Here’s a fun little trivia fact that you probably already know: Computers can’t really do randomness. A random number is usually generated by pulling outside data that appear to have an unpredictable pattern, shoving them through equations, and then outputting something that has the appearance of randomness. It’s not actually truly random, though; technically, the same seed for randomness would produce the same result. You can even use this in various ways (authentication dongles and apps work off of that basic principle).
Despite that fact, randomness or the appearance of randomness is baked into lots of MMOs, since it was baked into lots of single-player games and so on back down the line. And this ties into a lot of other issues within games, the sort of things that weird nerds who enjoy thinking about this stuff (including me) tend to enjoy talking about. So today, let’s share some random thoughts on… random things.
Single-roll vs. multi-roll systems
Here’s a fun question with two different answers. Say that you have a 100% chance to hit a target, a 20% chance for a critical hit, and a 20% chance for a solid hit, and the target itself has a 10% chance to evade. What is your actual chance to land a normal hit? The answer depends on how the game handles those odds.
World of Warcraft classically used a single-roll system for this. Final Fantasy XIV uses a multi-roll system. And it’s interesting to understand how the two interact because different systems produce different results.
In a single-roll system, you have only one random roll determining what happens when your ability is used. This means that you have a priority system for how likely certain outcomes are to happen. Tanks relied upon this back in the day to ensure that a boss couldn’t critically hit or land a crushing blow; by stacking up defensive values high enough, they could ensure that both of those impacts were pushed off the potential hit chart.
In this scenario, your chance of landing a normal hit would be 50%. Your base chance to hit is modified by a 20% chance to crit, a 20% chance for a solid hit, and a 10% evade. 90% of the time you’ll land a hit, but 40% of the time it won’t just be a normal hit.
By contrast, a multi-roll system rolls each chance separately, meaning that you have a different roll to determine if you hit at all, then if you score a critical hit, and so on. Using a multi-roll system, you have a 57.6% of landing a normal hit when all is said and done (since you have a 90% chance to hit at all, an 80% chance to not get a critical hit, and an 80% chance to not get a solid hit).
So which system is superior? Well… the real answer is “they’re both superior for different things and different goals.” A single-roll system is useful when there’s going to be one result as opposed to multiple particular results; for example, a piece of gear dropped from a boss can be only one of a specific number of things, but it’ll only ever be one thing for a given drop. On the other hand, multi-roll systems are good for other pieces of loot, like determining whether said boss also happens to drop a mount that might not show up every time.
In combat terms, the single-roll system has the advantage of being a little more immediately straightforward to understand. If your crit chance is 20%, you know that means you will crit one out of every five hits without any additional elements. However, the multi-roll system has the advantage of being able to layer effects; in the above scenario, you’ll have around a 4% chance to get a critical hit and a solid hit at the same time, presumably for even more damage. It also means not having to deal with chances being modified by circumstances in the same way (“yes, technically you have a 30% chance to crit, but this character’s defense pushes that down to 15%”).
Loot and drop rates
So hey, let’s go ahead and segue to talking about loot. How do drop rates work? The answer is not “a 10% drop rate means you’ll get it in 10 runs.” In fact, the answer is really “it varies,” but it’s useful to drop this down here in the “later reference material” column.
Generally, things dropped by random creatures in the world follow a multi-roll system. The specifics vary by game, but conceptually it’s pretty easy to understand. This enemy drops between 0-3 items; only the third slot can be a worldwide valuable drop. Or the enemy has a chance to drop three items, each separate from one another. Or it rolls for one drop, then what the drop is, then to see if there’s another… it’s not really all that complex.
However, we tend to make it complex because it’s easy to kill two dozen wolves and have none of them drop fangs, and what’s wrong here?! And the answer, in short, is that we don’t really understand the way that statistics for things like drop rates actually work.
Let’s say that those fangs have a 10% drop rate. That means 90% of the time, you get no fang. So what are your odds of killing two dozen wolves and still getting no fang? Right around 8%. That’s unlikely, but it’s still entirely plausible. Because of the way that percentages multiply, even if you killed twice that number, you’d still have a 0.6% chance of getting no fangs. There’s never a point when you absolutely must get a fang.
For most people, drama doesn’t start around lack of random fangs, though. It starts in games like WoW or FFXIV or Star Wars: The Old Republic when you’re looking for that one piece of gear the game will not drop. And that is a different situation.
In most of these games, boss drops are single-roll systems. Kill a raid boss in WoW and it will drop a fixed amount of loot based on party size. That loot can be differentiated by slot – e.g., this boss always drops a piece of gear and a shoulder or glove tier token – but it can just as easy be two drops from the same master table.
The odds of a given piece dropping on a table are thus easy to figure out; if there are twelve items available, any given piece has a 1/12 chance of dropping. But we have a bad habit of thinking in terms of “well, that means that after 12 runs, I should see everything.”
But scaling percentages work there as well, because each roll is independent of the subsequent roll. After 12 runs, you you think that your number of chances has been multiplied by 12, but your number of possible outcomes has been multiplied by 12 as well. To be very mathy, your chances are not now 12/12, they’re 12/144. Or, you know… 1/12.
Some games will use a form of protection here, insofar as the percent chance of you getting something goes up over time, and that’s a more elaborate discussion. But just looking at math it should be clear that so long as you’re still talking about multiplying random percentages, there’s no such thing as a certainty. In order for your odds of not seeing that one drop you want for a 1/12 chance to reach below 1%, you’d need to get a shot at that item 53 times.
And the conclusion? I don’t have one this week. It’s just random thoughts on random chance, you know?