[Math] Improving queue times in Team Builder
How can we improve queue times in Team Builder? Maybe a mathematical model can help understand how long you have to wait before finding a team. The general formula for the average waiting time in Team Builder is the following: [average waiting time per game] = (1 - 5 * [fraction least popular position played]) * [average game duration]
Let me illustrate that formula with some concrete numbers.
- Not every position has the same popularity. Suppose the least popular position is chosen by 15% of players.
- There are 5 players per team, so at any given time at most 5 * 15 = 75% of players is in a team.
- The remaining 25% has to wait in a queue.
- Suppose the average time for one game is 30 minutes.
- The average waiting time per game is 0,25 * 30 = 7,5 minutes.
Note that this model is very simplified, but it does capture one of the biggest reasons why you have to wait. The least played position (support, jungle) is the bottleneck. Even a small increase in playrate for the most unpopular positions means a huge drop in queue times. In my example if the least chosen position went from 15% to 18% popularity, queue times would drop from 7,5 to 3 minutes.
So how can you do that? Many players have suggested incentives like small IP gains or icons if you play a less popular position. I think it would also help if junglers and supports got more appreciation. The community could show that it is not normal to blame your jungler or support for everything that goes wrong. And Riot could try to buff these roles to bring them closer to the power of solo laners and marksman.
Tl;dr Even a small increase in popularity for the least chosen roles would drastically improve queue times in Team Builder.
Below you find the assumptions I made for my model:
- I assumed you are either waiting in the queue or playing the game. In reality there is also waiting until everyone locks in, the log-in screen and post-game chat. For completeness you should incorporate that in the average time for one game.
- My approach with averages only works if enough players are in the system. For small groups (very high or low elo) this model heavily underestimates the queue times.
- The model is for meta team compositions (top, mid, jungle, adc, support). Compositions like 5 mid do not have the bottleneck of the least played role.
- I neglected queue time for the least popular role. As a support I usually find a match almost instantly.
- My assumption for the least played role is based on this thread. Lyte: "When we surveyed players and asked what their preferred role was, about 15% of players preferred playing Support, 14% of players preferred playing Jungle, and 5% of players were willing to fill any role."
- I chose 30 minutes for average game length, because it is a round number. The actual length may be a bit longer.
Thank you for reading! Please tell me if you see errors in my calculations.
