A Matching Law Analysis of Risk Tolerance and Gain–Loss Framing in Football Play Selection

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Abstract

Using an operant model of choice, the generalized matching law, we evaluated widely held assumptions that play selection in American-rules football is risk averse and that it is subject to gain–loss framing effects. Consistent with risk aversion, relatively risky passing plays occurred less often than expected, an effect depicted by the matching law as a bias for selecting rushing plays. Consistent with gain–loss framing, magnitude of the rushing bias varied with game score. These effects were evident in analyses that treated risk as a categorical variable (passing > rushing). When risk was instead quantified for specific game situations, risk aversion remained evident but framing effects disappeared. Overall, the study illustrates how analytical tools derived from operant choice theory can be useful in testing predictions, based on cognitive decision theory, about behavior under the control of probabilistic outcomes.

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