There are 14 statistics on Decorated permutations in the database:
(and possibly some waiting for verification)

St001425Decorated permutations ⟶ ℤ
The number of negatively decorated fixed points of a decorated permutation.
St001426Decorated permutations ⟶ ℤ
The number of positively decorated fixed points of a decorated permutation.
St001538Decorated permutations ⟶ ℤ
Sum of decorated fixed points as signed integers.
St001539Decorated permutations ⟶ ℤ
Number of changes in decorated fixed points.
St001540Decorated permutations ⟶ ℤ
Difference in positively decorated fixed points and negatively decorated fixed points.
St001542Decorated permutations ⟶ ℤ
The dimension of the subspace of the complex vector space for the associated Grassmannian.
St001543Decorated permutations ⟶ ℤ
The largest step for the associated bounded affine permutation.
St001544Decorated permutations ⟶ ℤ
The inversion number of the associated bounded affine permutation.
St001547Decorated permutations ⟶ ℤ
The sum of all indices from every element of the Grassmann necklace.
St001548Decorated permutations ⟶ ℤ
The sum of the indices of the first term of the associated Grassmann necklace.
St001567Decorated permutations ⟶ ℤ
The number of weak exceedances of a decorated permutation.
St001818Decorated permutations ⟶ ℤ
The number of alignments of a decorated permutation.
St001824Decorated permutations ⟶ ℤ
The number of crossed alignments in a decorated permutation.
St001825Decorated permutations ⟶ ℤ
The size of the Grassmannian interval associated with a decorated permutation.