There really wasn’t much paladin-specific information provided in the MoP media event – at least, not the sort of crunchy, math-y sort of information I usually blog about. However, there was a lot of talk about the new LFR loot system they’re going to put in place, and a lot of controversy/outcry/confusion on the part of the players. I worked out a little bit of the math during an e-mail conversation with Anafielle, and we decided it was interesting enough to turn into a blog post after all.
I think the system is good, it just wasn’t explained very well at first. And there’s still some confusion, even on Blizzard’s part it seems, about whether your roll is truly independent of other players or not. But for the moment, let’s assume it is (either system works, really – I’ll touch on that again at the end).
The most common complaint I’ve seen in the past few days is that players feel like they’ll have less control over what they win. “But if item X drops,” they say, “I only have to roll against the other people that need it, and not the people who don’t need it.” The flaw in this logic is that “if item X drops” encapsulates a whole bunch of RNG that isn’t in their favor. That statement self-selects a small subset of the possible scenarios (e.g., that item X has dropped) and compares that subset to the entirety of the new system, which isn’t a fair comparison.
In other words, you don’t have control in LFR, you have the illusion of control. If it were a guild run, and you could guarantee that “next time item X drops, it’s my turn,” then you’d have control. If you’re alone in an LFR, the expectation is that all 24 other people in the raid are after gear, and all of them that can roll on your item will. Unless you’re participating in trading cabals, you don’t have any more control over what drops and whether or not you win it than you do in a completely random system.
To show this, let’s compare the systems. The correct way to do that is as follows:
chance_to_win_X = (chance_X_drops) / (num_players_rolling_on_X)
Consider that most items have a ~15-35% drop rate, so let’s use 25% as a baseline for item X to drop from the boss. Note that this is after all of the combinatorics involved in the drop happening (i.e., did it drop once, did multiples drop, etc.). Let’s say that 4 other players in the raid are rolling on the item as well. That means you’ll have a one in five chance (20%) of winning the item if it does drop.
Your net chance of winning a specific item in the current system is (0.25)/5 = 0.05 = 5%. And it gets worse – far worse – if more people roll. Have 8 people roll and you’re down to around 3%. Have a Vanquisher token (10 rollers in an average 25-man group) and it’s down to 2.5%.
Your net chance of winning any item (i.e. not just item X, but item Y or Z from the same boss as well) is a lot more complicated, because it depends on several details about the boss’s loot table. How many items does he drop? How many of those items can you actually use? What is the individual probability of each drop (i.e. on a tier table, Vanquisher is 40% but Conqueror/Protector are each 30%)? And it’s complicated further by the fact that the loot table is usually split in two to prevent 4 of the same item from dropping. So for example, if the boss drops 4 items, 2 are from one loot table and 2 are from another. Bosses that drop tier generally have one table for the 3 tier tokens, and one table for non-tier drops.
So let’s make some assumptions. We’ll say the boss can only drop 2 different items you can use, which seems reasonable for DS after quickly browsing a few drop tables on wowhead. Let’s also assume those two items are on separate tables – maybe one is a tier token, and the other is an off-set item like a ring, bracers, etc. That makes the two item rolls independent, which means your chance of winning either or both of the two items is (1-(1-0.05)^2) = 0.0975 = 9.75%.
That might look confusing, but it’s actually quite simple. You have a 5% chance to win one drop, and a 95% (1-0.05=0.95) chance to not win that one drop. The chance of winning one, the other, or both drops is just 100% minus the chance that you lose both drops (because there are only four possible outcomes: win+win, win+lose, lose+win, and lose+lose). The chance that you lose both drops is 0.95^2, so the chance that you win anything is 1-0.95^2 = 0.0975 = 9.75%.
New LFR system:
chance_to_win_X = (chance_you_roll_high_enough) / (num_usable_drops)
Let’s say the boss drops 2 items you can use, and assume they’re equally probable. Let’s also say that Blizzard sets the roll threshold at 90 (i.e., you have to roll 91 or higher to win an item – a 10% chance to win). You have a (0.1)/2 = 0.05 = 5% chance of winning the exact item you want. But you have a 10% chance of winning at least one item that you need.
I’ve simplified things a bit here by assuming all items are equally probable – in other words, if there are 3 usable items the boss drops, each has a 33.3% chance (repeating, of course) to be the one you get. That isn’t necessarily the case. They could have some items be more common than others by weighting things differently (i.e. tier token is 40% chance, each of two off-set items is 30%). But that doesn’t really change much, apart from making specific items more or less likely. It doesn’t change the average.
Also note that we’ve made up a lot of these numbers – they could make it a 15% chance to get any item (increasing your odds for both overall and for single items), and they could distribute loot such that there’s 3 or more items you’ll want off of a given boss (decreasing your odds for a single item – but this becomes less likely in a tier with more bosses, it was much worse in Firelands and Dragon Soul than it was in T11 or will be in T14).
Declaration of Independence
I said in the beginning that it doesn’t matter whether your roll is truly independent of other players. Here’s why:
In the new system, your chance of winning is the chance you roll high enough divided by the number of useful items that boss drops for your class. Now, they could set “chance_of_rolling_high_enough” to an arbitrary value, like 10%. That’s what I did in my example. Then you’re truly independent of other players, because you could all win one item, or nobody could, or anything in-between.
What happens if instead, the system performs a /roll for each player and just awards items to the top 4? Well, it means that instead of rolling to beat a certain arbitrary threshold, you’re rolling to beat 21 other players. In other words, you need to be in the top 4 out of 25, or in the top 4/25 = 0.16 = 16%. It doesn’t matter who those players are, either, because they’re all rolling automatically. So if they did implement that system, it would be no different on a personal level than just setting the bar arbitrarily at 84 in the independent system. You’re not really competing against the other players for anything, because statistically it will always work out such that you’ll have a 4 in 25 chance to win once you average over many boss kills. The only difference is that the variance in the number of items awarded goes to zero. In other words, there’s always 4 items awarded rather than randomly fluctuating between 0 and 25 with an average of 4.
Until we know the percentages, we won’t know for sure which system truly gives you faster loot accrual. But it’s far more likely that your chance of winning items will increase with the new system. And more importantly, it will be much more consistent, because it won’t be as subject to group composition. No more zoning into LFR and groaning because there are 5 DPS DKS, 3 Ret paladins, and 4 Warriors all trying to get a two-hander.
The “extra bonus roll” stuff looks interesting too – it’s basically a way to weight the dice in your favor for a particular boss, which has some neat strategic implications. If you’re really after item X, you can load your dice for that particular item. Sort of nifty.
Given that the new system streamlines the looting process, eliminates loot drama from LFR, and adds the ability to use loaded dice on certain bosses (something that would be abysmal to implement in the old system), I’m on-board. Especially since the only cost is the illusion of control.