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Emotions and Randomness - Loot Drops

The math behind loot drops is not generally given much thought past a flat percentage drop rate, but the type of randomness used can greatly influence a player's emotional game experience. I'd like to bring a bit of light to these considerations.

Chris Grey, Blogger

April 3, 2013

12 Min Read

Even though randomness can be used to greatly influence a player's experience with a game, I haven't seen many people put much thought into crafting it. We've all got war stories about a rare drop that took us hours to get, if not tens of hours. Gamefaqs is loaded with forum threads talking about the despair of the random drop. Even worse are the threads made by people who got the drop in one go, bragging and taunting the rest of the community, as if luck with the random number generator were something they actively controlled. For better or worse, randomness currently colors the play experience tremendously; why not talk about crafting it more actively from our side so that these experiences are less accidental?

Today, I'd like to focus on drops. I'm being a bit loose with the word because I'd like the ability to talk about both items dropped by defeated monsters and the monster taming process in Ni No Kuni, where enemies randomly become recruitable after you beat them up. I'm going to avoid giving hard numbers wherever possible; my aim here is to give a few heuristics about how randomness feels to the player.

First, let's look at the way it's done now. Typically, designers look at the in-game economic value of an item and decide how scarce it should be. More powerful items either appear later in the game or drop with a much lower constant percentage chance. The idea here is that players should feel some kind of sense of accomplishment when they obtain the item, or at least see how lucky they've been. Either way, it'll bring the players to value the item, hopefully in accord with the designer. If players manage to get the drop in the average number of tries, if the designer has valued the item correctly, the player will typically have a similar valuation of and appropriate attachment to the item.

With a constant drop rate, here's the graph that captures the farming experience. You might be expecting a bell curve here, but I want to illustrate something else born from this data. To do so, we're going to change the vertical axis to reflect the following: assuming your players kill enemies until they get one of the items, here's how long the player population will be farming.


 Population of Players Still Farming for Their First Drop Over Time

Pay attention to the shape; the key point to notice here is that the graph never actually hits zero. That means some of your players are never going to successfully acquire the item, and they will have a terrible time trying to farm it because they will spend tremendous amounts of time doing a task the designer had only pictured them doing for a fifth of that time. Even the good feeling at getting the drop if they eventually manage to get it is generally overshadowed at this level. What's worse, the time farming the item will skew a player's value of it; most players will resent having to grind a massive amount of time if others did not have to, and they will focus their resentment on the item in question. Naturally, this resentment will also spill over to the game, and they will undoubtedly vent about how unfair the game is to anyone that will listen. These players will be overfarmed by the nature of the task, and this also ruins the otherwise carefully crafted difficulty curve. Their frustration can lead to quitting the game, and if this player was dedicated enough to stick it out that long, you probably alienated an incredibly passionate player. All this angst for a random drop that probably didn't matter much in the bigger picture of the game.

...and the Queen save the poor souls who feel compelled to get the collect all random drops achievement. That synergy can quickly lead to tens of hours of despair and compulsion, if there are many items or especially rare items.

The problem with using averages to balance in this case is myriad. In the graph, notice that about sixty percent of players will receive the drop before the average number of attempts, and half of the population gets the item significantly before the average. This means most players won't be seeing the event as many times as the designer probably designed for, and in reality, as any one player usually only goes through this process to get any one drop once, this will become the general consensus on how long the experience takes. Potentially a happy mistake, but it does diminish the feeling of effort the designer probably wanted the most players to feel. Of the rest, it can be expected that about twenty-five percent of players will take more than one and a half times the average to get the drop, and more than ten percent will take more than twice as long as average. If these players look to the rest of the player population, they will see their experience taking more than two to three times as long as the lucky half, respectively.

A designer with fixed resources would be drawn to craft the average experience when, in all honestly, it's the fifty percent who finished significantly early and the twenty-five percent on the tail that need the attention more. Additionally, the latter will be the ones to really begin to see the activity for the warts it has. If the designer neglects the tail experience and has several different drops required or encouraged in game, the designer will eventually fail all of their players; the more drops the player needs, the more likely that the player will be in that tail at some point in the game. By focusing on the mathematical average experience, the designer is effectively neglecting seventy-five percent of their players on any single drop.


Other Kinds of Randomness - Escalating Drops


I want to present two simple alternatives. The first is an escalating drop rate. Each time a player fails to get the drop at the end of the event, the probability it drops next time increases. This probability caps at a guaranteed drop, and once the item drops, the probability resets to some level. It can reset at zero if you only ever want one in the game; it can reset at the initial probability if you want to make the experience to get another item take the same amount of time, more or less, as the first time; it can reset at a high probability if you want the item to be valuable now but easy to come by later.

Here is the new chart for this experience.

 Population of Players Still Farming for Their First Drop Over Time With Escalating Drops


Notice how the line now hits zero on the right of the graph. It eliminates the abysmal experience we spoke of above. There will be unlucky players, but there's a cap on the amount of time they'll have to spend with their misfortune. There will still be war stories, but if designed well, the worst-case player experience can be designed for more easily, as it will more closely match the average. This can lead to those war stories that can enhance the player experience, as they feel like they struggled, but not much harder than the designer expected, which is nice way to give a bit of fiero. The angst of trying to get the item will always be fulfilled.

Additionally, if you set the initial drop rate low and let the growth rate accelerate, you'll have fewer lucky people as well. This could help if you want to make the player master a challenging fight through repeated attempts to potentially get a powerful item. It’s worth noting that the player who gets the item on the first try will have their difficulty curve distorted, even though this case tends to be more subtle than the player who takes many tries. Empowerment is not a bad thing, but it can lead the lucky player to think the game is much easier than it is because of a fortuitous break. In general, the escalating drop approach will make the experience a little more uniform for any given player, and usually, it will be relatively invisible to them.

There's a temptation here to wonder what would happen if you had to kill several of the same kind of monster before the item could even become available. If the player understands what's happening, and they know that they will be fighting several times before they could even get a drop, that fighting suddenly becomes work. Gambling in this form works because the payoff is potentially always right around the corner. It cannot be understated how powerful this force is to motivate. Asking someone to do something fifty times makes it a chore, and times ten through forty will not be savored because after the initial novelty of doing it, you know it will not net reward any time soon. If a task could be rewarded randomly after any one attempt, more attention to detail and care will go into it from the player. The player will appreciate the experience more if they feel like what they are doing could pay off at any moment, not just some long time in the future.


Other Kinds of Randomness - Diminishing Returns


This is the invert of above. The idea is that the player has a limited number of chances to get an item in game before it goes away completely. Typically, the initial probability of the drop will start high, and either decrease with each failure, or the event will disappear after a set number of attempts. Either way makes the drop impossible to get after a certain number of chances.

This randomness is tricky to deal with as you are, in no uncertain terms, guaranteeing that a percentage of your player base will never get the item. It can be more humane than the traditional way as you are giving no option to exchange time (farm) for in-game value. If the item has significant value to the player, and the player knows the stakes, there will generally be a significant amount of urgency put on the outcomes, and a skilled designer could use this as a way to make a large emotional mark.

There is an unspoken rule with these kinds of drops. They can be gamed by reloading. As with permadeath mechanics, players can still get some tension from the outcome while using the load function to try as many times as they want to obtain the drop. If the ability to reload is removed, as it was in Demon's Souls, then you may want to consider making the game short, but replayable, or having several different drops, only one achievable in the game. This can force players to actually have to adjust their playstyle based on what they got. Be careful with this kind of randomness, as it can easily inspire rage. You are very close to a core expectation of most players: "I am master of this game world, and given effort, I should not be deprived of anything I want."


 Some General Heuristics


Since most people aren't taught well to think about probability, I wanted to give a few guidelines to work with.

When in doubt, make a simulation. When you use any type of probability distribution besides the constant percentage drop, you do not need to do a full mathematical workout of all cases. I highly recommend writing a program (or bribing your friend the coder to do so) to simulate the effects and generate graphs of how the system behaves when tested a huge number of times. That information, while not guaranteed to be exactly right, will be good enough, and the calculations required to get an exact answer are not worth the time required to compute them in most cases.

Generally speaking, the more random drops the player is compelled to farm, the closer their total experience will be to the average experience overall, and the more likely they are to face the worst case short term scenario sometime in their experience. Look at it this way: if everyone rolls fifty dice, it's likely that the roll totals won't differ much, and everyone will have probably rolled at least a couple of ones. The trap here is subtle: you cannot assume that poor luck will only affect some players in this case; it is almost guaranteed to strike everyone. Design accordingly.

The reverse of this is true, too. A small number of random drops in your game will mean that the player experience will be very uneven and different from person to person.

People tend to be terrible at estimating probabilities in their head, and dry spells leave bigger scars than lucky breaks feel good. The lower the probability, the worse the estimation ability. This can manifest especially with rare drops; people tend to start becoming frustrated long before the average if they know the drop is rare going into the session. Additionally, people will typically experience negative emotion for a significant portion of a farming session they consider to be long, while players who get lucky tend to move on quickly after experiencing the short-lived joy over a drop.

People conflate luck and skill quite often. It might be interesting to investigate mechanics that would reinforce this: increased drops for skilled play would allow those who have already mastered what the game is teaching to move on to something more interesting to them, while giving the less skilled players a way to both potentially improve and still get whatever item is at stake. This is something I've rarely seen, but I think would have huge potential.

Randomness is lovely, and if players buy into what is at stake, gambling can be used to craft incredible emotional experiences. It's a shame that something so close to our hearts is so ill-understood because a little extra crafting of the probabilities behind the game mechanics could yield incredibly diverse experiences, both from game session to game session for any one player and between players. There is an amazing amount of potential, and I was only able to scratch the surface with a huge amount of text so all I can recommend for those who are willing to is: experiment.

As I didn't get to show examples this time, I'm splitting them off into another entry. When it is done, I'll link to it here.

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