MATLAB COMPUTATIONAL FINANCE CONFERENCE 2017 … · MATLAB COMPUTATIONAL FINANCE CONFERENCE 2017...
Transcript of MATLAB COMPUTATIONAL FINANCE CONFERENCE 2017 … · MATLAB COMPUTATIONAL FINANCE CONFERENCE 2017...
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MATLAB COMPUTATIONAL FINANCE CONFERENCE 2017
Quantitative Sports Analytics using MATLAB
Robert Kissell, [email protected]
September 28, 2017
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Important Email and Web Addresses
• AlgoSports23/MATLAB Competition
Are you smarter than the Algo?
Email: [email protected]
Website: AlgoSports23.com
Please check the website for data updates, and contact [email protected] for further information.
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Presentation Outline
• Quantitative Sports Modeling
• Modeling Techniques from:
• “Optimal Sports, Math, Statistics, and Fantasy”
• Probability Models
• Rank Sports Teams
• Estimate Winning Probability
• Calculate Winning Margin
• Computing Probability of Beating a Spread
• AlgoSports23/MATLAB Competition
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Presentation Outline
• Quantitative Sports Modeling
• Modeling Techniques from:
• “Optimal Sports, Math, Statistics, and Fantasy”
• Probability Models
• Rank Sports Teams
• Estimate Winning Probability
• Calculate Winning Margin
• Computing Probability of Beating a Spread
• AlgoSports23/MATLAB Competition
• Are you smarter than the Algo!
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Transaction Cost Analysis and Algorithm Trading
• Suite of TCA Models and Optimizers have been fully integrated into MATLAB’s Trading Toolbox.
• These suites of tools are being used for Algorithmic Trading and Portfolio Management.
• These include:
• Market Impact Estimation
• Pre-Trade
• Post-Trade
• Trade Schedule Optimization
• Liquidation Cost Analysis
• Portfolio Optimization with TCA
• Various Libraries are Available
• Access to a full suite of TCA libraries and MI Data is available upon request.
• Contact: [email protected] or [email protected]
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Optimal Sport Math, Statistics, and Fantasy
Key items addressed include:
• Accurately rank sports teams
• Compute winning probability
• Demystify the black-box world of computer models
• Provide insight into the BCS and RPI selection process.
• Select optimal mix of players for a fantasy league competition
• Evaluate player skill and forecast future player performance
• Select team rosters
• Assist in salary negotiation
• Determine Hall of Fame eligibility
• Sabermetrics on Steroids!
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What is Quantitative Finance?
• Quantitative Finance is the application of methods and analyses
from the different sciences to solve financial problems.
• This include: Math, Statistics, Physics, Engineering, Economics,
Computer Science, Biology, Psychology, Business, etc.
• Quantitative Finance is all about proper utilization of the
“Scientific Method” and drawing statistically significant
conclusions.
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Scientist or Engineer
• A Scientist is someone who “loves” surprises. This is an
opportunity to learn and make further advancements. The goal is
to learn, improve, and progress.
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Scientist or Engineer
• A Scientist is someone who “loves” surprises. This is an
opportunity to learn and make further advancements. The goal is
to learn, improve, and progress.
• A Engineer is someone who “hates“ surprises. Surprises are
usually a indication that something “failed” or gone wrong and
often results in a loss or slowing of progress.
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What about a Quant?
• A Quant is someone who learns from a proper application of the
scientific method by finding “Scientific” surprises and “profit”
opportunities.
• Quants go through great lengths to learn the cause of these
surprises and to ensure that these relationships are statistically
significant.
• Quants then seek to implement these scientific surprises without
suffering any “Engineering” surprises and losses.
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The Scientific Method in Practice
ScientistData
Data
Data
StatisticallySignificantConclusion
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The Scientific Method in Practice
ScientistData
Data
Data
StatisticallySignificantConclusion
Attorney Desired OutcomeFind supporting data
Data Mining
Data
Data
Data
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The Scientific Method in Practice
ScientistData
Data
Data
StatisticallySignificantConclusion
Attorney Desired OutcomeFind supporting data
Data Mining
Data
Data
Data
Doctor Educated GuessTest Data
Worse Case Scenario?
Data ?
Data ?
Data ?
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Moral of the Story:
Be a Scientist!
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Moral of the Story:
Be a Scientist!
Don’t be that Anti-Scientist!
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Quantitative Sports Modeling
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What is Quantitative Sports Modeling?
