The anchoring effect is defined as the tendency of human thought to the fixation on certain pieces of information that affect decision-making. In the same context, the underconfidence bias is understood as an agent’s propensity to underestimate his or her own objective performance. While some aspects of these phenomena are well known, there are no formal models that specifically describe the relationship between both. This paper presents: i) an experiment that illustrates the anchoring effect on the underconfidence bias by both reducing and amplifying such bias in the domain of geographic decision tasks and ii) the foundations of a new mathematical model that promotes precision in the study of the relationship between anchoring and underconfidence.