  We present first analytic, resummed calculations of the rates at which
widespread jet substructure tools tag QCD jets. As well as considering
trimming, pruning and the mass-drop tagger, we introduce modified tools with
improved analytical and phenomenological behaviours. Most taggers have double
logarithmic resummed structures. The modified mass-drop tagger is special in
that it involves only single logarithms, and is free from a complex class of
terms known as non-global logarithms. The modification of pruning brings an
improved ability to discriminate between the different colour structures that
characterise signal and background. As we outline in an extensive
phenomenological discussion, these results provide valuable insight into the
performance of existing tools and help lay robust foundations for future
substructure studies.
