  We introduce a quantitative notion of lawlessness for finitely generated
groups, encoded by the "lawlessness growth function" $\mathcal{A}_{\Gamma} :
\mathbb{N} \rightarrow \mathbb{N}$. We show that $\mathcal{A}_{\Gamma}$ is
bounded iff $\Gamma$ has a nonabelian free subgroup. By contrast we construct,
for any nondecreasing unbounded function $f: \mathbb{N} \rightarrow
\mathbb{N}$, an elementary amenable lawless groups for which
$\mathcal{A}_{\Gamma}$ grows more slowly that $f$. We produce torsion lawless
groups for which $\mathcal{A}_{\Gamma}$ is at least linear using
Golod-Shafarevich theory, and give some upper bounds on $\mathcal{A}_{\Gamma}$
for Grigorchuk's group and Thompson's group $\mathbf{F}$. We note some
connections between $\mathcal{A}_{\Gamma}$ and quantitative versions of
residual finiteness. Finally, we also describe a function
$\mathcal{M}_{\Gamma}$ quantifying the property of $\Gamma$ having no mixed
identities, and give bounds for nonabelian free groups. By contrast with
$\mathcal{A}_{\Gamma}$, there are no groups for which $\mathcal{M}_{\Gamma}$ is
bounded: we prove a universal lower bound on $\mathcal{M}_{\Gamma}(n)$ of the
order of $\log (n)$.
