Picking Winners is For Losers: A Strategy for Optimizing Investment Outcomes Clay graham DePaul University Risk Conference Las Vegas - November 11, 2011
REMEMBER Picking a winner is not at all the same as making a smart investment!
Pathway Mission Implementation Investments Control Decisions Methods Probabilities
Some Questions Sought to Be Addressed Is the amount of the investment as important as selecting a winner? Market inequities identified? Pricing of investment Value market
Ripped From Today s Headlines
Mission Have Fun Make Money Tom Peters
Our Credo Learn to cope with variance Keep a perspective on long term and commitment to invest Go where the numbers take you Capture the greatest long term reward as a function of a tempered risk What gets measured gets done Discipline Discipline Discipline!
Investments Value > Price
Some Value Measurements (can be compounded and complex) Return on Investment Yield Capital gain Risk Price volatility Probability variation of success Money management Duration Short versus Long Term Available liquidity
Various Investments (Sure things just don t exist) Stocks Options (and derivatives) Bonds Currency Metals (other hard assets ) Real Estate Gaming
The Process (gaming) Sniff and kick Kind of investments available What game Probabilities of success Payoff and price Invest or not If so How Much? Modeling game and economics
Methods..(join) the ultimate baptism into the religion of statistics. Jeff Ma
da Vig (as we say in Chicago) Vigorish, or simply the vig, is also known as juice or the take, is the amount charged by the house for its services. Bets: -110 Home, -110 Road House receives 220 in bets pays out 210 Makes 10/220 or 4.5% profit or Juice
Methods of Sports Gaming Investments Money Line Select team to win at specific price Over Under Pick above or below a specific total Grand Salami (same as above but for games that day) Spread Win or lose by fix number of points (runs)
Probabilities ( v a l u e > p r i c e ) Probability Winning (event) > Implied Probability of Line + Vig Implied probabilities: -125 = (125)/(100+125) = 56% 100 = (100)/(100+100) = 50% 150 = (100)/(100+150) = 40%
Probabilities Probabilities of success must be associated and tailored to each method of investment. Money line - Probability of Team winning Over Under - Probability over x or under x Spread - Probability Team A wins by y points (runs)
Modeling Baseball First and Foremost: Runs are the Currency of baseball
Modeling Baseball Traditional measures ineffective in quantifying run production Key Metric must be: Comparable among and between: Batters Pitchers Teams Additive Accurate & reproducible Expected Runs / Plate Appearance (EVR/PA)
Production Function Runs = k(evr/pab) α (1/ EVR/PAP) β Where: EVR/PAB means expected value of runs per plate appearance batter (pitcher) Hey Dude: this is linear in logs and you can solve it! Solve for α, β and anti log of k (since above equation is linear in logs!) ( r / B) = α = elasticity of run production attributable to batters (.66) ( r / P) = β = elasticity of run production attributable to pitchers (.34)
Probability of Winning (game) 1. Pythagorean (traditional): P(W H ) = (R H ) 2 / [(R H ) 2 + (R R ) 2 ] 2. Neutral (player based): P(W H ) = f(evr/par P,B, EVR/PAH P,B ) 3. 8 Variable: P(W H ) = f(evr/par P,B, EVR/PAH P,B, RANKR O,D, RANKR O,D ) 4. Sigma (dispersion & variance): P(W H ) = f(δr O / δh O, δr O / δh O, Δ Rank)
Decisions They (all) have a way of looking at numbers in a truly creative way. They understand the right question to ask to let numbers solve these problems. Michael Lewis
Money Line Price of investment set by the market Nomenclature (US lines) -180 means: pay 180 to win 100 125 means: pay 100 to win 125 Select one team as having an economically viable return on investment Keep in mind that the home team is favored: 70% of the time yet wins only 52%
Over Under (total points or runs) Points (runs scored) either over or under a specified total Market usually tends to be balanced; i.e., price of bets closely symmetrical. Caveat: Grand Salami Over / under on all games played on given day
Observation (baseball) 60% of the time the winning team scores an odd number of runs Source: Baseball Prospectus.com 2011 Season Tabulated by: CJG
Negative Binomial vs. Gamma (Expected Runs / Game)
Decision Processes Quantify all possible investments EVROI Expected run margin Performance ranking variation Filter above criteria to add accuracy to forecat Identify just where there is an Edge Accuracy an imperative Probability of winning Price (line)
Home Team Considerations (market inequities) Basketball favored 71% yet wins just 61% Baseball favored 70% wins 52% Over Under Basketball over / under with line 50/50 Baseball Over / under: 52% / 48% Odd number of runs 60% 90% of Sport Gamblers Loose!
