# Making Optimal Decisions with Minimum Risk: Fantasy Football - PowerPoint PPT Presentation

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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
• 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