The way it worked with bf3stats was that upon updating your stats the site would crawl your recent battlereports from Battlelog, but only the last 20 are listed there. So to not miss any battlereports, you need to update at least every 20 games.
This text is shown in bf3stats when viewing reports:
You can update your battle reports manually by clicking the UPDATE button.
We recommend to update your reports at last after every 20 rounds to not miss any reports.
This does not seem to be the case with BF4, there you can list more battle reports than the last twenty in Battlelog. Also bf4stats makes no comment on the update process for battlereports.
There is also a confusing forum posts where reports are listed under "not done yet"
- Add Battle Reports to bf4stats.com (might not be shown for some players, if they are not sharing them publicly)
and one where it says:
I'm sorry we do not support battle reports at the moment.
My own profile only show 4 battle reports (there are many more), so it looks like an unfinished feature to me.