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Deterministic Evolution of Strength in Multiple Comparisons Models: Who is the Greatest Golfer?

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  • Rose D. Baker
  • Ian G. McHale

Abstract

type="main" xml:id="sjos12101-abs-0001"> We present a statistical methodology for fitting time-varying rankings, by estimating the strength parameters of the Plackett–Luce multiple comparisons model at regularly spaced times for each ranked item. We use the little-known method of barycentric rational interpolation to interpolate between the strength parameters so that a competitor's strength can be evaluated at any time. We chose the time-varying strengths to evolve deterministically rather than stochastically, a preference that we reason often has merit. There are many statistical and computational problems to overcome on fitting anything beyond ‘toy’ data sets. The methodological innovations here include a method for maximizing a likelihood function for many parameters, approximations for modelling tied data and an approach to the elimination of secular drift of the estimated ‘strengths’. The methodology has obvious applications to fields such as marketing, although we demonstrate our approach by analysing a large data set of golf tournament results, in search of an answer to the question ‘who is the greatest golfer of all time?’

Suggested Citation

  • Rose D. Baker & Ian G. McHale, 2015. "Deterministic Evolution of Strength in Multiple Comparisons Models: Who is the Greatest Golfer?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 180-196, March.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:1:p:180-196
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    File URL: http://hdl.handle.net/10.1111/sjos.12101
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    Cited by:

    1. Bell Andrew & Smith James & Sabel Clive E. & Jones Kelvyn, 2016. "Formula for success: Multilevel modelling of Formula One Driver and Constructor performance, 1950–2014," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(2), pages 99-112, June.
    2. Vladimír Holý & Jan Zouhar, 2022. "Modelling time‐varying rankings with autoregressive and score‐driven dynamics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1427-1450, November.
    3. Glickman Mark E. & Hennessy Jonathan, 2015. "A stochastic rank ordered logit model for rating multi-competitor games and sports," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 11(3), pages 131-144, September.
    4. Santos-Fernandez Edgar & Wu Paul & Mengersen Kerrie L., 2019. "Bayesian statistics meets sports: a comprehensive review," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(4), pages 289-312, December.

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