I have seen posts from time to time about drop rates of seals and shards. One of the recent posts got me to thinking about probability theory and I looked into the dusty corners of my mind to see what I could remember. If anyone is fresher on the subject, please feel free to chime in. The last post I read was about drops in the Web of Chaos chain (a.k.a. LoD), so I'll use that as a reference point.
To say that on epic hard that there is a 15% drop chance for a seal, is to say that 85% of the time no seal will drop. As far as I know there is nothing that ties one drop to another, even between individuals in the same party. So they are likely independent events. So if you take the failure rate and multiply it by itself the number of times that a drop event happens, you get your failure rate for a streak of farming. Let me give you an example.
Suppose you form a party of 6 and decide to farm seals on epic hard from Lords of Dust. You manage to zerg through it quickly three times in a row. No seals drop at all for anyone. How improbable is this? Without doing the math, it would appear that the loot drop table is broken. However if you take the failure rate and raise it to the 18th power (6 party members times 3 runs), you find out that it has a little over a 5% chance of happening for any given set of epic hard, 6 member party, 3 consecutive runs. That means roughly 1 time out of 19, there will be no seal drops in this scenario. Even on epic elite, a 6 member, 3 set run would still have a 1 in 177 chance of no seal drops at all. So even on epic elite, although it would be really bad luck if you got no seals to drop at all, statistically such a thing has to happen from time to time.
The equations are thus :
epic hard : 0.85^18 ~ 0.05364
epic elite : 0.75^18 ~ 0.00564
Again, assuming that all drops are completely independent (which I find likely), if instead you solo'd epic hard 18 times and got no seal drops whatsoever, you would just be that unlucky 1 in 19 people who it happens to. Being in a party of 6 instead of going solo, you are only increasing the number of events per run, not the odds of a drop happening. You just see 6 at once in a full party instead of just the 1 if you are solo. This of course assumes you are carefully watching what people do or do not pull, which could affect your count.
Having said all this, I cannot of course speak to what is actually happening with actual drops. Anything I said would be pure speculation and based solely on my own experience and other anecdotal evidence. Sum both of them up and you do not have a large enough set of events to be statistically significant.
To all the posters who have questioned various drop rates, I am in no way saying you are wrong. My personal farming efforts have often frustrated me to the point in believing that maybe the drop tables are off, or some complex bit of code is skewing the results from what they are intended to be. Sometimes it seems like it takes forever to see even one seal drop, and then suddenly it seems like a seal or two drops every run. This is the way random chance works. This is not to say that perhaps a change has happened during an update that does affect drop rates, whether intended or unintended by the developers.
If I roll snake eyes three times at the craps table, it doesn't mean that the house switched to loaded dice while I wasn't looking. Although too many in a row would make me really suspicious, and if I roll snake eyes more often than not, I might start looking at the dealer funny. But rolling dice takes a lot shorter time than running a quest. So to all those who are frustrated in trying to get that one last seal or shard, you have my sincere wish that your luck changes soon. I sure hope mine does.
To the developers and management of Turbine, if there is an internal audit system that verifies with actual data that the drop rates are working as intended, could you please just hint to us that it exists? And if it doesn't, would you consider taking some of your valuable time to evaluate how difficult it might be to implement it? I am sure I and probably other players with coding experience would gladly volunteer ideas on how it might be accomplished.