Bayesian Analysis of Draft Pick Value in Major League Soccer
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Transcript of 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
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
JMM 2017: Mathematics & Sports 3
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)
JMM 2017: Mathematics & Sports 4
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
JMM 2017: Mathematics & Sports 5
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
JMM 2017: Mathematics & Sports 6
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!)
JMM 2017: Mathematics & Sports 14
Thank You!
www.soccermetrics.net@soccermetrics
Howard H. Hamilton, Ph.D.