Baddeley was born in Melbourne, Australia and educated at Eltham High School there, and studied mathematics and statistics at the Australian National University (honours supervisor: Roger Miles) and the University of Cambridge (PhD supervisor: David George Kendall).
He was elected a Junior Research Fellow at Trinity College, Cambridge in the second year of his PhD.
Classical methods of stereology were limited by the requirement that the cutting plane be randomly oriented.
Baddeley developed an alternative technique[4] in which the cutting plane is "vertical" (parallel to a fixed axis, or perpendicular to a fixed surface) making it possible to apply quantitative microscopy to cylindrical core samples, samples of flat materials, and longitudinal sections.
With Cruz-Orive he demonstrated the role of the Horvitz-Thompson weighting principle and the Rao-Blackwell theorem in stereological sampling.