Why autofill is a necessary evil in a world with role selection.

tl;dr at the bottom. This post is primarily in response to the sentiment that people are willing to wait 5 minutes to not have to deal with auto fill, so if that's you please read at least the tl;dr. Also, hoping that this is the right board for this as this is primarily going to be a discussion about queue times (and math).

With that out of the way, technically, I could just say "Look at DPS queues in an mmo" and be done with it, but that doesn't actually explain anything so instead I'm going to run through an extremely simplified queue to make the point before discussing how this simplified queue relates to the real world. For this simplified queue I am going to make the following assumptions:

1. Each player queues for only one roll and will always get the roll they queue for (no auto fill).

2. Whenever a full team of five people are in the queue, a game is immediately formed with each person at the front of their respective queue.

3. Players enter queue for each roll at a constant rate. In particular, a support enters the queue once every 20 seconds, a mid enters the queue once every 10 seconds, and every other roll enters the queue at some time between these two (so that supports enter the queue most infrequently).

With these assumptions, we first have that every support gets a game as soon as they enter queue. Now, the first mid to enter after the queue opens has to wait 10 seconds for their queue to pop (they enter 10 seconds in and must wait an additional 10 seconds for the first support to enter), the second mid waits 20 seconds (they enter 20 seconds in and must wait an additional 20 seconds for the second support to enter), and in general the n th mid has to wait 10 n seconds to enter (the coefficient is 10 as that is the difference between the support and mid queue times). Now, after a 1 minute period, the 6th mid laner enters the queue and will wait 1 minute to enter the queue due to the above. In general, if you enter queue as a mid laner, your queue time will be equal to the amount of time the queue has been open. Now, the queue time will obviously vary depending on the exact numbers involved but the key point is that, in this queue, queue time for every roll but the least popular scales linearly with the amount of time the queue has been open.

Now, obviously, in a real world scenario queue times can't increase infinitely. In particular, players don't actually enter queues at fixed rates (the other two assumptions are somewhat simplified but close enough to the real world scenario that it doesn't significantly alter the result). In fact, since queue times themselves are a disincentive for joining a queue, the rate at which players enter queue for a specific roll will decrease as queue time for that roll increases. None the less, the primary conclusion still holds, namely, that

• Without auto fill, queue time will increase with time as long as any other roll has people entering that queue at a slower rate.

While performing a realistic analysis of what would happen if you simply disabled auto fill but left the rest of the queue as is is more difficult than I'm going to bother with, I can go back to the initial comparison to DPS queues in an mmo to say that the queue time for popular rolls would likely hit somewhere between the 1 to 2 hour mark before stabilizing. This isn't to say that auto fill is perfect (certainly, if a team consists of only people who have been auto filled the system is failing at its purpose), but some sort of system to equalize the number of people queuing for rolls MUST exist in order for queue times to remain remotely reasonable (and, yes, not being able to queue for rolls is one such system).

As promised, tl;dr without an auto fill system queue times for popular rolls would increase dramatically, likely into the 1-2 hour range.

Edit 1: As Oleandervine below points out, you need to 10 players to form a game. Consequentially, assumption 2 should be changed to "When a full game of 10 players is formed, a game is immediately formed with the front two people of each queue." While this doesn't fundamentally change the point, it does mean that the first and second mid must wait for the second support, so that there's some minor fluctuation in queue time depending on whether you enter queue as an even or odd player to the queue.