Selection Optimizing Filtration (using Evolver for Road and Home Models) EVROI Lines Rankings P(W) DB Duratio n Maximize: Profitable Investments
How Much to Invest? (% bankroll or each bet) Bob Stoll, aka, Dr. Bob Football about 2% Basketball about 1.5% San Francisco betting community Consensus 1% to 6% Kelly Criteria (major investors)
Kelly Criterion (I) Objective: maximize bankroll (long run) f = (bp-q) q / b Where: f = fraction of bankroll to wager b = profit (proportion of payoff) p = probability of winning q = probability of losing
Kelly Criterion (II) f = (bp q) / b = (p(b+1) -1)/p Note: 1. f = expected winnings / bet net winnings 2. Definition of the Edge = p*b q (numerator) 3. Expected value ROI = edge/cost
Kelly Criterion (III) More Risk = Increase Probabilities of: Both Good and Bad Outcomes Road @ 13% Home @ 9% Overbetting is worse than Underbetting
Some Problems with Kelly Proportion of bankroll too much exposure Pragmatic gaming judgment not considered Maximum bet Maximum at risk on a given day Over dependence on probability of winning Nominal emphasis on economics
Seasonal Return on Bankroll Period Bob Stoll 1 (Dr. Bob) 1999-2000 162.6% 2000-2001 140.2% 2001-2002 165.2% 2002-2003 -49.7% 2003-2004 62.9% 2004-2005 81.6% 2005-2006 210.7% 2006-2007 -.1.1% 2007-2008 -77.4% 2008-2009 34.8% 2009-2010 2010-2011 average 73.0% Source:(1) DrBobSports.com; Spread - football @ 2% and basketball @1.5%
Actual Bankroll Pattern 350,000 300,000 250,000 Fund per contract Bankroll 200,000 150,000 100,000 50,000 0 4/29 5/6 5/13 5/20 5/27 6/3 6/10 6/17 6/24 7/1 7/8 7/15 7/22 7/29 8/5 8/12 8/19 8/26 9/2 9/9 9/16 9/23 9/30 10/7 10/14 10/21 Client Cut Available Bankroll
Money Management Reasonable Criteria Bet size upper and lower constraints Economically targeted Invest more when with higher expected value of return Transition over finite range Different formulations predicated upon Type of investment Investment configuration
Goal Focused Control Equation Staking % = A b +((A t -A b ) / (1+Exp (-(EVROI-X 0 ) / W))) Where: A b = minimum proportion of bankroll A t = maximum proportion of bankroll W = transition slope X 0 = shifting factor EVROI = expected ROI of specific investment
Staking Level Tied to Expected ROI
What are the Results? Money Line Description Flat Kelly Slade Average Invest Rate 2. 5 % 2. 5 % 2. 5 % Maximum bet 10,000 10,000 10,000 Starting Bankroll 200,000 200,000 200,000 % Profit (season) 1 2. 5 % 7. 2 % 4 9. 8 %
What are the Results? Over / Under Description Kelly Slade Average Invest Rate 2. 5 % 2. 5 % Maximum bet 10,000 10,000 Starting Bankroll 200,000 200,000 % Profit (season) 90% 210%
Implementation Do not put your faith in what statistics say until you have carefully considered what they do not say. William Watt
Data Preparation Implementation Model(s) Day to day updating Players Lines Exogenous factors Placing investments Accuracy Timing
Why Betters Fail? Implementation Inaccurate implementation (making wrong bet) Head for the hills syndrome (short term perspective) Reactive (reduce investment after losses) Realistic expectations Dumb ass rules,i.e., no bets when probability of winning is less than 50% Violate 3Ps Preparation Persistence Patience
Control Winning (profitability) isn t everything; it s the only thing. Vince Lombardi
Control To assure success it is an imperative to: Maintain a History of all decisions including logic in their derivation Review and validate functional algorithms Maintain daily, weekly, monthly and TYD records performance Never be content with just good results
The Magnitude of Investment can play a more dominant role to long run profitability than that of the probability of winning!