Degree vs Self-Taught:
In my experience, people who are self-taught or who learned by experience tend to have odd gaps in their knowledge.
For example, the Shazam app. I knew right away it must be using Fourier analysis. But if one was self-taught, one might have never understood what the point of FA was, or even have been aware of its existence, and instead used kludgy, inept methods.
For a personal example, I was once given the job of taking the graphic display on a CRT and mapping it onto a printer page. The addressing was different, the axes were different, the pixels/per inch were different. I knew what the tool was - a transformation matrix. Had it ginned up in an hour and it worked first try.
A co-worker was completely baffled at this. He didn't know what a transformation matrix was, and likely would have otherwise spent a couple weeks on the problem and done a crappy job.
I.e. one doesn't know what one doesn't know. The advantage of an accredited degree program is the curriculum is selected by people who know what you need to know, and the order in which information is best presented.