Bayesian Analysis of Draft Pick Value in Major League Soccer

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A Bayesian Analysis of Draft Pick Value in Major League Soccer Howard Hamilton Founder, Soccermetrics Research

Transcript of Bayesian Analysis of Draft Pick Value in Major League Soccer

Page 1: Bayesian Analysis of Draft Pick Value in Major League Soccer

A Bayesian Analysis of Draft Pick Value in Major League Soccer

Howard HamiltonFounder, Soccermetrics Research

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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

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MLS Player Data Set

Biographical Data

Initial AcquisitionData

FinancialData

(2007-2015)

PerformanceData

Player Name(s)Date of BirthNationality

Default Position(s)

Acquisition YearAcquiring TeamAcquisition Path

Draft Path:Draft Type

RoundSelection NumberGeneration Adidas

(N=1813)

Contract YearContracting TeamCompensation:

BaseGuaranteed

MinutesAppearancesSubstitutions

Yellow/Red CardsField Player-specificGoalkeeper-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)

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Analysis ParametersNormalization of Draft Position

α=k−1N−1

α :[1,N ]→[0,1]Career Player Value

V=√ ( MMmax

)2

+( GGmax

)2

+( AAmax

)2

3, field players

V=√ ( MMmax

)2

+(1− GA

GA ,max)2

+( SSmax

)2

3, goalkeepers

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Modeling Draft Value with Gaussian Processes

V={V 1,V 2,⋯,V n−1 ,V n}For everyα={α1,α2,⋯,αn−1 ,αn}…

V=f (α) ⇒ V∼N (0, k (α ,α ' ))

k (α ,α ' )=ηexp([−ρ(α−α ' )2]) + σn2δ(α ,α ' )

ρ∼Beta(20,5)

η∼InverseGamma(10,1)

σn∼HalfCauchy (5)

Gaussian Process Regression Model

Hyperparameter Priors

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Draft Pick Valuation ModelsTraining 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= Δ eα ,Δ>0Δ e1−α ,Δ<0

Draft Performance Rating

Value Differential Scaled by Draft Position

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Hyperparameter Posteriors2012 Present Value Model

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Comparison of Present and Club Models

1999 Draft Models 2012 Draft Models

Greatest uncertainty observed in early draft picks

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Evolution of Draft PickDrafting Clubs Don't See Most of Drafted Player Value

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2013 MLS SuperDraft Value CardPick 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

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Draft Performance Extremes:Present Draft Valuation Model

Year Pick Player Position Club1997 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 Club1998 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

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Which MLS Clubs Find Draftees That Benefit Them?

MLS College Draft/SuperDraft, 1997-2013

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MLS Draft ValuationBayesian analysis expresses modeling strategy

Quantify expected draft value and uncertaintyEvaluate draft strategies

Identify best performing organizations

For Future Consideration

Alternative valuation metricValuation model from draft transaction data

Incorporate compensation (with uncertainty!)

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Thank You!

www.soccermetrics.net@soccermetrics

Howard H. Hamilton, Ph.D.