Empirical probability of k-SAT satisfiability Given a random instance $I_m = I_m(n,k)$ of $k$-SAT with $n$ variables and $m$ clauses, what's the probability $I_m$ is satisfiable?

It's believed that there's a threshold above which satisfiability becomes less likely as $m/n$ increases. The reverse is true as $m/n$ decreases.

Is there an empirical formula for $3$-SAT and other $k$'s that describe the rate at which satisfiability becomes more/less likely as you move away from the threshold?
see eg sec 4.7.4 p103 of this thesis where a finite-size scaling formula based on a power law is applied and coefficients fit with experimental data.


PHASE TRANSITIONS OF BOOLEAN SATISFIABILITY VARIANTS, Bailey 2004