• The application of quantitative tools and analytics, and sound
scientific methods, to sports related problems and questions.
• Quantitative sports modeling consists of the same tools used in
quantitative finance and is comprised of: mathematics, statistics,
engineering, machine learning, economics, business, etc.
• Sports Modeling is based on the same framework as Quantitative
Finance, but solves different set of problems.
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What do we want to solve?
• Expected Winning Team
• Probability of Winning
• Expected Winning Margin
• Probability of Beating a Specified Margin
• Future Player Performance
• Roster of Players (Best set of Complementary Players)
• Best Mix of Players given Opponent
• Salaries & Salary Negotiation
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Sports Modeling Data: What we want to Predict (LHS)
• Win/Loss
• Win Margin
• Probability of winning by more than X points
• Player Statistics (Fantasy Sports)
• Evaluating Player Ability
• Roster Selection
• Salary and Salary Negotiations
• Line-up and Match-ups
• Player Trades
• Hall of Fame Selection
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Sports Modeling Data: Explanatory Factors Data (RHS)
• Win/Loss Result
• Game Scores
• Game Data
• Team Statistics• (AVG, OBP, ERA, HR, Comp. Ratio)
• Venue Location• (Home Field Advantage)
• Momentum
• Players, Injuries
• Career Statistics
• Salary
• Age
• Teammates & Roster
• Principal Component Analysis
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Different Sports Prediction Models
• Probability Models
• Non-Linear Regression
• Non-Parametric Statistics
• Neural Networks / Machine Learning
• Sabermetrics on Steroids!
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Head-to-Head Competitions – How do we Rank Teams
A
B
E
C
D
F
Ranking:A
B & CD & E
F
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Head-to-Head Competitions – How do we Rank Teams
Ranking:A, B, C
A
B C
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Head-to-Head Competitions – How do we Rank Teams
Ranking:A & GB & C D & E
F
A
B
E
C
D
F
G
Ranking:A
B & C & GD & E
F
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Head-to-Head Competitions – How do we Rank Teams
Ranking:A
B & C D & EF & H
Ranking:A
B & C D & E & H
F
A
B
E
C
D
F
H
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Sports Models To Discuss Today
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Probability Models: Probability (X>Y)
• Power Function:𝜆𝑥
𝜆𝑥 + 𝜆𝑦
• Logit Regression
𝑏0 + 𝑏ℎ − 𝑏𝑎 = ln𝐹−1 𝑧
1 − 𝐹−1 𝑧
• In probability models, the LHS variable is (0,1) !
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Power Function
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Power Function
The Power function is derived from the Exponential Distribution.
Let,
𝑓 𝑥 ~𝜆𝑥𝑒−𝜆𝑥𝑡
𝑓 𝑦 ~𝜆𝑦𝑒−𝜆𝑦𝑡
Then,
𝑃𝑟𝑜𝑏 𝑥 > 𝑦 =𝜆𝑥
𝜆𝑥 + 𝜆𝑦
where, 𝜆𝑘= Team “k” Rating
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Power Function with Home Field Advantage
Let X be Home Team
Prob X > Y =λx + λ0
λx + λy + λ0
Let Y be Away Team
Prob Y > X =λy
λx + λy + λ0
λk= Team “k” Rating
λ0= Team “k” Rating
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Power Function: Solving Parameters
Function
𝐺 =
λx + λ0λx + λy + λ0
𝑖𝑓 ℎ𝑜𝑚𝑒 𝑡𝑒𝑎𝑚 𝑤𝑖𝑛𝑠 𝑔𝑎𝑚𝑒
λx + λ0λx + λy + λ0
𝑖𝑓 𝑎𝑤𝑎𝑦 𝑡𝑒𝑎𝑚 𝑤𝑖𝑛𝑠 𝑔𝑎𝑚𝑒
Max 𝐿 = ς𝐺𝑖
Max log 𝐿 = σ log 𝐺𝑖
Solve using Maximum Likelihood Estimates (“MLE”)
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Power Function: Estimate Spread
Run Second Regression,
𝑆𝑝𝑟𝑒𝑎𝑑 = 𝑑0 + 𝑑1 ∙ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦
Results,𝑑0, 𝑑1, 𝑠𝑒𝑌
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MATLAB – Solving Power Function Parameters
% Power Function Model
% Num = matrix of winning team and location (HFA if at home)
% Denon = matrix of all teams including HFA
[b,fval,exitflag,output]=fmincon(@(b) myPower(b,Num,Denom),...
b0,[],[],[],[],LB,UB,...
