For example would a late game team be stronger or as strong as a team that has good early game AND late game champs? Would having a team of all early game champs have the same effect?
How much should my teams early/late game potential influence what champion I should pick?
The goal of early game champions is to get enough snowball going early game so that either the game doesn't last til late game or they're so fed by late game winning is easy.
The goal of late game champions is to hold out, farm up, and not get snowballed until late game when they can then dominate.
Having a mix of early/late game may be useful, but it all really depends on how the laning phase goes. If the early game champs fail to make an impact early game then their usefulness is diminished. If a late game champion fails to farm well during the early/mid game they're not going to be stronger than the early game champion late game anyway. Ex: Tristana 0/5/0 250 cs vs a 5/0/5 draven with 250 cs the draven will most likely win, even if its 50 mins into the game.
In summary (and disclaimer this may be somewhat personal opinion), late game/early game shouldn't influence champ select. You should try to get a team comp that synergizes well. Once you have that, analyze whether you're late game or early game and play accordingly (see above).
I agree with Brian answer but I want to add a point.
You saw the summer NA LCS? Cloud 9 was the best team by far, and they always pick early/mid champs. Why? It's better to take early champs? Not always.
But if you take early champs you need to know how to play good at lane or do a lot of teamwork for get fast objectives and get early gold to get better than the other team even in lategame.
If you are playing solo/duo and you like to play mid (thats my main) I advise to you to take mid champs like kassadin/Diana/Akali/Lissandra/ahri if your bot is late like vayne. Cause if you see your vayne is 20 cs less or 0/2/0 you can roam fast to help her to get feed.
But like brian said: "You should try to get a team comp that synergizes well." Like taking orianna if zac or j4 in your team.
And another advise. If you dont see any great pick to do a great teamplay, take a champ that can split push really well like tryndamere or Yi and push one lane all you can. In my experience, that can win a game. (e.g. See fnatic games).
Sorry for my bad english.
