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
(value > price)
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 ) = (RH )2 / [(RH )2 + (RR )2 ]
H
2. Neutral (player based):
P(WH) = f(EVR/PARP,B, EVR/PAHP,B)
3. 8 Variable:
P(W ) = f(EVR/PARP,B, EVR/PAH , RANKRO,D ,
RANKRO,D)
H
P,B
4. Sigma (dispersion & variance):
P(WH) = f(δRO / δHO , δRO / δHO , 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)
Considerations
(market inequities)
• Home Team
– 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)
Lines
EVROI
P(W)
Rankings
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 Stoll1
“(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
Fund per
contract
250,000
Bankroll
200,000
150,000
100,000
Client Cut Available
Bankroll
50,000
10/21
10/14
10/7
9/30
9/23
9/16
9/9
9/2
8/26
8/19
8/12
8/5
7/29
7/22
7/15
7/8
7/1
6/24
6/17
6/10
6/3
5/27
5/20
5/13
5/6
4/29
0
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 % =
Ab+((At-Ab) / (1+Exp (-(EVROI-X0) / W)))
Where:
Ab = minimum proportion of bankroll
At = maximum proportion of bankroll
W = transition slope
X0 = 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)
12.5%
7.2%
49.8%
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
Implementation
• Data Preparation
– Model(s)
– Day to day updating
• Players
• Lines
• Exogenous factors
• Placing investments
– Accuracy
– Timing
Implementation
• Why Betters Fail?
–
–
–
–
–
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!