Highly variable based on competitiveness and applicant supply of the sites you apply to. In here, many will say apply to fewer, as I was told, too. But if you apply to formal postdocs with only 1 position open (at least a few of the sites I pursued needed just one person), your chances aren’t going to be great if there are many applicants.
For reference, I think I applied to 8 sites, all in California. Got a fair number of interviews, but one site never even contacted me after applying to let me know if I’d been selected for interviews or not. At that point I realized that my sites were probably far more competitive than I’d expected (I knew it would be competitive, but had hoped my app would stand out enough), and I ended up empty-handed.
That said, college counseling (and possibly other) postdocs appear to be more insular and networking-based in very saturated states. Colleagues whose TD knew other college counseling site TDs in the area had an easier time securing interviews and a postdoc than I did (I was coming from out-of-state).
I’d suggest applying to several sites in a wide geographical area and of varying levels of competitiveness to maximize chances.