[],...
options);
exitflag;
function f = myPower(b,Num,Denom)
Z=(Num*b)./(Denom*b);
f=-sum(log(Z));
end
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Steps to Solve Power Function
• Set up Objective Function:
• Estimate Team Ratings using MLE
• Compute Winning Probabilities using Power Function Formula
• Run Regression of Home Team Win Margin (Spread”) as function of
Predicted Home Team Winning Probability (“Prob”):
• 𝑆𝑝𝑟𝑒𝑎𝑑 = 𝑑0 + 𝑑1 ∙ 𝑃𝑟𝑜𝑏
• This provides:
• 1) Probability that Home Team Wins Game
• 2) Expected Home Team Win Margin
• 3) Teams can be ranked based on Model Parameter (from highest to lowest)
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Logit Regression
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Logit Regression Model
Start with Logistic Distribution Function:
1
1 + exp − 𝑏0 + 𝑏ℎ − 𝑏𝑎= 𝑧1
s = Home Pts − Away Pts = Home Team Spread, (-inf, +inf)
z =𝑠 − 𝑎𝑣𝑔(𝑠)
𝑠𝑡𝑑𝑒𝑣(𝑠), (−𝑖𝑛𝑓, +𝑖𝑛𝑓)
𝑧1 = 𝐹−1 𝑧 = 𝑛𝑜𝑟𝑚𝑐𝑑𝑓 𝑧 , (0,1)
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Logit Regression Model
We transform the logistic function into the logit regression:
𝑏0 + 𝑏ℎ − 𝑏𝑎 = ln𝑧1
1 − 𝑧1
s = Home Team Spread, (-inf, +inf)
z =𝑠 − 𝑎𝑣𝑔(𝑠)
𝑠𝑡𝑑𝑒𝑣(𝑠), (−𝑖𝑛𝑓, +𝑖𝑛𝑓)
𝑧1 = 𝐹−1 𝑧 = 𝑛𝑜𝑟𝑚𝑐𝑑𝑓 𝑧 , (0,1)
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Steps to Solve Logit Spread Regression (Part 1)
• Calculate LHS Spread Values = Home Team Spread, (-inf, +inf);
z =𝑠 − 𝑎𝑣𝑔(𝑠)
𝑠𝑡𝑑𝑒𝑣(𝑠), −𝑖𝑛𝑓, +𝑖𝑛𝑓 ; 𝑧1 = 𝐹−1 𝑧 = 𝑛𝑜𝑟𝑚𝑐𝑑𝑓 𝑧 , (0,1)
• Solve parameters from OLS
• 𝑏0 + 𝑏ℎ − 𝑏𝑎 = ln𝑧1
1−𝑧1
• Estimate Home Team Win Margin
• 𝑧1 = 𝐹−1 𝑧 =1
1+exp − 𝑏0+𝑏ℎ−𝑏𝑎
• 𝑧 = 𝑛𝑜𝑟𝑚𝑖𝑛𝑣 𝑧1
• 𝑠 = 𝑧1 ∙ 𝑠𝑡𝑑𝑒𝑣 𝑠 + 𝑎𝑣𝑔(𝑠)
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Steps to Solve Logit Spread Regression (Part 2)
• Run second regression:
• 𝐴𝑐𝑡𝑢𝑎𝑙 𝑆𝑝𝑟𝑒𝑎𝑑 = 𝑑0 + 𝑑1 ∙ 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑆𝑝𝑟𝑒𝑎𝑑
• 𝑌 = 𝑑0 + 𝑑1 ∙ 𝑠
• 𝑑0, 𝑑1, 𝑠𝑒𝑌
• Compute Home Team Win Probability
• 𝑃𝑟𝑜𝑏 𝑆𝑝𝑟𝑒𝑎𝑑 > 0
• 𝑃𝑟𝑜𝑏 𝑌 > 0
• 𝑌~𝑁 𝑠, 𝑠𝑒𝑌
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MATLAB – Logit Regression
% Logit Regression
% s = home team win margin,
% s>0, home team won game by s
% s<0, home team lost game by s
% z=zscore(s), mu = mean(s), stdev = stdev(s)
% Finv=normcdf(z)
% Y=log(Finv/(1-Finv))
% X=matrix of games, home team = +1, away team = -1
whichstats={'beta','tstat','r','yhat','mse','rsquare'};
myStats = regstats(Y,X,'linear',whichstats);
beta=myStats.tstat.beta;
beta=[beta(2:end);beta(1)];
TeamRating=beta;
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NFL
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NFL Data: Only Three Weeks of Games (47 Games)
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NFL Data: Only Three Weeks of Games
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NFL Data: Only Three Weeks of Games
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Power Function: Estimating Spreads
𝑝𝑟𝑜𝑏 =λx + λ0
λx + λy + λ0
spread = 𝑑0 + 𝑑1 ∙ 𝑝𝑟𝑜𝑏
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NFL - Power Function
Estimating Home Team Win Probability:
𝑝𝑟𝑜𝑏 =λx + λ0
λx + λy + λ0
Estimating Home Team Spread
𝑠 = 𝑑0 + 𝑑1 ∙ 𝑝𝑟𝑜𝑏 = −12.601 + 28.154 ∙ 𝑝𝑟𝑜𝑏
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Example: Power Function
New England (Home) vs. Carolina (Away)
