Does the percentage of proper divisor sums of x, which are greater than x, converge to a known value?

I'm playing around with the sum of proper divisors of x, and I've noticed that about 25% of them are larger than x. This ratio remains more-or-less constant as x grows into the tens of thousands. Whether (sum of proper divisors of x) > (x) doesn't seem to have an immediately obvious consistent pattern, as I thought it might. Is it known which value this proportion converges to, if any? I assume people have already looked into this, but I haven't found anything on it.