  We consider mixed integer linear sets defined by two equations involving two
integer variables and any number of non-negative continuous variables. The
non-trivial valid inequalities of such sets can be classified into split, type
1, type 2, type 3, and quadrilateral inequalities. We use a strength measure of
Goemans to analyze the benefit from adding a non-split inequality on top of the
split closure. Applying a probabilistic model, we show that the importance of a
type 2 inequality decreases with decreasing lattice width, on average. Our
results suggest that this is also true for type 3 and quadrilateral
inequalities.
