Assignment for Economics of Betting Markets (Final Version)
This assignment is to be submitted on Brightspace (not via email) as a PDF ile before 11.30pm on Wednesday March 27, i.e. the day of the irst lecture after the two-week break. I will apply UCD’s policy regarding grading of late submissions for the assignment.
The assignment will have 4 questions. I will add the questions as soon as we cover the topics in class. I plan to have the last of the questions posted by the end of February.
About Plagiarism
Please read UCD’s plagiarism policy so that you know what it is. I have posted it in Brightspace. I do not want “I didn’t understand this was plagiarism” to be used as an excuse. A few points.
❼ The plagiarism checker in Brightspace will be turned on for the assignment. It will lag assignments that look like things available on the internet or that look like another student’s work.
❼ As you read the questions, you will see that you are required to submit work that is unique to you. If you submit something that looks like another student’s work, I will have to apply the plagiarism policy.
❼ ChatGPT or other AI technologies will not be much use to you in doing the assign- ment. They are really bad at the kinds of tasks it requires and using them greatly increases your chance of being lagged for plagiarism.
❼ Do not even think about using an online “paraphrasing” tool to re-write someone else’s work. They are utterly useless and scream that the work has been plagiarised.
Question 1: Odds, Probabilities and Margins (40% of the marks)
Pick an upcoming sporting event with either two or three possible outcomes that a book- making irm are ofering odds on. I don’t care which bookmakers the odds come from but I do want them to come from one speciic bookmaker. Fractional odds ofered by bookmakers for many events can be found on Oddschecker, here
❼ Show me a screencap of the odds and tell me whether you think they are decimal odds, fractional odds or American Odds.
❼ Show how these odds would be quoted if they were the other two types of odds. For example, if they are fractional odds, tell me what the decimal odds and American odds are for each of the bets.
❼ Assuming the bookmaker has set odds so they believe each bet has the same expected return, answer the following, showing how you worked out the answers.
– What does the bookmaker believe is the expected payout on ➾1 bets on each of the possible outcomes? What is the bookmaker’s proit margin?
– What are the probabilities of success of each of the bets?
– What does the bookmaker believe is the variance of the expected payout to bettors for each possible ➾1 bet?
Question 2: Utility and Risk (20% of the marks)
Consider someone who has a utility function of the form U (W) = W where W is their wealth and is between zero and one. They make decisions by picking the option that has the highest value for expected utility. Pick a value of wealth for this person and pick a value of for them (something unique to your submission with at least 2 decimal places).
❼ Describe some 50/50 bets this person will turn down. For example, would they turn down a 50% chance of winning 110 and a 50% chance of losing 100.
❼ Describe some 50/50 bets this person will accept.
❼ Would you accept some of the bets that they would turn down or reject some of the bets they would accept?
I recommend using a spreadsheet package like Excel to do these calculations. It will make it easier for you to adjust the terms of the bets to get ones that will be accepted or rejected.
For example, if you igure out a bet they will accept, you can then use the spreadsheet to adjust the bet to make it worse and, at some point, you wil come up with a bet they they will reject. I will accept screencaps of well-described spreadsheet output as answers.
Note that this problem does not relate to Matt Rabin’s method for calculating which bets people would reject and so you are not being asked to use the spreadsheet I made available to illustrate his point.
Question 3: Volumes with Pari-Mutuel Odds (20% of the marks)
Go back to the odds you used for the event in Question 1. If someone now told you that these odds were the inal odds posted by a pari-mutuel betting operator, what fraction of the money was placed on each of the possible outcomes? Show how you worked out the answer.
Question 4: Implications of Favourite-Longshot Bias (20% of the marks)
Again going back to the odds you used for the event in Question 1. You have found out that the bookmaker that set the odds did not set them so each bet would have the same expected return. Instead, they set the odds so they would earn a higher proit margin on bets with lower probabilities of winning. In other words, there is a favourite-long shot bias.
Answer the following questions, preferably providing a worked-out example in which you state explicitly how the bookmaker is setting odds.
❼ What can we say now about the average payout rate across all available bets?
❼ What can we say now about the estimated probabilities of bet success that you worked out in Question 1?