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Chula! Using all sorts of SAS to simulate and handicap jai-alai games for fun (and profit ???) Steve Grilli Life Office Management Association Presentation Outline Intro: Steven Skiena’s Calculated Bets Jai Alai -- The Game -- Betting Terminology -- Pari-mutuel Wagering

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chula using all sorts of sas to simulate and handicap jai alai games for fun and profit

Chula! Using all sorts of SAS to simulate and handicap jai-alai games for fun (and profit ???)

Steve Grilli

Life Office Management Association

presentation outline
Presentation Outline

Intro: Steven Skiena’s Calculated Bets

Jai Alai

-- The Game

-- Betting Terminology

-- Pari-mutuel Wagering

-- How Games are Scored

Using SAS to Engineer the System

-- Simulating Games

-- Parsing Internet Files

-- Bet Selection Analysis

SAS and Selected Research Issues

-- Confidence Limits on small proportions

-- “Hot hands” and players’ skill levels

-- Modelling mean payouts

Conclusions

disclaimer
DISCLAIMER

“Fun” SAS application

Not advocating gambling ! ! !

Internet gambling is considered illegalby US Dept. of Justice, and State of Georgia ! ! !

the book
THE BOOK

Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win

by Steven Skiena

Professor of Computer Science

SUNY Stony Brook

(Cambrigde University Press and

Mathematical Association of America, 2001)

the game of jai alai
THE GAME OF JAI ALAI
  • Originated in the Basque Region
  • Players use a “basket” (cesta) to fire a hard ball (pelota) against a wall.
  • Must be caught and returned on the fly or one bounce
  • In U.S. eight players or doubles teams rotate
  • Pari-mutuel gambling allowed at fronton and off-site betting establishments
betting terminology
BETTING TERMINOLOGY

Money goes into POOLS

  • Win, Place, Show
  • Quinella
  • Exacta (Perfecta)
  • Trifecta
pari mutuel wagering
PARI-MUTUEL WAGERING
  • Different from casino games where you play against the house
  • No fixed odds
  • Fronton (Jai Alai Stadium and its operators) take a cut of each pool off the top
  • Quite high (over 20%)
  • Good news: they don’t care who wins
  • More that’s wagered, the more the fronton makes
how games are scored
How Games Are Scored
  • Eight players (or double teams)
  • Color-coded Posts 1-8
  • Player 1 serves to Player 2
  • Winner of point stays on the court
  • Loser goes to the end of the line
  • Next player in the queue takes the court
  • First time through rotation points worth one
  • After all 8 players have taken the court points worth two
  • Games played to 7 or 9 points
simulating games 1 what do we need
Simulating Games 1: What Do We Need?
  • A basic player skill measure: Point-win Percentage (PTWPER)
  • A probability function that generates the probability that Player A with PTWPER-A wins the point against Player B with PTWPER-B
simulating games 2 the probability function
Simulating Games 2: The Probability Function

Alpha is the key

Ex: Player A PTWPER = 0.525

Player B PTWPER = 0.475

Alpha= 1.0; A wins 52.5%

Alpha= 0.4; A wins 65.1%

simulating games 3 sas code
/* simulate winner */;

do until(win gt 0);

pt+1;

alpha=&alph;

if wper(Op1) ge wper(Op2) then

winop12= .5*(1 + (wper(Op1)-wper(Op2))**alpha);

else winop12= .5*(1 - (wper(Op2)-wper(Op1))**alpha);

if ranuni(0) lt winop12 then do;

Ppt(Op1)+1;

Ppt(Op2)+1;

Pptw(Op1)+1;

q(pt+6)=Op2;

Op2=q(pt);

if pt le 7 then Sc(Op1)+1;

else Sc(Op1)+2;

if Sc(Op1) ge game then do;

win=Op1;

Sc(Op1)=-1;

end;

end;

else do;

Ppt(Op1)+1;

Ppt(Op2)+1;

Pptw(Op2)+1;

q(pt+6)=Op1;

if pt le 7 then Sc(Op2)+1;

else Sc(Op2)+2;

if Sc(Op2) ge game then do;

win=Op2;

Sc(Op2)=-1;

end;

Op1=Op2;

Op2=q(pt);

end;

end;

Simulating Games 3: SAS Code
simulating games 4 some sas output
Simulating Games 4: Some SAS Output

