages with probabilities. The chance of winning an item in a given fight with only you and one other person rolling on the same gear is 35%, not >54.5%. How can you have a >54.5% chance of winning an item in a fight where a useful item only drops 70% of the time when you only have a 50% chance of winning in cases when an item is guaranteed to drop every single time?

Following your logic, let's look at your chances of winning an item against one other person when three drops are guaranteed every single time:
0.5 * 1 (1st of 3 items)
+ 0.5 * 1 (2nd of 3 items)
+ 0.5 * 1 (3rd of 3 items)
= 1.5 or 150%
Congratulations! You win items more often than you even queue!

The correct calculation is
0.5 (chance of winning the first roll)
+ 0.5 * (1 - 0.5) (i.e. 0.25 chance of winning the second roll if you lost the first)
+ 0.5 * (1 - 0.75) (i.e. 0.125 chance of winning the third roll if you lost the first two)
= 0.875 or 87.5 %

This wasn't the topic of the thread, but I have to respond because I find your point of view rather...well...astonishing. I've always found the pleasure of raiding to be found in coordination, teamwork, and flawless (or nearly flawless) execution. In the absence of that, it's just work.

A famous alpinist from the early part of last century wrote (roughly translated from the French): "If it weren't for the fear, all the hunger and thirst and exhaustion and monotony and pain would just be boring."

LFR is like mountain climbing with the fear removed.

Quite an interesting analogy.
I see the problem! You're confusing point probability with statistical averaging.
You're confusing point probability with averaging:

The probability of winning an item is NOT 0.7 * 0.5. It's:
0.5 * 0.41 (1 item)
+ 0.5 * 0.23 (1st of 2 items)
+ 0.5 * 0.23 (2nd of 2 items)
+ etc.

Here are my results (sorry don't know how to make a table without html)
Number of Items you already have: 0 1 2 3
Chance of winning, old system: 21.9% 14.6% 7.3% 0%
Chance of winning, new system: 15% 10% 5% 0%
Am I the only one who saw people running LFR and hitting need on every single item whether they needed it or not just for the lulz?

Or people playing raid leader and distributing loot to those who "deserved" it

Or guilds only looting to their own..

Or all the other !@#$ty situations that happened because of the old system?
Good analysis. I agree with all of your points.
Well, there you go. For example, take that 21.9% average. If you already have everything you need from that boss, or there are 12 other people who need the item, then the probability will not be 21.9%. That's the average probability spread across N boss kills, where N is very large. (EDIT: Or, better yet, where N is very large because "you" means "the whole WoW population.")
The thing is you didn't show the math you used to arrive at the 21.9% number. You correctly said that it could be found by multiplying the probability of a useful item dropping by the probability of winning against other players, but you never stated the probability of a useful item dropping. Instead you stated the average number of useful drops per fight, implying that you could multiply that by the probability of winning a roll against x players (a calculation, by the way, that you also neglected to show), and that's not the case. If you could show the math you used to arrive at the 21.9% figure you would be more credible.
2) Give every player a hidden variable of their chance of getting loot, and for each failed roll increase that variable by a small amount. Say, 2%. If you go an entire week of full LFR with no loot, your next roll would get a +32% roll.

I think something like this would be a great addition to the loot system. It mirrors popular methods guilds use like dkp or suicide kings.

However I think the increase you stated is too high. Just because of the sheer amount of bosses and how gating and rng should still exist I would put it at only .2% or .1% increase for no loot. It helps the perennially unlucky and is hard to abuse. And charms would be unaffected by this.
01/17/2013 02:19 PMPosted by Neckface
That's the average probability spread across N boss kills, where N is very large.
The probability of an item dropping on a given boss doesn't change, no matter how many fights you include, so there is no "average probability." The probability that you will have obtained the item in one of the fights goes up as the number of fights goes up, but it will always converge to 99.999999...% without actually reaching 100%. Please show us how you calculated a 21.9% drop rate on a single "useful" item for a single boss fight because that's the number you're comparing against the current 15% rate. The current rates are listed correctly (15% 10% 5% 0%), but it's the old rates that I'm skeptical about.

I'll show you the calculations myself. There are, according to you, 2.125 other classes sharing loot with you. When you include your own class that's 3.125/11 classes rolling on gear. You multiply that by 25 players to get an average of 7.1 players rolling on gear on a given run. So on an average run you have a 1/7.1 chance of winning the roll. 1/7.1 * 0.7 probability that a useful item dropped for you comes out to 0.09856, which is about a 10% chance of winning a single useful item on a boss fight under the old system. That's far lower than the 21.9% you were claiming and also lower than the 15% drop rate under the current system.

If Blizzard was trying to calibrate the new system based on the old, it would seem that in their model they assumed their customers always behave as selfishly as possibly.

I think that's the exact assumption that they were working with when they developed the system... or rather that assumption is:

Given that a player will have no extraneous interaction with the raid, and no consequence from hitting need, what emotional burden is placed on the player in this situation? How can complexity and the capacity for disagreement be removed from random player interaction?

Much like LFR difficulty, it is favorable in their situation to create a system designed around the lowest common denominator. Because the weakest link in the chain can, and will break, and that ruins the experience for multitudes of other people. The ripples felt by one bad player who rolls need on every piece of gear are much greater than those felt by one good player who only rolls on upgrades.

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