B\'ar\'any showed that there is a constant $c_d>0$ such that if $S$ is any $n$-point set in $R^d$, then there exists a point in $c_d$ fraction of simplices spanned by $S$. We present a simple construction of a point set for which there is no point contained in many simplices. The construction is optimal for $d=2$ and gives the first non-trivial upper bounds on $c_d$ for $d\geq 3$. We will also discuss generalizations to stabbing simplices by affine spaces. Joint work with Ji\v{r}\'\i{} Matou\v{s}ek and Gabriel Nivasch.