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Bayesian Analysis of Draft Pick Value in Major League Soccer

Presented at the 2017 Joint Mathematics Meeting in Atlanta, GA. Draft selections in Major League Soccer -- and all North American sports leagues -- can be viewed as an asset that can be exercised or traded, so it is useful to understand a draft selection's value and its evolution over time. This slide deck presents valuation models that result from a Bayesian local regression of the expected career value of a draft pick. The models are valid for a specific draft year and are trained by the career values of draftees in previous years. The models are differentiated by the use of a time horizon to filter players in the training set and restricting career values to those earned at the drafting team. The resulting regression curves and the 95% credible regions surrounding them demonstrate a significant difference between the expected value of an early drafted player over his MLS career and the expected value while playing for the club that drafted him. These valuation curves can be used to determine relative value of draft slots, assess individual draft selections, and identify over- and under-performing team organizations in MLS player drafts.

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Bayesian Analysis of Draft Pick Value in Major League Soccer

  1. 1. A Bayesian Analysis of Draft Pick Value in Major League Soccer Howard Hamilton Founder, Soccermetrics Research
  2. 2. JMM 2017: Mathematics & Sports 2 How do you value a draft pick? Estimate draft pick value given prior expectations and performance of previous draftees Apply Bayesian approach to draft pick valuation
  3. 3. JMM 2017: Mathematics & Sports 3 MLS Player Data Set Biographical Data Initial Acquisition Data Financial Data (2007-2015) Performance Data Player Name(s) Date of Birth Nationality Default Position(s) Acquisition Year Acquiring Team Acquisition Path Draft Path: Draft Type Round Selection Number Generation Adidas (N=1813) Contract Year Contracting Team Compensation: Base Guaranteed Minutes Appearances Substitutions Yellow/Red Cards Field Player-specific Goalkeeper-specific All players acquired by Major League Soccer between 1996-2016 (N=3250 players) Data Sources: MLS Players Union (Financial Data), ENB Sports Soccer Player Database (Performance Data), Major League Soccer (Acquisition Data)
  4. 4. JMM 2017: Mathematics & Sports 4 Analysis Parameters Normalization of Draft Position α= k−1 N−1 α:[1, N ]→[0,1] Career Player Value V = √( M Mmax ) 2 + ( G Gmax ) 2 + ( A Amax ) 2 3 , field players V = √( M Mmax ) 2 + (1− GA GA,max ) 2 + ( S Smax ) 2 3 , goalkeepers
  5. 5. JMM 2017: Mathematics & Sports 5 Modeling Draft Value with Gaussian Processes V={V 1,V 2,⋯,V n−1 ,Vn}For every α={α1, α2,⋯,αn−1 ,αn}… V=f (α) ⇒ V∼N (0,k(α,α')) k(α ,α')=ηexp([−ρ(α−α')2 ]) + σn 2 δ(α,α') ρ∼Beta(20,5) η∼InverseGamma(10,1) σn∼HalfCauchy(5) Gaussian Process Regression Model Hyperparameter Priors
  6. 6. JMM 2017: Mathematics & Sports 6 Draft Pick Valuation Models Training Data Career value of drafted player up to current year Cumulative value of drafted player while playing for drafting club up to current year Present Model Club Model R= Δeα ,Δ>0 Δe 1−α ,Δ<0 Draft Performance Rating Value Differential Scaled by Draft Position
  7. 7. JMM 2017: Mathematics & Sports 7 Hyperparameter Posteriors 2012 Present Value Model
  8. 8. JMM 2017: Mathematics & Sports 8 Comparison of Present and Club Models 1999 Draft Models 2012 Draft Models Greatest uncertainty observed in early draft picks
  9. 9. JMM 2017: Mathematics & Sports 9 Evolution of Draft Pick Drafting Clubs Don't See Most of Drafted Player Value
  10. 10. JMM 2017: Mathematics & Sports 10 2013 MLS SuperDraft Value Card Pick Value Pick Value Pick Value Pick Value 1 100 11 20.8 21 0.7 31 0.5 2 91.6 12 14.8 22 0.7 32 0.4 3 83.2 13 10.1 23 0.7 33 0.3 4 75.0 14 7.0 24 0.7 34 0.2 5 66.8 15 4.8 25 0.7 35 0.1 6 58.8 16 3.3 26 0.7 36 0 7 50.9 17 2.3 27 0.7 37 0 8 43.2 18 1.7 28 0.6 38 0 9 35.7 19 1.2 29 0.6 10 28.2 20 0.9 30 0.5
  11. 11. JMM 2017: Mathematics & Sports 11 Draft Performance Extremes: Present Draft Valuation Model Year Pick Player Position Club 1997 29 Kevin Hartman GK LA Galaxy 2002 50 Davy Arnaud F Sporting Kansas City 2005 35 Gonzalo Segares D Chicago Fire 2010 51 Sean Johnson GK Chicago Fire MLS College Draft/SuperDraft, 1997-2013 Year Pick Player Position Club 1998 3 Ben Parry D San Jose Earthquakes 2005 1 Nik Besagno M Real Salt Lake 1997 2 Mike Fisher M Tampa Bay Mutiny 2011 1 Omar Salgado F Vancouver Whitecaps Draft Busts Draft Gems
  12. 12. JMM 2017: Mathematics & Sports 12 Which MLS Clubs Find Draftees That Benefit Them? MLS College Draft/SuperDraft, 1997-2013
  13. 13. JMM 2017: Mathematics & Sports 13 MLS Draft Valuation Bayesian analysis expresses modeling strategy Quantify expected draft value and uncertainty Evaluate draft strategies Identify best performing organizations For Future Consideration Alternative valuation metric Valuation model from draft transaction data Incorporate compensation (with uncertainty!)
  14. 14. JMM 2017: Mathematics & Sports 14 Thank You! www.soccermetrics.net @soccermetrics Howard H. Hamilton, Ph.D.

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