  We define and study positional marked patterns, permutations $\tau$ where one
of elements in $\tau$ is underlined. Given a permutation $\sigma$, we say that
$\sigma$ has a $\tau$-match at position $i$ if $\tau$ occurs in $\sigma$ in
such a way that $\sigma_i$ plays the role of the underlined element in the
occurrence. We let $pmp_\tau(\sigma)$ denote the number of positions $i$ which
$\sigma$ has a $\tau$-match. This defines a new class of statistics on
permutations, where we study such statistics and prove a number of results. In
particular, we prove that two positional marked patterns $1\underline{2}3$ and
$1\underline{3}2$ give rise to two statistics that have the same distribution.
The equidistibution phenomenon also occurs in other several collections of
patterns like $\left \{1\underline{2}3 , 1\underline{3}2 \right \}$, and $\left
\{ 1\underline234, 1\underline243, \underline2134, \underline2 1 4 3 \right
\}$, as well as two positional marked patterns of any length $n$: $\left \{
1\underline 2\tau , \underline 21\tau \right \}$.
