Recovery arithmetic
Drawdown is nonlinear in the only direction that matters: the way back.
The ladder's logic starts with an asymmetry every trader knows and few internalize: losses and recoveries are not symmetric. A −7% drawdown needs roughly +7.5% to recover — nearly linear, barely a detour. −19% needs about +23.5%. −34% needs over +51%. −40% needs +66.7%. The required recovery grows faster than the drawdown that caused it, which means every additional band of depth costs more future performance than the last. The band boundaries are placed against this curve: the upper bands are wide because shallow drawdowns are cheap to recover and normal in any live edge; the lower bands compress because each marginal percent of depth is progressively more expensive to undo.
The recovery function R = d/(1−d): the gain required to return to peak grows nonlinearly with depth. Band boundaries (dashed) sit progressively closer together as the curve steepens — the ladder compresses where recovery gets expensive.