GAME 6

  • PTWPER GACT TEAM POST

0.49598 93 JAIRO-LARREA 1

  • 0.54231 77 LECUE-CHASIO 2
  • 0.45431 104 TOTO-MADARIETA 3
  • 0.50832 82 SCOTTY-ERKIAGA II 4
  • 0.51901 64 OCHOA-PEDRO 5
  • 0.47931 68 OLATE-CARVALHO 6
  • 0.46634 30 BARRE-AZPIRI 7
  • 0.48200 122 ARECHA-URTARAN 8
simulating games 4 more sas output
Simulating Games 4: More SAS Output
  • The FREQ Procedure
  • Cumulative Cumulative
  • EX Frequency Percent Frequency Percent
  • 1-2 9495 3.80 9495 3.80
  • 1-3 4606 1.84 14101 5.64
  • 1-4 5443 2.18 19544 7.82
  • 1-5 6382 2.55 25926 10.37
  • 1-6 4219 1.69 30145 12.06
  • 1-7 4040 1.62 34185 13.67
  • 1-8 3747 1.50 37932 15.17
  • 2-1 12541 5.02 50473 20.19
  • 2-3 7509 3.00 57982 23.19
  • 2-4 8429 3.37 66411 26.56
  • 2-5 9609 3.84 76020 30.41
  • 2-6 6408 2.56 82428 32.97
  • 2-7 6250 2.50 88678 35.47
  • 2-8 6536 2.61 95214 38.09
simulating games 5 bet selection
Simulating Games 5: Bet Selection

GAME 6 EXACTA SELECTIONS

  • GDATE GTIME GM GT GPTS TYP SEL PR RET
  • 16828 EVE 6 D 7 E 2-1 0.05016 1.16647
  • 16828 EVE 6 D 7 E 2-5 0.03844 1.06245
parsing internet files results files
GAME 6

2 Lecue-Chasio 9.40 4.40 4.20

1 Jairo-Larrea 5.40 3.60

5 Ochoa-Pedro 3.80

QUINIELA 1-2 24.60

EXACTA 2-1 101.70

TRIFECTA 2-1-5 221.60

SAS FUNCTIONS

INDEX ()

SCAN ()

Also, conditional input statements

Parsing Internet Files: Results Files
bet selection analysis
Bet Selection Analysis

GAME 6 ANALYSIS OF RET CUTOFFS

  • RET N MEANPROF PERCOR TPROF COR LOWER UPPER
  • 1.19 137 0.84672 0.058394 116.0 8 0.027991 0.10715
  • 1.03 1443 0.66334 0.038808 957.2 56 0.029749 0.04971
  • 1.23 63 0.61905 0.063492 39.0 4 0.021809 0.14391
  • 1.04 1294 0.61731 0.037867 798.8 49 0.028478 0.04932
  • 1.05 1152 0.55104 0.036458 634.8 42 0.026771 0.04847
  • 1.02 1618 0.54042 0.037083 874.4 60 0.028687 0.04713
  • 1.17 211 0.50616 0.052133 106.8 11 0.028010 0.08840
  • 1.01 1790 0.44134 0.036313 790.0 65 0.028382 0.04574
  • 1.15 299 0.41271 0.046823 123.4 14 0.027085 0.07526
  • 1.18 163 0.39264 0.049080 64.0 8 0.023473 0.09046
  • 0.89 5330 0.36968 0.033396 1970.4 178 0.028823 0.03848
  • 0.93 3854 0.35864 0.034510 1382.2 133 0.029092 0.04063
  • 0.94 3538 0.35579 0.033917 1258.8 120 0.028329 0.04027
system structure summary
System Structure Summary
  • Parse entries .txt file from fronton website
  • Simulate games; select bets
  • Parse entry changes .txt file; resimulate any games with changes
  • Finalize bets
  • Parse results .txt file
  • Update SAS data sets (PTWPER, Mean Payouts, et. al.)
research 1 confidence interval on small proportions
Research 1: Confidence Interval on Small Proportions

95% Jeffreys interval:

  • LOWER=BETAINV(.025,COR+0.50 ,N-COR+0.50);
  • UPPER= BETAINV(.975,COR+0.50, N-COR+0.50);
research 2 hot hand and player skill estimation
Research 2: “Hot Hand” and Player Skill Estimation
  • Statisticians still argue about the existence of streaks in sports
  • If we had actual point-win data, we can conduct research
  • Use GEE option in PROC GENMOD
  • Use PROC FACTOR to build a weighed index of long and short term PTWPER
conclusions
CONCLUSIONS

SAS works for the three major areas of this type of gaming application: parsing internet files, simulation of the games, and analysis & research

Profit? System is still under construction, but profitable in terms of personal development as statistician and SAS programmer