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Making Optimal Decisions with Minimum Risk: Fantasy Football

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Fantasy sports have participants that build and manage a team of professional ... Maximize expected performance (fantasy points) ... – PowerPoint PPT presentation

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Title: 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
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