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%.
Pythagoras and the National Hockey League
The nature of the relationship Bill James found between the win/loss percentage of a Major League Baseball team and the number of runs the team scores and allows over the course of a season is investigated for the National Hockey League (NHL). We find the optimal form of James' model for the NHL using the absolute error criterion and demonstrate that far more complex forms of James' model yield little in additional predictive power. We also provide empirical evidence that the relationship between win/loss percentage and goals scored and allowed varies relatively little across recent seasons.
Study on Electrical Explosion Mechanism and Ignition Characteristics of Copper and Aluminum Powder Under Ignition Solid Propellant
In order to study the characteristic of the electrical explosion of copper and aluminum powders, a multilayer generator was designed, an experimental system was set up, and the parameters of metal powder electrical explosion were measured and analyzed. The results show that the duration of the electrical explosion process increases significantly due to the addition of metal powder. The duration of aluminum powder electrical explosion jet flow is ~86.36 ms due to its self-sustained combustion, which releases a large amount of energy, and a small fraction of aluminum powder particles is not burned. The duration of copper powder electrical explosion jet flow is ~15.84 ms, and most of the copper powder particles are in the solid state. The current pause process is absent; instead, the first discharge process is connected to the second discharge process. The effect of copper powder on the first discharge process is greater than that of aluminum powder. Furthermore, the ignition ability of copper powder electrical explosion to solid propellant is stronger than that of aluminum powder in a closed bomb experiment. These results are indubitably meaningful for the application of metal powder electrical explosion and ignition of solid propellant in an electrothermal chemical gun.