Making Optimal Decisions with Minimum Risk: Fantasy Football

1
Making Optimal Decisions with Minimum
RiskFantasy Football

• Project by
• JD Yamokoski
• Ben Smarslok

2
Outline

• Introduction to Fantasy Football
• Scenario Generation
• 3 methods based on prior performance
• Problem Formulation
• Maximizing expected performance
• Minimizing risk
• Results
• Conclusions

3
Introduction

• Fantasy sports have participants that build and
  manage a team of professional athletes, which
  gains fantasy points based on the athletes
  statistical performance
• Fantasy Football - Fantasy soccer?, Fantasy
  cricket?
  

• Yahoos Salary Cap Football
• Objective Maximize fantasy points each week
• Rules
• Roster consists of 1 QB, 2 RB, 3 WR, 1 TE, 1 K,
  and 1 Def
  
• Buy a combination of players, while remaining
  under the 100 salary cap
  
• Highly ranked players have higher salaries

4
Introduction

• Yahoo!s Salary Cap Football interface

5
Objective

• Predict player performance to determine who to
  choose each week
  
• Develop models to generate realistic scenarios of
  potential fantasy point outcomes (3 methods)
  
• Formulate and solve optimization based on
• Maximize expected performance (fantasy points)
• Minimize risk of selecting a very poorly
  performing team
  
• Compare and analyze results to determine best
  model
  
• What other observations can be made?

6
Scenario Generation

• SPH - Player History
• Each players weekly fantasy output was used
  directly as a scenario
  
• Players performance history was sorted in
  ascending order
  
• Scenario N corresponded to every players best
  fantasy performance while scenario 1
  corresponded to every players worst performance

SPH sample output
7
Scenario Generation

• SHA - Home/Away
• Scenarios consider players average performance
  and the opponents allowed fantasy output
  
• It is a widely held belief that a football team
  is at a slight disadvantage when playing on the
  road in another city
  
• SHA algorithm attempts to capture this factor as
  well as the players defensive match up using the
  following equation to predict player performance

8
Scenario Generation

• SHA - Home/Away (contd)

SHA sample output
9
Scenario Generation

• SN - Normal model approximation
• Scenarios randomly generated from normal fit of
  player and opponent history (sorted)
  
• Player and their defensive opponents data were
  integrated into a predictor

SN sample output
10
Problem Formulation

• Fantasy performance of the average NFL player
  fluctuates greatly from week to week
  
• A risky roster is one with a high probability of
  under performing relative to their expected
  performance
  
• Conditional value-at-risk (CVaR), mathematically
  models our definition of risk very well

Expected coefficient of variation across all NFL
players
11
Problem Formulation

• Reward function
• Let xi ? 0,1 represent the decision to choose
  player i.
  
• Then let fX x s?R be a reward function defined as

12
Problem Formulation
Stochastic optimization program
Subject to the following constraints
13
Problem Formulation
Constraints (contd)
14
Results
Week 10 Out-of-sample optimal roster results
Week 11 Out-of-sample optimal roster results
15
Results

• CVaR Minimization vs. Expected performance
  maximization

(a)
(b)
Optimal rosters found by (a) minimizing CVaR80
and (b) maximizing expected performance.
16
Conclusions

• Drawbacks Poor predictions of lower-tier players

Minimum CVaR80 roster for week 11 using SPH
17
Conclusions

• Drawbacks Poor predictions of lower-tier
  players
  

18
Conclusions

• Drawbacks
• Only computed out-of-sample results for two
  weeks
  
• Only modeled the players composite fantasy score
  instead of the component statistics in the
  calculation of the Yahoo! Fantasy Points
  
• Future work
• Investigate alternative scenario generation
  methods which better predict performance of
  lower-teir players
  
• Compute out-of-sample results for more than two
  weeks ideally for an entire season
  
• Develop a more fine-grain probabilistic model
  based on the component statistics of the Yahoo!
  fantasy scoring algorithm