Playing League of Legends without a team is almost like a wild card. Most of the times, the chances of winning will always depend on the team that you will end up with. You can consider yourself lucky if your team can actually act like a team with coordination and teamwork. The chances are definitely very slim especially because of the fact that most players who are actually good already have their own teams. Most of the times, you will end up with a team that are full of kids and newbies. There are some instances when you can find a good player who you can partner up with.
There are a lot of players who have already tried partnering up with someone for several games. This allowed both of their ranks to actually go up faster than just getting a random team. There are also some people who are going for duo queue services. Basically, this is when you will hire another player to play with you in the games. With a skilled partner, the victory is almost assured. There are many people who are offering duo queue services all over the internet. You can also hire some of the people you know who are already really good at playing.
Looking for a partner in these kinds of games is not really that easy. If you want, you can do a trial and error and look for someone who is actually very willing to partner up. Aside from the fact that you can learn some of the things together, you will also rank up faster mainly because you already have a good combination in mind and the communication is a lot better than having a random team to back you up. This can also be a start of having a really good team which can compete in competitions.