JSM 2004 - Toronto

Abstract #302216

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Activity Number: 410
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistics in Sports
Abstract - #302216
Title: U-Statistics in Olympics and Baseball: Objective Scores for Profiles of Medals and Hits
Author(s): Knut M. Wittkowski*+ and Lubomir Merkov
Companies: Rockefeller University and Rockefeller University
Address: General Clinical Research Center, New York, NY, 10021,
Keywords: multivariate ; rank test ; ordinal ; U-statistics ; profile ; sport
Abstract:

Scoring countries by their profiles of gold, silver, and bronze medals and scoring batters by their profiles of singles, doubles, triples, and home runs is traditionally done by weighted averages based on arbitrary weights. While different media ranking countries differently has drawn little attention, Sabermetricians have long debated over batting average (all hits are given equal weights) and bases per plate appearance (all hits are weighted by the number of bases reached). The consensus is that the best weighting scheme should be somewhere between these extremes, but no solution has been found. It is not clear, however, why the best scores should be based on a linear combination, ie, why the same weights should apply across the whole scale and over time. When applying u-statistics to multivariate ordinal data, this unrealistic restriction can be overcome. For the first time, batters and countries can be scored objectively, i.e., without the need for arbitrary weights. The new approach for profiles of graded variables is applied to the data from the 2002 Winter Olympics and the 2003 MBL.

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