I have yet to experience this because I'm VERY new. I have yet to get close to racing. After reading your question and being a primarily solo cyclist I would think that I would feel solace. I get a lot of satisfaction from competing with myself. Again disclaimer: I'm not there yet. In fact I probably have at least a good couple of years to go. Not to mention I need many more group rides.

Interesting question and I'm sure those that are more seasoned will have a better answer for you.