Authors: Raymond H Gallucci
Comments: 55 Pages.
In Situational Underlying Value for Baseball, Football and Basketball – A Statistic (SUV) to Measure Individual Performance in Team Sports, an all-encompassing, overall statistic to measure “clutch” performance by individual players in the team sports of major league baseball, professional football, and NCAA men’s college basketball was developed, called “Situational Underlying Value” (SUV).  Based on the concept of “run expectancy,” it assigns an SUV to each base as a function of the number of outs, including a negative value for making an out. There, and in “Proof of Principle” for Situational Underlying Value (SUV) – A Statistic to Measure Clutch Performance by Individuals in the Team Sports of Major League Baseball,  it was applied exclusively to hitters and pitchers. Its derivation is explained in Reference 1, with additional discussion provided in Reference 2. Reference 1 provides two example games to show how the SUVs accrue for each team’s hitters and pitchers. The goal of this third work, which includes “Proof of Principle” as in Reference 2, is to track the performance of a team’s individual fielders defensively, including an enhancement to the approach for pitching previously developed in Reference 2, over the same substantial portion of an entire season. One-third of the 2017 season, i.e., 54 games, have again been selected for the Seattle Mariners, starting with Game 002 and tracking every third game up through Game 161. The SUVs are based on the play-by-play descriptions provided in “Baseball Reference,” https://www.baseball-reference.com/.  Summary SUV analyses for all 54 games are provided below, with a roll-up of cumulative SUVs every six games. Also, the actual play-by-plays are included for every third game analyzed, starting from Game 005 (i.e., for Games 005, 014, 023, 032, 041, 050, 059, 068, 077, 086, 095, 104, 113, 122, 131, 140, 149 and 158), providing a total for 18 games. For the rest (which are only summarized), the reader should consult Reference 3. There is an important change to the above table for defensive tracking, also applied to the enhanced pitching analysis, namely the reversal of all the SUV signs. This enables “positive” defensive outcomes (outs) to be assigned positive SUVs, while “negative” outcomes (reaching base or advancing) are assigned negative SUVs. The assignment of defensive SUVs is somewhat more involved than that for hitting. Specific assignments, most frequently encountered, are presented below.
Authors: Stephen P. Smith
Comments: 10 Pages.
The autoregressive and rolling moving average time series models are describe with discrete time steps that may be unequal. The standard time series is described, as well as a two-dimensional spatial process that is separable into two one-dimensional processes. The K-matrix representations for each of these are presented, which can then be subjected to standard matrix handling techniques.
Authors: Stephen P. Smith
Comments: 13 Pages.
A piece-wise quadratic spline is introduced as a time series coming with unequal time steps, and where the second derivative of the spline at the junction points is impacted by random Brownian motion. A measurement error is also introduced, and this changes the spline into semi-parametric regression. This makes a total of two dispersion parameters to be estimated by a proposed REML analysis that unitizes the K-matrix. The spline itself only has three location effects that are treated as fixed, and must be estimated. A proposed prediction of a future observation beyond the spline’s end point is presented, coming with a prediction error variance.