A pedal connection arrangement includes a pedal having a spherical portion with an outer spherical surface. The pedal connection arrangement also includes a bicycle shoe that has a pedal gripping cavity that directly engages at least portions of the outer spherical surface of the pedal when the shoe is engaged with the pedal. The shoe is configured so that the pedal gripping cavity securely grips outer spherical surface of the pedal, yet remains free to swivel in various directions about the spherical portion of the pedal when the shoe is engaged with the pedal. The various directions include directions other than about the pedal longitudinal axis, thereby giving more flexibility for movement of the rider's foot while maintaining positive contact between the shoe and the pedal.