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A mapping methodology has been applied to data of the national apprentice and trainee collection to identify and quantify key factors that affect apprentices' and trainees' likelihood of successfully completing their contract of training. By carefully taking account of the expected duration of training contracts, sets of apprenticeship and traineeship commencement records are mapped to sets of completion records. This allows estimation of the proportion of apprenticeships and traineeships likely to result in completions, and the identification of characteristics of individuals and contracts influencing completions in Australia's apprenticeship and traineeship system. The analysis suggests that the likelihood for completion declined from 1995 to 1997 and then increased again from 1998 to 2000 coinciding with the introduction of New Apprenticeships. It also indicates that contracts with a high completion likelihood are more likely to be full-time contracts, contracts of one to three years duration, contracts in trades occupations, Australian Qualifications Framework (AQF) Certificate III contracts, and contracts with government employers. Indigenous people and people with a reported disability appear to have a markedly smaller likelihood of completion than people who respectively did not identify themselves as Indigenous or report a disability.