How do I know if I'm good at programming?

Lots of us are good at being excited, moving fast, when something grabs our focus. Some of us are just as excited at the quality of our "how" as we are the size and shape of the finished "what".

That is a bold statement. All the things you list are true, but it also depends on what you are doing. For most Web/Mobile/Enterprise apps you are probably right. But then there are also some areas like graphics programming or AI were the algorithms can absolutely be the hard part.

I consider myself fairly good in my domain (Fullstack but mostly backend) but when i see what some people in graphics programming (or Games in general) or AI are doing, i feel like a newbie. In my domain, i rarely have to deal with complex math, it's more about writing readable, clean and well tested code that is well designed in terms of architecture. But in some other areas you actually regularly have to face pretty complex problems where the stuff i just listed kind of becomes the easy part.

In security and high-availability related environments – where I've spent most of my time – it is important that you validate all ins and outs, system and function returns, check if writes succeed, in short, not unlike a chess player, to be able to fit all possible moves and scenarios that could go wrong inside your head. You probably need to naturally possess a mind that is precise and can find all loopholes.

Another way is to see efficiency through layers of algorithms and realities of real-life systems. Universities focus too much on mathematical formulas in my opinion; real systems are not clean and simple like a math function with few variabes. To understand by experience where complex systems with remote databases, shared disks and network can go wrong and write code that foresees, prevents or deals with unexpected complications is an important skill that sadly enough is hard to quantify on a resume. A lot depends on experience and knowledge, but you need to have interest and curiosity to get there.

And finally, you have those programmers that can create a more-or-less working mock-up in mere hours. In my experience, those are not always the people that want to spend a year ironing out all the bugs, but it is a valuable skill to be able to adapt and churn out something fast and iterate on it. Dare I say, the Javascript mindset. You probably need to be pretty enthusiastic about new technologies and quick on your feet.

To find not only a motivated person but the right "type" for a job position is probably not an easy task, just as it is hard for a programmer to find the right job that fits your own particular strengths and way you like to work. You might be a good programmer, but end up in the wrong environment. If you are a thorough and perfectionistic person, you're probably not going to be happy in a mockup-a-day start-up.