Indeed, you can just sit in your home “office” and start a business without as much of a letter on paper. To be succesful, you need focus, clear goals, good understanding of what opportunities you intend to capitalize on and what obstacles you expect to counter on that road. You need a mission statement, a one-liner that tells anyone asking what you do what it is you do, without reverting to minute-long explanations. If you ever need financing (banks or investors) they will expect you to have a good business plan (although they will only like to see a 1- or 2- page investment summary outlining what they have to put in and can expect out of it and how you plan to accomplish that.
So, the long story short, a businessplan will GREATLY enhance your chances of succes, by focussing your attention and efforts and forcing you to think in advance about what you are going to do and how.
Greetinx.