The number of bidders, N, involved in a construction procurement auction is known to have an important effect on the value of the lowest bid and the mark-up applied by bidders. In practice, for example, it is important for a bidder to have a good estimate of N when bidding for a current contract. One approach, instigated by Friedman in 1956, is to make such an estimate by statistical analysis and modelling. Since then, however, finding a suitable model for N has been an enduring problem for researchers and, despite intensive research activity in the subsequent 30 years, little progress has been made, due principally to the absence of new ideas and perspectives. The debate is resumed by checking old assumptions, providing new evidence relating to concomitant variables and proposing a new model. In doing this and in order to ensure universality, a novel approach is developed and tested by using a unique set of 12 construction tender databases from four continents. This shows the new model provides a significant advancement on previous versions. Several new research questions are also posed and other approaches identified for future study.