In a recent communication, Van Damme et al (1) presented a statistical analysis of the performance of world-ranked decathletes, and made inferences about the ability of these athletes to respond uniformly to the demands of the ten events in the decathlon. Their argument was based on an interpretation of the negative correlation in a sample of 600 world-ranked decathletes between the best performance in an event and the overall performance. They used the principle of allocation (2) to argue that excellence in one task may only be attained at the expense of average performance in all other tasks. We present here a complementary view. We considered the 92 decathletes who competed in the last five Olympic games. For this elite sub-sample we found an opposite result to that of Van Damme et al (1): to compete successfully at this level, a uniform, relatively high performance in all individual disciplines is required.
David Hilbert was a mathematician who in 1900 delivered the most influential speech in the history of mathematics (Hilbert 1902). He outlined 23 major problems to be studied in the next century, while outlining a philosophy for how mathematics should be studied. In the 2000 edition of Baseball Prospectus, Keith Woolner wrote an essay entitled "Baseball's Hilbert Problems."(Kahrl, et al. 2000) Woolner's essay, in the spirit of Hilbert, listed 23 unanswered questions about baseball. If baseball research is now about where David Hilbert was in 1900, football research is about where the Arabs were when they invented algebra. Analysis in football has a long way to go. The football Hilbert Problems do not merely consist of questions that need to be answered. They start with problems collecting the data that would help answer those questions.
Existing paired comparison models used for ranking football teams primarily focus on either wins and losses or points scored (either via each team's total or a margin of victory). While reasonable, each approach fails to produce satisfactory rankings in frequently arising situations due to its ignorance of additional data. We propose a new, hybrid model incorporating both wins and constituent scores and show that it outperforms its competitors and is robust against model mis-specification based on a series of simulation studies. We conclude by illustrating the method using the 2003-04 and 2004-05 college football seasons.