Application of the generalized matching law to point-after-touchdown conversions and kicker selection in college football

Coaches make a variety of complex decisions in American-rules college football, especially related to point-after-touchdown (PAT) conversions and, historically, kicker selection. However, little research has characterized the pattern of these choices and whether they are sensitive to environmental manipulations, such as increased effort to score. In the present study, the generalized matching law (GML)—a model that predicts a linear relation between log-transformed choices for two alternatives and the amount of reinforcement garnered from them—was applied to PAT-conversion (1 point vs. 2 point) and kicker (soccer-style vs. conventional-style) selection using archived data from the National Collegiate Athletic Association. Overall, PAT-conversion and kicker selection exhibited matching. Further, narrowing the goal-post width was associated with decreased preference for one-point (relative to two-point) PAT attempts and enhanced sensitivity to increases in points scored from one-point (relative to two-point) PAT attempts. This investigation provides support for the ecological validity of the GML and demonstrates that complex decisions in football conform to an orderly pattern that can be described using the GML.     

DEFENDING NIEBUHR FROM HAUERWAS

In his 2001 book, With the Grain of the Universe, Stanley Hauerwas has made an extended case for Karl Barth as the model for how to do Christian ethics, and for Reinhold Niebuhr as the model for how not to do it. Though Barth's closer and deeper theological connection to the Christian tradition appeals to a Jewish traditionalist by analogy, nevertheless, Niebuhr's approach to social ethics, based as it is on a version of natural law, is of greater appeal. That is because it is more philosophically arguable in a secular society and culture, and because it is more politically effective there. It is what made Niebuhr a more effective opponent of Nazism than was Barth. Also, Niebuhr's version of natural law is not a christianized version of Stoic natural law teaching but, rather, a profound use of the biblical prohibition of idolatry, having heretofore unnoticed affinities with rabbinic developments of that prohibition.