Consistency and Pythagoras
Pythagorean win share has been one of the fundamental contributions to Sabermetrics. Several hundred articles, both academic and non-academic, have explored variations on Bill James' original formula and its fit to empirical data. This paper considers a variation that is previously unexplored on any systematic level, consistency. After discussing several important contributions to the line of literature, we demonstrate the strong correlation between Pythagorean residuals and several notions of run distribution consistency. Finally, we select the "correct" form of consistency and use it to construct a simple regression estimator, which improves RMSE by 11%.
Is there a Pythagorean theorem for winning in tennis?
Abstract Bill James’ discovery of a Pythagorean formula for win expectation in baseball has been a useful resource to analysts and coaches for over 30 years. Extensions of the Pythagorean model have been developed for all of the major professional team sports but none of the individual sports. The present paper attempts to address this gap by deriving a Pythagorean model for win production in tennis. Using performance data for the top 100 male singles players between 2004 and 2014, this study shows that, among the most commonly reported performance statistics, a model of break points won provides the closest approximation to the Pythagorean formula, explaining 85% of variation in season wins and having the lowest cross-validation prediction error among the models considered. The mid-season projections of the break point model had performance that was comparable to an expanded model that included eight other serve and return statistics as well as player ranking. A simple match prediction algorithm based on a break point model with the previous 9 months of match history had a prediction accuracy of 67% when applied to 2015 match outcomes, whether using the least-squares or Pythagorean power coefficient. By demonstrating the striking similarity between the Pythagorean formula for baseball wins and the break point model for match wins in tennis, this paper has identified a potentially simple yet powerful analytic tool with a wide range of potential uses for player performance evaluation and match forecasting.
Heat Transfer Characteristic for a New Plate Metal Hydride Reactor
The property of major metal hydride reactors in the world was analyzed and a new plate metal hydride reactor was designed.An experimental facility to test the metal hydride reactor was also designed correspondingly.The effective thermal conductivity of the plate metal hydride reactor was measured by varying the initial metal hydride packing fraction,the kind of filled gas and the pressure of the filled gas,cycle numbers.The test results show that the effective thermal conductivity of the reactor,has exceeded(7.5) W/(m·K) before activation,which is increased greatly.After alloy activation,the effective thermal conductivity of the reactor has a linear change trend with the hydrogen pressure during the interval 0.1~3.5 MPa.The effective thermal conductivity of the reactor just only decreases quickly at the beginning,but becomes stable after several cycles.