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I'm trying to develop a model to forecast the behavior of the public... specifically, in horse racing.

Most models in horse racing use whether or not the horse won as the dependent variable and then use a variety of predictive variables within the independent set.

The public does the same thing as a whole, however, they tend to over bet and/or under bet certain variables. What are some techniques for capturing this behavior in a logit model?

The core problem I'm having... If I were to use a variable the public tends to over bet, the model would automatically discount it slightly and thus nullify any potential advantage a fundamental model would have over it.

Make sense? Any thoughts?

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  • $\begingroup$ Note that "multinomial" LR refers to models that predict the probability an observation is in 1 of >2 categories, NOT using multiple IVs to predict 2 categories (winning vs losing). Likewise mlogit is an R package for fitting such models. $\endgroup$ – gung - Reinstate Monica Oct 9 '14 at 19:21
  • $\begingroup$ Right... I'm not a "stats" guy so I'm probably messing up the vocabulary. In STATA, the tool I use is "conditional logistic regression" ... those who do the same thing in this space have referred to it as multinomial, multiple etc. Essentially, a race is a group, the dependent is 1 or 0 for win or loss etc. $\endgroup$ – TravisVOX Oct 9 '14 at 19:41
  • $\begingroup$ My comment wasn't intended as criticism; only as information. The terminology is not as intuitive (or consistently used) as one might prefer. $\endgroup$ – gung - Reinstate Monica Oct 9 '14 at 19:46
  • $\begingroup$ I'm totally unfamiliar with betting on horse races. In a pari-mutuel, do the bettors know how much has already been wagered on each horse? $\endgroup$ – JenSCDC Oct 9 '14 at 20:06
  • $\begingroup$ Yes, throughout the wagering, the $ bet on each horse is known. I'm trying to forecast this value in advance of the race. $\endgroup$ – TravisVOX Oct 9 '14 at 20:13
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You should look into the Brunswik lens model.

To better understand how people are betting, use what they bet to win as your response variable, not what actually won. Then the parameters estimate the log odds they are intuitively using.

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The posted odds should reflect the "market"'s consensus because the bookies will set them in order minimize their exposure to the outcome of the race. So if you use the posted odds (or the associated probabilities, or the order of finish they predict) as your dependent variable, you should be able to find out what influences the public's behavior.

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  • $\begingroup$ Thanks, Andy. In a multinomial logit model, however, the ultimate outcome can be a set of probabilities that sums to one which gives me a useful set of data. If I were to regress say the ultimate odds, then the final set would not sum to one. I'm using pari-mutuel odds in this case... no bookies, so the odds are purely a % of the total money bet in the race. Ultimately, the multinomial logit approach is what I'm trying to do, but capturing where the public over/under bets is the challenge. $\endgroup$ – TravisVOX Oct 9 '14 at 19:25
  • $\begingroup$ And I thought I had a good answer:( But if you're using odds as the dependent variable, you wouldn't need to use logistic regression, since the odds are a continuous variable. $\endgroup$ – JenSCDC Oct 9 '14 at 20:03

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