Hello Everyone,

I am completely new to the realm of probability and statistics and would very much appreciate some assistance. My plan is to learn the whole subject, or at least as much as I need by myself. As preparation I intend to work through Calculus for Dummies before working through Grinstead & Snells Introduction to Probability that I found online.

Is this the best intro or would I be better served using another text? I have a copy of Schaum's Introduction to Probability & Statistics but found it assumed a certain amount of knowledge on the part of the reader.

My motivation for learning this is because I have more than a passing interest in investing on the outcome of sporting events. Particularly English soccer and Greyhound Racing. It is my belief that by developing an understanding of the mathematics behind my bets I can organise my operation more effectively. The English bookmakers employ statistitians and so in order to be able to compete with them I need to operate in the same intellectual sphere.

In case I am offending anyone's sensibilities by discussing these areas then I apologise, but as probability has it's roots in the solution of problems concerning games of chance then hopefully I will find a receptive audience.

My aim is to develop my knowledge to the point where I can have a thorough understanding of the probabilities of certain events happening moving on the the distributions of results that I can then expect. Once I have this I can then move on to assessing what the optimum staking level is with regard to maximising returns whilst minimising the risk to bankroll.

Has any work been done in this area already or are there any books/papers that may be of interest. Also, as I will be doing this completely by myself do you think that it will be possible to reach the required level of understanding.

Many thanks, Tony.

Tony,

Welcome to the forum. It requires pretty heavy statistical machinery to calculate the odds of soprting events. In addition you'll need data on past events, which is hard to find. Below is an article on http://www.dailyspeculations.com/.

If you are betting for the win, you run a McFadden conditional logit regression (available in Stata and Limdep) which "explains" the dummy variable, win or lose and yields the "underlying" winning probabilities constrained so that they sum to one per game. (This is why regular logit, probit is wrong). One can also use the old linear probability model if the explanatory variables are differences. Some reading on the subject:

Dugan, M. & Levitt, S.D. 2004. Winning isn't everything: corruption in sumo wrestling. American Economic Review 92: 1594-1605.

Dobra, J.L., Cargill, T.F., & Meyer, R.A. 1990. Efficient markets for wagers: the case of professional basketball wagering. In: Goff & Tollison (ed.) Sportometrics. Texas: College Station.

Zuber, R.A., Gandar, J.M., & Bowers, B.D. 1985. Beating the spread: testing the efficiency of the gambling market for national football league games. Journal of Political Economy 93: 800-806.

Sauer, R.D., Brajer, V., Ferris, S.P., & Marr, M.W. 1988. Hold your bets: another look at the efficiency of the gambling market for national football league games. Journal of Political Economy 96: 206-213.

Schnytzer, A. & Weinberg, G. 2004. Is the NBA betting market efficient? In: Papanikos, G.T. (ed.) The economics and management of mega athletic events: Olympic games, professional sports, and other essays. Athens: ATINER.

But this market is a minefield of specification and other problems. For the simplest form of modelling (where only past prices are used) blown up to show just how messy life can be, see:

Schnytzer, A. & Weinberg, G. 2005. The Australian Rules Football Fixed Odds and Line Betting Markets: Econometric Tests for Efficiency and Simulated Betting Systems. Unpublished Manuscript (currently under review in the Journal of Sports Economics).



I suggest you search for sport betting forums on google. It's a hot topic I'm sure there are many forums. They may have introduction and discussion on statistics that better fit your needs. If you have any questions on mathematical statistics we are more than happy to help.

Good luck :)

Tony,

Thanks for stopping by. There are a few good beginner-level books, and I will list them here, but on your own, you will never achieve parity with people who have been successfully doing this kind of thing for a living.

Not only does it take a strong knowledge of probability and an application of it to the specific betting/gaming activity, but you really need to now how it plays into the business.

As an example, with sports betting in the U.S., especially football with its "point spreads" (i.e., not just picking the winner of the game, but also betting on the margin of victory) - it has nothing to do with what the odds makers think the game outcome will be, and everything to do with equalizing the amount of money bet on both sides - big-time psychology.

But anyway, here are a few good titles to get you going:

The Complete Idiot's Guide to Statistics - Robert Donnelly
The Cartoon Guide to Statistics - Larry Gonick
Probability for Dummies - Deborah Rumsey

All of these are very inexpensive and are highly recommended!

Good luck,
John

Thank you both for your considered reply. My calculus book has arrived and so as a prerequisite I will now be working through that.

Although you point out that this could be difficult to accomplish by myself I've never been one to shirk a challenge and intend to address probaility as soon as I can. Once I begin my probability & statistics studies will it be OK to check with you what certain notation means and for explanations of theory that I don't understand?

The point about the NFL pointspreads still applies in the UK but in a slightly different way as follows:

In a game between Team A & Team B the odds could be home win evens, the draw 9/4 and away win 9/4. The idea again is to try to split the weight of money. In reality the favoured team will receive more action. The psychology of the UK gambler plays into the bookies hands though. Instead of selecting one match to bet on the average punter will pick five and combine them all in an accumulator where the winning from one goes onto the next & so on. The average punter is a long term loser.

If you are interested and have not read it yet there is an outstanding book by JR Miller called How Professional Gamblers beat the Pro Football Pointspread. I'd have to say that this book is the best book on betting that I have ever read and I have never made an NFL bet. It was this book that made me think about the implications of the mathematics behind sports events. He did actually employ the services of Dr Jeffrey Allbritten to verify his mathematics. I did try to contact Jeffrey, but found him particularly unhelpful.

I shall be back in the future for certain. It's too late for me to stop trying to get to the bottom of sports/dogs investing. I've put in way too much time & thought.

Thanks, Tony.

I am doing research on soccer scores modelling, refer to Dixon&Coles(1997) and Karlis&Nuoztras(2003).... any body get interest to discuss?

When it comes to sports investments, the best way is to invest in teams(or player) that are underdogs. This gives you a lot of profit with little stake. Of course finding the right underdogs is very important. You can find more professional help at the Sportbetting Forum (http://www.betting-forum.com/). There are users that post their advices.