Simple Analytics: Why queue times are longer even if the player population is growing

Queue times are maybe the largest current issue as they are absurdly long, especially at higher levels of play. However, thinking that League dying is the reason why is just not true, in fact based on some statistics for games played to date this season, we are on pace for more total games. While that doesn't necessarily mean more total players, it's a sign of growth.

So why longer queue times? Here's a simplistic example to explain what's happening:

Assume a player base of 1000 players. Note these ratios below arent correct but it doesn't matter in proving my point.

500 solo 60 parties of three 160 duos

That's 720 parties looking for games, maximum. Obviously at any one time there will be those in active games, reducing the number of parties in queue significantly.

Now look at the former system, making the assumption all the above 3man parties were former duos.

500 solo 250 duo

That's 750 parties. In the current system, that's 30 less parties total. Multiply the player base by 1000 (1 million total players). That's 30,000 less parties looking for games with the same population as before.

Now,

Add the fact that in reality there are 4 and 5 man parties, reducing this party total further. I would assume that over time the percentage of premades has increased as people have gotten used to the possibility of not having to play solo or duo.

Add the fact that 3 mans can only be matched with a group of 2 or two solos, etc etc etc. This reduces the #of potential maximum parties you have potential to match with. For the example above, if you are in one of the 60 3man groups, your total parties potential in queue isn't 720, it's only 660.

Add the conditional fact that matchmaking looks to create fairness by pairing 3+2 teams with another 3+2 for example.

Add the fact that some parties are unlikely to be matched with others based on roles selected for queue. Every party now has a conditional factor added to matchmaking, it is no longer just about the player quantity. For example a solo Mid/Top player is not likely to get paired with a 3 man group where 2 players having similar mid/top prefs. Here is the area with the most opportunity for Riot to fix.

It should be clear that even with the exact same player population, or even with one that is somewhat larger, the total parties you can potentially match with, even if playing solo, is less than before and this means longer queue times.