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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 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 ???)

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  1. Chula! Using all sorts of SAS to simulate and handicap jai-alai games for fun (and profit ???) Steve Grilli Life Office Management Association

  2. 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

  3. DISCLAIMER “Fun” SAS application Not advocating gambling ! ! ! Internet gambling is considered illegalby US Dept. of Justice, and State of Georgia ! ! !

  4. 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)

  5. 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

  6. BETTING TERMINOLOGY Money goes into POOLS • Win, Place, Show • Quinella • Exacta (Perfecta) • Trifecta

  7. 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

  8. 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

  9. 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

  10. 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%

  11. /* 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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.)

  18. 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);

  19. 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

  20. Research 3: Improving the Estimate of Mean Payout

  21. 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

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