  We give a simple quantitative condition, involving the "mapping content" of
Azzam--Schul, that implies that a Lipschitz map from a Euclidean space to a
metric space must be close to factoring through a tree. Using results of
Azzam--Schul and the present authors, this gives simple checkable conditions
for a Lipschitz map to have a large piece of its domain on which it behaves
like an orthogonal projection. The proof involves new lower bounds and
continuity statements for mapping content, and relies on a "qualitative"
version of the main theorem recently proven by Esmayli--Haj{\l}asz.
