Diamonds on the Line:
Profiting from the Grand Salami
Clay Graham
DEPAUL UNIVERSITY
Risk Conference
Las Vegas
November 20, 2013
Goals
Input From Our Crack Research Team
What We’re Discussing Today
• Observations
• How it Works
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–
–
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Probability
Expected value
Bet decision
Investment decision
• Results & Predictions
Did You Know?
• Baseball:
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–
–
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Home team favored 68%, wins 54%, gap = 14%
92% games total runs over/under line from 6.5 to 9
Total runs spike on odd number totals
½ run impact Δ probability 5%
• Hockey:
– Home team favored 75%, wins 55%, gap = 20%
– 92% games total runs over/under line either 5 or 5½
– ½ goal impact Δ probability 14%
How it Works?
• Determine probability of winning (the bet)
• Calculate Expected Value of ROI
• Bet selection (using filters and performance
criteria)
• Determine amount to invest
PROBABILITY
Baseball: What do you See?
Does it make sense?
AL Scores More
Home Teams Score More
Runs/Game Distribution (discrete)
Impact: Odd number of runs
5%
Runs/Game to Gamma Distribution
Runs/Game to Cumulative Gamma Distribution
(note: “S” curve)
Runs/Day All Games - 15 Games / Day
(individual games distributed as Gamma, aggregate normally distributed)
Central Limit Theorem in heat
Hockey Goals/Game Distribution
Impact: Odd number of runs
14%
Goals/Game to Gamma Distribution
Goals/Day All Games - 10 Games / Day
(individual games distributed as Gamma, aggregate normally distributed)
Central Limit Theorem in heat
Gaining an Edge
Cumulative Probability Win Gamma Distribution
Hockey: Heart of Statistical Accuracy
Hockey: Rank Summary
• Home Rank Value:
-(Home team offense – Road team defense)
+(Road team offense – Home team defense)
• Larger number better home team advantage
• Use to calculate probability of home team winning
(incorporating logistic regression)
Hockey: Probability of Home Team Winning
as a Function of Summary Ranks
Hockey: Road Goals Scored
StatTools Report
Analysis:
Performed By:
Date:
Updating:
Variable:
Regression
graham
Sunday, August 25, 2013
Static
RdScr
Multiple Regression for RdScr
Multiple
Summary
Adjusted
StErr of
R-Square
Estimate
0.1237
0.1201
1.527361
Degrees of
Sum of
Mean of
Freedom
Squares
Squares
3
720
237.1512
1679.6388
R
0.3517
ANOVA Table
Explained
Unexplained
Coefficient
Regression Table
Constant
Hm Rank
Hm GA x̄
RdGS Adj
-0.606
-0.008
0.639
0.595
R-Square
Standard
Error
0.500
0.004
0.141
0.144
F-Ratio
p-Value
79.0504
2.3328
33.8860
< 0.0001
t-Value
p-Value
-1.211
-2.187
4.522
4.122
0.226
0.029
0.000
0.000
Confidence Interval 95%
Lower
Upper
-1.588
-0.016
0.361
0.312
0.376
-0.001
0.916
0.878
EXPECTED VALUE
Expected Value
P(win) = P(w) = probability of positive outcome
r = positive outcome payoff - receipts ($)
P(loss) = P(l) = probability of negative outcome {P(l)=1-P(w)}
c = cost of negative outcome ($)
EV = expected value of Investment
EV = P(w)*r – [P(l)]*c
EVROI = Expected value of return on investment
EVROI = {P(w)*r – [1-P(w)]*c}/c
Types of Bets
•
•
•
•
Money Line – Picking the winner
Over/Under - Total runs above or below
Spread – Points given to make more equal
Grand Salami:
– Total of all Runs Scored, Above or Below
– Road vs. Home Scoring
What’s the Basic Money Line?
• The Line is the price of a bet
• Example:
– Cubs 125
– Cardinals -135
(bet 100 to win 125)
(bet 135 to win 100)
Runs/Game to Cumulative Gamma Distribution
(note: “S” curve)
Market Inequities
Source of Gaining an Edge
Lines: Implied Probability of Winning
• Example: Cost/ (Payoff + Cost)
– Cubs 125 (plus line)
• P(Wcubs) = 100 / (125+100) = 44%
– Cardinals -135 (negative line)
• P(Wcards) = |135| / (|135|+100) = 57%
The Edge
Calculated Probability of winning bet –
Implied Probability of winning
P(Wc) – P(WI) = Edge
65% - 57% [line of -135] = 8% Edge
EVROI
Expected Value of Return on Investment
(P(Wc) * Payoff– (1-P(Wc)*cost))/ Cost = EVROI
(65%*100 – 35%*135)/135 = 13% ROI
BET DECISION
Selection Optimizing Filtration
(using Evolver for Road and Home Models)Gaining an Edge
EVROI
Lines
P(W)
Rankings
DB
Duration
Maximize: Profitable Investments
Hockey: Money Line Investment Decision
Kelly Criterion
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
Edge vs.
1
Investment
Notes: (1) Trading Bases, Joe Peta
Expected Return vs.
Notes: (1) Trading Bases, Joe Peta
1
Investment
Generalized S Curve
% Bank Roll (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
Expected Return vs. Investment1
Peta Model
Notes: (1) Trading Bases, Joe Peta
Actual Returns over 2010 Season
Source: 2010 investment history
Tabulated by: CJG
Grand Salami: Actual Returns to 5/30/13
Source: 2010 investment history
Tabulated by: CJG
Grand Salami: Actual Returns to 7/30/13
Source: 2010 investment history
Tabulated by: CJG
Grand Salami: Actual Returns to 8/15/13
Source: 2013 investment history
Tabulated by: CJG
Predictions 8/20/2013
• Grand Salami: Over 22.5 @105, 17% EVROI
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•
•
•
Washington +105, EVROI = 27%
Anaheim 165, EVROI = 31%
Columbus 105, EVROI = 23%
Columbus/Calgary Over 5.5, -115, 56% EVROI
Palisade Software is: