Gambling Strategies and Prize-Pricing Recommendation in Sports Multi-Bets

Round 1

Reviewer 1 Report

1. You may want to qualify by jurisdiction or add context to the last sentence of paragraph 2 of the introduction.  The statement is not accurate in all jurisdictions.

2.  The last sentence of paragraph 3 is inaccurate.  Not all gamblers look at data to make betting decisions.  You could qualify by adding "smart money: gamblers do.

3. Regarding the wisdom of crowds discussion in paragraph 4 of the introduction, I don't buy into the assertation that placed wagers ultimately lead to pricing efficiencies when setting betting lines.  Betting lines are created weeks, sometimes months in advance.  Certainly placed wagers affect the betting lines but so does additional information that is uncovered or revealed as the wagered upon event draws nearer.  Information such as player injury, illness, weather conditions, etc. as well as action taken on both sides of the line factor into the tightening of betting lines as the date of play for events approach.

4. The last sentence of the conclusion states that there is a "fairer way to bet"  that may be the case but unless the margins are appealing to the betting operator, it is unlikely that fairness will be a consideration.

Author Response

1. You may want to qualify by jurisdiction or add context to the last sentence of paragraph 2 of the introduction.  The statement is not accurate in all jurisdictions. - 

Thank you for this observation. We added to the text that it is true in most jurisdictions.

2. The last sentence of paragraph 3 is inaccurate.  Not all gamblers look at data to make betting decisions.  You could qualify by adding "smart money: gamblers do.

Thanks for this suggestion. We rephrased to say that smart money gamblers look at the data etc.

3. Regarding the wisdom of crowds discussion in paragraph 4 of the introduction, I don't buy into the assertation that placed wagers ultimately lead to pricing efficiencies when setting betting lines.  Betting lines are created weeks, sometimes months in advance.  Certainly placed wagers affect the betting lines but so does additional information that is uncovered or revealed as the wagered upon event draws nearer.  Information such as player injury, illness, weather conditions, etc. as well as action taken on both sides of the line factor into the tightening of betting lines as the date of play for events approach.

Thank you for this helpful remark. We inserted a similar text into the manuscript under the wisdom of crowds paragraph.

 The last sentence of the conclusion states that there is a "fairer way to bet"  that may be the case but unless the margins are appealing to the betting operator, it is unlikely that fairness will be a consideration.

The system we described can retain the same average percentage of earnings for Winner, and be beneficial for the “smart” gamblers. We rephrased the sentence to emphasize this point.

Reviewer 2 Report

The manuscript reviews a very interesting case study – WINNER 16 – run by the Israeli state. Overall the manuscript takes advantage of good statistical analysis, good data use, and relevant results. 

I believe some more work is required to make sure the manuscript can reach broader audiences who are not familiar with the game but have an interest in similar schemes. To improve the paper I suggest the following:

1) You talk about the WINNER 16 as if it is common knowledge. I struggled a bit grasping what the entire prize scheme is about and what are the relevant rules. In the introduction, consolidate all briefing information into a paragraph or two on the mechanics of the game and why it is important for readers outside Israel with an interest in multi-bets. Alternatively include this description in an appendix. At the moment the description is all over the text (abstract, intro, and Section 3).

2) On page 2 "In sports betting, every betting house has its own fees, which normally are much higher (~10% or higher)" the house edge can be anything from 2/3% for binary or outcomes with high probabilities up to 50% for correct scores and events with low probabilities and high odds. Not sure how the 10% benchmark can be accurate. 

3) You use William Hill and Bet365 as external bookies. You can use BetBrain data which is averages across 30+ bookies. 

4) You can do a random subsampling of historical matches in England/Italy to see how simulations of a similar game with different datasets would look like. This would expand the paper and highlight further the merits of your analysis. 

5) Regarding the kelly criterion, it is designed mostly to control losses. I suggest citing previous studies that use the same for forecasting football outcomes e.g. "Hassanniakalager, A., Sermpinis, G., Stasinakis, C. and Verousis, T., 2020. A conditional fuzzy inference approach in forecasting. European Journal of Operational Research, 283(1), pp.196-216."

6) By suggesting Eq. 3 you actively change the nature of the game from a fixed-odds game into a Parimutuel gambling setting. This shall be signposted and establish why such change which reducing the profit of the house would be necessary. I suggest expanding on this part

Author Response

See attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The revisions are satisfactory.