If you think you deserve a higher rank, you should be able to win most of your games
Just something I've noticed with myself. I was placed in Silver 4 which I'm satisfied with because last season I was placed in bronze 3 (my first season). Towards the end of preseason I was able to climb to gold 5, so I just assume I should be able to stomp my way through low silver...
And I was right!
My primary is fill (fastest queue times ever. Like, a match is found less than a second after I queue up, really), meaning I've gotten support for like 90% of my games, which is okay because I actually enjoy support. Every game I play a support I'm comfortable with I think to myself: My adc is doing well we should be able to win this (the supports I play are supporty supports like nami/janna).
Then, low silver happens.
Our team is getting rekt, we have no objectives, nobody think we'll win but want to play it out anyways (it's silver after all). And even if we were ahead we threw our lead.
I'm going to cut to the chase. Look at our team's gold disadvantage in my promos for silver 3:
http://matchhistory.na.leagueoflegends.com/en/#match-details/NA1/2080554799/227737595?tab=overview
(if you don't feel like clicking)
We are doing hilariously bad. Jinx who was doing garbage in lane got a quadra 13 minutes in because of a crap teamfight at drag (then a delayed penta, but not official). Illaoi actually one-shotted me and could easily 1v3 when we didn't coordinate (we eventually baited out her ults and kited her). We had no dragons at all. Our first baron attempt was stolen. We lose all of our inhibitor turrets and one of our nexus turrets.
BUT
The magic of low elo happened and we came together. We killed their rek'sai that had just gotten their 4th or 5th drag so I suggest we baron while their jungler is down. We secured baron, won the teamfight because they tried to go in and steal (everyone did a good job protecting from a steal), and ended the game. Thankfully nobody on our team was flaming/raging other than a teensy weensy argument when the jinx got a quadra 13 minutes in, but we agreed that she wasn't that good and shouldn't be too much of a problem and moved on.
Placements aren't supposed to put you in your rank from last season, it's just a starting point. If you really think you deserve better you should be able to easily climb. I've won so many games just from good shotcalling (fill primary = support primary so I have been able to learn a lot about when to do what)