Wednesday, January 21, 2015

The Problem with Low Drop Rates

I've been playing Marvel Heroes, taking advantage this week of the wonderfully bouncy and powerful redesigned Hulk. I've run a lot of cosmic Taskmaster terminals, then transitioned to cosmic Kurse runs. These runs are useful because Kurse drops one of the pivotal items in the game, the Gem of the Kursed. The Gem is the best kind of loot --- i.e., the kind that automatically increases your DPS almost no matter what your build, requires virtually no decision-making, and offers no options. You get the Gem, you equip it, you have more fun.

So I would like to get a Gem! Hulk wants. The problem is that the Gem is rare. Supposedly, it has a 1/200 drop rate in the Cosmic Kurse instance. Drop rates of 0.005 are an anti-fun mechanic.

Of course, the community-approved response to a low drop rate item that every player wants is: suck it up, work harder, grind more. Well and good. Often people making this argument will talk about how they tried hard and have gotten 3 (5? 7?) Gems of the Kursed, so they know you are just whining.

The math of low-probability events explains why something like Gem farming feels so unenjoyable and futile to some players, while seeming like a tedious but ultimately rewarding task to others. With a low drop rate like that reported for the Gem, how many runs can a player do before seeing the desired reward? The range is huge.

This chart shows the probability of completing a certain number of Kurse runs without seeing a single Gem. Half of players will get their first Gem by run number 138 --- which is a lot, demonstrates absolute mastery over the instance and then some, and is clearly well into the zone of simple grinding. 20% of players will have much better luck, getting their first Gem by run number 45. The least lucky 20% of players will have to run 321 instances or more to get a Gem. The difference between the first and last quintile is, to my eye, immense --- a factor of roughly 7.

Things get even worse from here, however. The least fortunate 5% of players will have to kill Kurse 598 times before getting a single Gem. 1% will have to run the instance a truly phenomenal 919 times to get a single drop. Let's be honest: nobody is going to grind an instance fruitlessly 900 times.

Of course, the numbers above are not the half of it. Suppose you've killed Kurse 300 times without seeing a Gem. How many more times might you expect to run before seeing a drop? Well, the loot system is a random process with no memory --- so the answer is 138. If you run another 600 times without a Gem? You can still expect another 138. There is no progress.

So players who are lucky end up with a grind that is long but manageable. Players who are unlucky get to run the same instance for 50+ hours without any sense of progress. Is it any wonder that the second category complains, and that the first category brushes them off? If as seems likely unlucky players quit more often than lucky ones, the population of players will ultimately be made up disproportionately of people who had a moderate but acceptable grind to get the Gem --- because the game drove the rest of the players away.

The issue is this: low drop rates create very long tails in the random process of getting the desired item. A game play element that is fun or at least tolerable for some players will be effectively never-ending for others. For this reason, very low drop rates on important items are ultimately a good tool for narrowing down the player base.

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