The travel distance between two cities of rectangular shape is considered. Two uniformly distributed random points, one from each city, are taken. Their straight path travel distance is then measured. The explicit forms for the probability density function of this distance and its expected value are obtained. Numerical results of calculating the exact expected distance and the estimated distance as well as computer simulation are given for various cases. The integer moments of the distance are also discussed.

We study the r‐content Δ of the r ‐simplex generated by r+ 1 independent random points in R”. Each random point Zj is isotropic and distributed according to λ||Zj||2 ∼ beta‐type‐2(n/2, v), λ, v > 0. We provide an asymptotic normality result which is analogous to the conjecture made by Miles (1971). A method is introduced to work out the exact density of W = (rλ)r(r!Δ)2/(r + |)r+l and hence that of Δ. The distribution of W is also related to some hypothesis‐testing problems in multivariate analysis. Furthermore, by using this method, the distribution of W or Δ can easily be simulated.

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In this paper, we study the relationship between sports analytics and success in regular season and postseason in Major League Baseball via the empirical data of 2014-2017. The categories of analytics belief, the number of analytics staff, and the total number of research staff employed by MLB teams are examined. Conditional probabilities, correlations, and various regression models are used to analyze the data. It is shown that the use of sports analytics might have some positive impact on the success of teams in the regular season, but not in the postseason. After taking into account the team payroll, we apply partial correlations and partial F tests to analyze the data again. It is found that the use of sports analytics, with team payroll already in the regression model, might still be a good indicator of success in the regular season, but not in the postseason. Moreover, it is shown that both the team payroll and the use of sports analytics are not good indicators of success in the postseason. The predictive modeling of decision trees is also developed, under different kinds of input and target variables, to classify MLB teams into no playoffs or playoffs. It is interesting to note that 87 wins (or 0.537 winning percentage) in a regular season may well be the threshold of advancing into the postseason.