A bicycle hydraulic disc brake master cylinder includes a housing having a bar clamp at one end configured for fastening the housing to a bicycle handle bar, the bar clamp receiving the handle bar along a clamp axis. A handle is pivotably connected to the housing to pivot about a pivot axis in operative association with a piston train to impart a drive force on the piston train. The handle defines a finger receptacle receiving at least one finger of a user defining an effective force point at a select distance from a distal end of the handle. A select ideal finger actuation path for the at least one finger of a user begins at a start point at the effective finger force point with the handle at an engagement point where the handle begins to drive the piston train against operative fluid resistance and extends along a line from the start point at a select angle relative to the clamp axis. A pivotable connection is provided between the handle and the housing and is located on the housing relative to the clamp axis so that with the handle actuated by a force applied to the effective finger force point along this select ideal actuation path, a mechanical advantage to the user resulting from the handle actuation does not diminish more than three percent as the handle is pivoted between the engagement point and a fully actuated position.