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.

1. A Bayesian Analysis of Draft Pick Value in
Major League Soccer
Howard Hamilton
Founder, 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 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)

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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

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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

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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

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Hyperparameter Posteriors
2012 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 Pick
Drafting Clubs Don't See Most of Drafted Player Value

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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

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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

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Which MLS Clubs Find Draftees That
Benefit Them?
MLS College Draft/SuperDraft, 1997-2013

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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!)

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Thank You!
www.soccermetrics.net
@soccermetrics
Howard H. Hamilton, Ph.D.