New England = 28.954
Carolina = 5.1099
HFA = 0.01
𝑝𝑟𝑜𝑏 =28.954+0.01
28.954+5.109+0.01= 85%
Estimating Home Team Spread
𝑠 = −12.601 + 28.154 ∙ 0.85 = +11.3 (need to adjust)
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Logit Regression: Estimating Spreads
Est. Spread = b0 + bH − ba
Act. Spread = 𝑑0 + 𝑑1 ∙ 𝐸𝑠𝑡. 𝑆𝑝𝑟𝑒𝑎𝑑
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NFL – Logit Regression
Estimating Home Team Win Probability:
ln𝑧1
1 − 𝑧1= 𝑏0 + 𝑏ℎ − 𝑏𝑎
Estimating Home Team Spread
Y (Actual Spread) = 𝑑0 + 𝑑1 ∙ 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑆𝑝𝑟𝑒𝑎𝑑 𝑠𝑑0, 𝑑1, 𝑠𝑒𝑌𝑃𝑟𝑜𝑏 𝑌 > 0 = 𝑛𝑜𝑟𝑚𝑐𝑑𝑓 0, 𝑠, 𝑠𝑒𝑌
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NFL Data: Only Three Weeks of Games
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Example: Power Function
New England (Home) vs. Carolina (Away)
New England = 1.0079
Carolina = 0.4869
HFA = -0.0592
Estimating Home Team Spread:
𝑠 = 𝐽 𝐾1
1 + exp(−(1.0079 − 0.4869 − 0.0592)= +6.7
Estimating Home Team Win Probability:
𝑝 = f 6.7 =74%
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NFL - Predictions
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NCAA College Football
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College Football: Only Four Weeks of Games (286 Games)Games with Div 1- FBS Teams Only
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NCAA Football: Only Four Weeks of Games
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NCAA Football - FBS: Model Results
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NCAA Football - FBS: Algorithmic Rankings (after 4 weeks)
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NCAA Football - FBS: Week 5 Predictions (Part 1)
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NCAA Football - FBS: Week 5 Predictions (Part 2)
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AlgoSports23/MATLAB Competition
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AlgoSports23 / MATLAB Competition
• Are you Smarter than the Algo!
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AlgoSports23 / MATLAB Competition
• Are you Smarter than the Algo!
• Can you Beat the Algo!
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AlgoSports23 / MATLAB Competition
Two Important Emails:
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AlgoSports23 / MATLAB Competition
• Rules of the Competition
• All Analysis & Programming MATLAB
• Game Results Data will be Posted Weekly
• Game Prediction File will be Posted Weekly
• Return Model Predictions by Specified Date
• Top 23 performing Algorithms each week will be included in
the AlgoSport23 Computer Rankings and Prediction
• National Media Attention!
• Are you smarter than the Algo?
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AlgoSports23 / MATLAB Competition
Your program and submission needs to include the following:
1) Ranking of Teams
2) Prediction of Home Team Winning Margin for all game in a week
Models are measured based on:
1) RMSE
2) Avg Difference
3) Number of Wins
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AlgoSports23 / MATLAB Competition
• Top 23 performing Algorithms each week will be included in the
AlgoSport23 Computer Rankings and Prediction!
• National Media Attention!
• Bragging Rights!