I tend to do the majority of my answering of questions at one time of the day - soon after I get to work.
I have a suspicion that if instead, I continuously checked Stack Overflow for new questions in my favorite tag (either using my browser or via some notification mechanism), I'd be more likely to be the fastest gun, and therefore get more reputation.
However, continuously checking Stack Overflow wouldn't be good for concentration on my day job - it'd be better to visit SO once for 20 minutes than to visit it four times for 5 minutes each, as you probably lose time "context switching" even after you've finished visiting SO. I also suspect that continuously checking up on SO could contribute to addiction.
Is "The Fastest Gun in the West" phenomenon rewarding behaviour that's not healthy for answerers?
Side note: answerers continuously visiting SO would, however, be good news for people asking questions, and for Stack Overflow's owners and advertisers - unless the answerers get fired and can't buy any more products.
Related question: What aspects of psychology does Stack Overflow take advantage of? talks about addiction, but mainly in terms of Intermittent Variable Reward contributing to it.