Flatfish

The Wigan Athletic v Manchester City game was profitable, although a draw or Wigan Athletic win would have been preferable. My spreadsheet was of the opinion that the goal expectancy here was too high, and that Manchester City were too short. The Unders came in comfortably enough, but a straight lay of Manchester City, 1.42 at kick-off, didn't. Laying at 1.42, or the 1.45 I was actually in at, is the same as backing at 3.38 or 3.22 as you all know, but the Asian Handicap markets are there as an alternative to a straight lay. I was already on Wigan +1.5 at 1.88, but @shevyten pushed me into adding the +1/+1.5 option, which was matched at 2.13 which worked out well. Twitter is profitable already! I must admit that it's not only Twitter that I have been slow to embrace, but also the Asian Handicaps. My excuse is that they weren't around in my youth, and it's hard to teach an old dog new tricks, but I am warming to using them. The markets on Betfair and BETDAQ do seem a bit gappy though.

There was an excellent 'Correct Score' market write up by Soccer Dude Eddie on the Football Trader's Path blog the other day, the best I have seen - article I mean, not blog! For me, as a dedicated follower of Poisson, albeit modified, the following paragraph was of special interest.

You could also use Poisson to calculate the percentage chances of each scoreline being achieved. If you do utilise pure Poisson, you should ensure that you increase the probability of 0-0 and 1-1, and reduce the probability of a 1-0 home win and a 0-1 away win. This is because the Poisson model is known to under forecast 0-0 and 1-1 draws and over forecast 1-0 and 0-1. There are also other well-known algorithms that you could use to calculate the goal expectation and, again, these would all help you to make a more reasoned selection for you to lay 0-0.

Soccer Dude mentions the adjustment that needs to be made for the binary scores, (i.e. not using the usual zero-inflated Poisson model) and this helps with the problem of Poisson underestimating draws as so many draws are 0-0 or 1-1. Getting the goal expectation and this 'adjustment' right are key, and while it's unfortunate that you can't simply use the POISSON function in Excel with the goal expectancies for each team and generate your odds, this difficulty is what can give you an edge. The maths is, to my simple mind, quite complex - here's one example:

Bivariate Poisson models can be expanded to allow for covariates, extending naturally the univariate Poisson regression setting. Due to the complicated nature of the probability function of the bivariate Poisson distribution, applications are limited. The aim of this paper is to introduce and construct efficient Expectation-Maximization (EM) algorithms for such models including easy-to-use R functions for their implementation. We further extend our methodology to construct inflated versions of the bivariate Poisson model. We propose a model that allows inflation in the diagonal elements of the probability table. Such models are quite useful when, for some reasons, we expect diagonal combinations with higher probabilities than the ones fitted under a bivariate Poisson model. For example, in pre and post treatment studies, the treatment may not have an effect on some specific patients for unknown reasons. Another example arises in sports where, for specific cases, it has been found that the number of draws in a game is larger than those predicted by a simple bivariate Poisson model (Karlis and Ntzoufras 2003)

but I am expecting a couple of books in the post any day now that were recommended to me, and if they are written in English, may improve my understanding, and more importantly, my pricing model. I studied some of this in my Pure Mathematics With Statistics 'A' Level, but that was oh so long ago, and I don't recall it being this complicated. Perhaps I wasn't paying attention. Again.

Why the Flatfish you may be asking yourselves? Well, 'zero-inflated Poisson' might be fine if you are French, but in English, can't we simply call it Flatfish?

I'll get my coat.