Introduction

Cornell University’s basketball team won the Ivy League championship in 2008, 2009, and 2010. Along the way the team set several team records for three-point shooting. In conversation, the basketball coach was asked about how he decides which players he will use in any particular game. He listed several key factors such as the particular matchups with the opposing team’s players, but he also mentioned the importance of putting in the guy who has been on a shooting streak in the last several games. When pressed, he admitted that there were several factors that could contribute to such a streak but felt that if in a single game a regularly good shooter was cold, he would sit him on the bench in favor of a player with lower average percentage shooting. In fact, many coaches, players, and fans feel they can quickly discern when a player is either on a streak or in a slump in terms of shooting.

In dealing with risky decisions, one must first come to grips with the underlying uncertainty. In other words, before one can make a decision between two choices that involve uncertain outcomes, one must first develop a perception of how uncertain each of the choices is. Thus, a coach deciding which basketball players to put on the court wants to determine how reliable his shooters are and how likely each of his players are to stop key players on the other team from scoring. The coach cannot know before placing a player in a game how that player will perform. But the coach can use previous performance to form beliefs about how the players will perform, thus helping to decide which will play and for how long.

Scientists often find themselves in a similar situation in trying to decide which of several hypotheses may be true. Before conducting experiments, they cannot know with certainty which hypothesis performs best. Often, scientific data are relatively weak, providing little information about the true underlying relationship. In this case it can be difficult to determine the causal effects that might have generated the data. Nonetheless, in order to publish the results, it is necessary to draw some conclusions even from weak data. This chapter deals with how people use available information to form beliefs when facing uncertainty. These beliefs are the basis for decisions regarding investment, hiring, strategy, and virtually every aspect of business management. In reality, we face uncertainty on a constant basis, and given our cognitive limits, we have developed heuristics and other tools to simplify the process of learning and forming perceptions when facing uncertain outcomes. To appreciate the impact of these heuristics on decision outcomes, it is first important to review some basic statistical theory.