Statistics Papers

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A recent report (Hendricks Sports Management, LP, et al, 2008) issued by Hendricks Sports Management, LP, claims to provide evidence for the lack of use of performance-enhancing substances (PESs) by Hall-of-Fame caliber pitcher Roger Clemens, a claim based on an analysis of his career statistics (using ERA = earned run average, K rate = strikeout rate, innings pitched), both in isolation and in comparison to other power pitchers of his era (Randy Johnson, Nolan Ryan, and Curt Schilling).

In this research, we re-examine Roger Clemens’ career using a more complete and stable set of pitching measures (WHIP = walks + hits per inning pitched, BAA = batting average against, ERA, BB rate = rate of walks per batter faced, K rate), and by using a broader (census) comparison set of pitchers with similar longevity in order to reduce the selection bias inherent in the Hendricks report. In contrast to Hendricks’ report, our analysis examines not only late career performance but also early- and mid-career trends. Our findings can be summarized as follows:

Using simple quadratic functions, and an occasional spline to relate the above pitching measures to age, we demonstrate a number of empirical regularities:

  • Roger Clemens’ career is atypical with respect to his peer group. While most pitchers with comparable longevity improve for the first half of their career, peaking just past the age of 30 and then declining (an inverted-U shape), Roger Clemens’ career statistics shows a decrease into his early thirties followed by a marked improvement late in his career (more of a U-shape).
  • This pattern is consistent across most measures for Roger Clemens, yet for certain measures is not unique to him. That is, other pitchers have atypical patterns as well for some, but not all other tested measures.

Our analyses suggest what we, as statisticians, have postulated all along: empirical association is not causation, and neither the Hendricks report nor ours can prove or disprove the use of PESs by any given player. This is because players are indeed unique, and due to the short-time series and sparseness of comparable players there is low power to assess specific hypotheses. However, our analyses clearly suggest that Roger Clemens’ career pitching trajectory is atypical.

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Date Posted: 27 November 2017

This document has been peer reviewed.