I checked with the devs and it turns out the answer is:
Heavy caching even. Each of our web servers buffer incrementing view counts until a threshold is met, then all the updates are written to the database. So, we have 9 web servers and the default site threshold is 10 views of all profiles for each site. Therefore a web server needs to get 10 views of Sports' users to have those views get saved. On large sites, the threshold is higher (SO = 300 views, SU and SF = 30 views) to avoid constant database updates. On child metas, which are far less likely to be updated, the threshold is 1.
So your views are being counted by whichever server the users happened to hit, but they haven't been pushed to the database because none has served up 10 or more profiles since the last time the view counts were updated. (In theory, it could take 82 profile views for that to happen. But probably not.)
As a result of this question, the threshold has been set to 5 for small sites, such as Sports.
Update: as an experiment, I clicked through to your profile (it was still at 37), then I clicked through 4 other profiles on the site. Since the threshold is now 5 and since I (presumably) was hitting the same web server, the threshold for profile views was reached. Sure enough, when I looked back at your profile, the view count had risen to 38. (And the other people who I'd viewed had their view count incremented as well.) So the system is working as designed.