Multinomial Logit Models
 

Picking up my black box building after an extended absence and had a couple of questions for those familiar with the topic...

1) Having only used binomial models previously (horse won =1, horse didn't win = 0) I am not sure how to generate other than a zero/one outcome for the dependent variable.

2) Does anyone have any idea where I can pick up a copy of Bolton's multinomial handicapping papers?

Happy Holidays to all!

Ian :)

Adjusted speed ratings for past races make good continuous variables.

Multinomial logit models(MNL) are generalization of binary logit models. Your DVs are still 1/0 variables. They are grouped together by race. For example, in a 5 horse race, your data would be made up of 5 observiations one for each horse. Each observation would have an indicator variable (1/0) if the horse won the race and post performance data associated with that horse. Unless there is a DH, one of the 5 observatations will have 1 and other 4 will be zero.

You would have to have a stat package that estimates MNL models. I use SAS. It is expensive, but I use it for my regular work. There is a very good free open source stat package called R that I know has the ability to estimate these type of models.

I have a copy of the original 1986 Bolton paper and could send you a scanned copy next week. To show you how far we have come in 25 years, the paper only uses 200 races to estimate its models because of the data entry time require to enter past performance data by hand.

For an implementation, take a look at

http://cran.r-project.org/web/packag...tes/mlogit.pdf

The model was first introduced in this article (the guy won a Noble prize for his work). The article contains the theory, and proposes an estimation routine.

http://www.econ.berkeley.edu/reprint...n/zarembka.pdf

You may also want to read up on Benter's work wrt the multinomial logit model.

Thanks very much for the two links. I found Benter's original paper on my hard drive today and am re-reading that one as well.

I know this is a pretty niche topic but I find the theory fascinating. More so because I personally know teams that have employed it successfully.

I very much doubt that last sentence.
Logistic Regression is not suited at all to solving horse race competition within competition type problems, as Benter found after years of struggling with it in a place with just two tracks. Being first in a blind market as the one eyed man, even with a half-assed method, is more convincing as to cause rather than imagining effect is the cause. That local success has evaporated and would not apply in any Western markets in any case.

I am having a hard time with the thought that the only take away from a race chart would be who won and who lost. This seems to be throwing away 99% of the useful information in the chart.

I have always thought that a computer handicapping scheme needs to use every scrap of information available to its human competition and to do it in greater detail and depth than a human would be capable of doing in a reasonable time. So for me a continuous measurement of each horse's performance makes sense.

I think the OP meant the Y variable being binomial in his previous analyses, and now having to be multinomial - not the X variables.

That is how I took his post but it seems to me that the quantitative measures (speed ratings and such) are far most meaningful than the won/loss stat.

If there was a limitless amount of data to analyze you could get at the information by averaging over a large amount of data but in reality the amount of available data is quite limited (and the 200 race sample is hilarious in retrospect).

I can gaurantee that Multinomial Logistic Regression is EXTREMELY suited to calculating win probabilities.

I can also gaurantee that other than the first 2 years, Benter (nor Woods and the rest) never struggled with implementing it.

So that is why you were in Hong Kong recently Dark Target?
Syndicate end of year meetings?

:cool:

Assume you post on PTT too Buchan?

Did you run into Marvin S?
or Paul L?
How about Vicki W?

You know how these things are... I suspect what i was doing there isn't what you are thinking though.

I can tell you I'm not actually "involved" in any HK syndicates however.

I forgot to ask what PTT is.
Punters Think Tank?