Bookdown contest submission: Odd

2018-09-08 本文已影响5人赢家黄氏江夏堂联富

Title : Odds Modelling and Testing Inefficiency of Sports Bookmakers

by ®γσ, Lian Hu ®

Source : https://community.rstudio.com/t/bookdown-contest-submission-odds-modelling-and-testing-inefficiency-of-sports-bookmakers/13889

Abstract

I learn R language since decade and finish my first research which was a backtest on the soccer betting. Today I tried to summarise it. Below two links are my research and submitted for the contest.

- Odds Modelling and Testing Inefficiency of Sports Bookmakers 4

- Application of Kelly Criterion model in Sportsbook Investment 1

1. Data

1.1 Odds Modelling and Testing Inefficiency of Sports Bookmakers

I collected the pre-match odds price (open and close price) of 1x2 of 40 bookmakers, 29 bookmakers among them have Asian-Handicap and Over-Under via soccer betting information website.

1.2 Application of Kelly Criterion model in Sportsbook Investment

I collected the Asian-Handicap and Over-Under odds price (whole price movement from open price until close price) of 13 bookmakers.

2. Odds Modelling

I used the Dimitris Karlis and Ioannis Ntzoufras (2005) and then fit the weighted function from Mark Dixon and Stuart Coles (1996) into it. All research are using Markov-Chain method to test every single match in 3 years soccer seasons. However, my model using 1st season to model for 2nd season, and then based on the Mavkov basic model in 2nd season to measure the weighted function, only the 3rd season started a weighted model, therefore 2 soccer season dataset required in order to predict coming soccer match.

There are 4 soccer seasons dataset and 1st and 2nd seasons is the datasets for modelling. The staking model started from 3rd season to 4th season.

2.1 Weighted Function

There has few adjustment onto the model.

- A constant weighted function over over whole moving windows for a soccer season based on last soccer season

- A weekly constant Markov-Chain weighted function

- A daily constant Markov-Chain weighted function

- An observation dynamic weighed function

2.2 Data Constrant

Secondly, due to constrant restricted on to the model, I tried to compare (Might similar with hidden factor for the Markov Chain).

All observation weighted function (for example, a soccer team played with another team more than once within a soccer season, all soccer matches will be counted)

Unique observation weighed function (for example, a soccer team played with another team more than once within a soccer season, only latest soccer matches will be counted. There will be no any duplicated Home vs Away match observation)

Source：Odds modelling and testing inefficiency of sports bookmakers

3. Model Comparison

Finally the model with below adjustment came with highest ROI.

- An observation dynamic weighed function

- Unique observation weighed function (for example, a soccer team played with another team more than once within a soccer season, only latest soccer matches will be counted. There will be no any duplicated Home vs Away match observation)

4. Betting Strategy

4.1 Odds Price

- probability with vigorish (directly convert from the odds price to probability)

- probability without vigorish 1 (the vigorish part divided to 2 to be 50% for both home and team)

- probability without vigorish 2 (the vigorish part divided based on the portion of odds price)

4.2 Betting Strategy

I took below probability as the baseline of bookmakers. After that applied a full Kelly Criterion betting model.

- probability with vigorish (directly convert from the odds price to probability)

- probability without vigorish 2 (the vigorish part divided based on the portion of odds price)

5. Profit and Loss

Due to the paper above using the normal betting strategy by refer to Mark Dixon and Stuart Coles (1996) is not profitable, here I try to use Kelly Criterion (staking on 13 bookmakers) and the ROI was outperformed.

NoCategoryWith Spreads (2011/12)Ratio (%)Without Spreads (2011/12)Ratio (%)With Spreads (2012/13)Ratio (%)Without Spreads (2012/13)Ratio (%)

1No of Matches4,89614,89615,51415,5141

2Total PL$353.9696655.57%$381.0629953.98%$448.899359.35%$488.9184158.60%

3No of Bets2,26846.32%2,40449.10%2,57046.61%2,69748.91%

4No of Won Bets1,53131.27%1,58432.35%1,76532.01%1,82433.08%

5No of Voided Bets1282.61%1432.92%1923.48%1963.55%

6No of Lose Bets60912.44%67713.83%61311.12%67712.28%

7Staking$636.983721$705.892031$756.29791$834.320321

8Won Bets Stakes$453.4372471.19%$496.0955570.28%$563.668574.53%$614.2479573.62%

9Voided Stakes$19.132963.00%$22.672413.21%$27.11513.59%$32.129993.85%

10Lose Bets Stakes-$99.46758-15.62%-$115.03256-16.30%-$114.7691-15.18%-$125.32954-15.02%

table 4.1 : Staking breakdown and result of the bets settlement.

CompanyPL (2011/12)Ratio (%)PL2 (2011/12)Ratio (%)PL (2012/13)Ratio (%)PL2 (2012/13)Ratio (%)

Ladbrokes$33.7724119.54%$38.2518410.04%$44.535078959.92%$46.77633629.57%

Bet365$34.1206249.64%$37.192639.76%$33.537437527.47%$40.67669488.32%

Macauslot$35.74006210.10%$40.2345410.56%$1.764086580.39%$1.93291710.40%

X10Bet$37.53848710.61%$41.6403410.93%$33.628920777.49%$40.69219768.32%

X188Bet$36.57928910.33%$38.2558910.04%$41.056682349.15%$46.11563789.43%

SBOBET$40.39246111.41%$41.9089811.00%$43.509154789.69%$47.83082129.78%

Mansion88$31.2195478.82%$32.389998.50%$42.444034049.46%$43.95216658.99%

YSB88$13.1677463.72%$14.341283.76%$45.9268866710.23%$46.83939639.58%

X12BET$36.80246610.40%$38.1901510.02%$36.030656568.03%$36.24499567.41%

VictorChandler$24.3919176.89%$25.957636.81%$45.1342063810.05%$46.21546209.45%

Canbet$10.3473932.92%$10.975162.88%$41.040192249.14%$46.96176599.61%

Betinternet$10.2868122.91%$11.187312.94%$40.205947528.96%$44.54352749.11%

Titanbet$9.6104412.72%$10.537262.77%$0.086049520.02%$0.13649440.03%

table 4.2 : Breakdown of Operators - Profit & Loss on the Odds Price with/without Overrounds.

6. Conclusion

Finally, the model is proof that profitable. However the odds price was collected from the information website but the from bookmakers website.

Niko Marttinen (2006) introduced a multinormial model which is more accurate than the bivariate poisson model. The bivariate poisson model by Niko Marttinen (2006) added the bookmakers odds price as the hidden effects where I need to upgraded beyond the future.