Upon a successful match, the match operator returns a list of the captures (or, in scalar context, the number of captures), one element for each set of capturing parentheses, even if the captured value is empty. By making the entire pattern optional, we ensure a successful match, and thus Perl will tell us how many groupings were.
As was pointed out by ysth and hugo, the case of no groupings will not return zero (because we need a true value to indicate a successful match), so we ought to put capturing parentheses around the expression, and subtract one from the result. And the possibility of embedded code, which we wouldn't want to run, is another caveat, so we want to use minimal matching. Hence:
my $regex = qr/foo/;
$_ = 'anything';
my $matches = (() = /($regex)??/) - 1; # oops! fixed
print "There were $matches groupings\n";
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