# Two-Step Conditional Logit Model In Horse-Racing

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#### jschatt

##### Guest
I'm reading "Comparing the effectiveness of one- and two-step conditional logit models for predicting outcomes in a speculative market" by Johnson and Sung (2007). The paper can downloaded as a .pdf here:

The part that I am having a problem with is the 2-step model. Can someone here explain more clearly the mechanics of this model? In particular, I have these questions:

1. I understand each fundamental and market variable is weighted, but how are these variables scaled? In "raw" form or in z-score form?

2. I'm very confused about the "explosion" process. In a practical sense, how do I select the best horse from the explosion process? It all seems unclear to me.

3. Would someone be able to walk me through the process of calculating a "winner" in a made-up numerical example?

I've been trying to work with this model for weeks, but my own sample is yielding consistently negative returns using this process. Thanks!

#### JesperHP

##### TS Contributor
With respect to the explosion ..... what seems unclear is what the article describes like this right?

This method involves
considering the finishing position of each horse in a given race as a set of
mutually independent choices. Consequently, it is assumed that the horse
which finished second would have won the race if the horse finishing first had
not participated in the race. For example, an explosion from depth one (the
original race) to three can produce two ‘extra races’ by sequentially
eliminating the ‘winner’ from the pared down races (i.e. a race where the
original winner is eliminated and a race where the original winner and second
are eliminated).

#### jschatt2

##### New Member
Sorry, I was original poster and was locked out of my account. I mean I see the words obviously from the text, but how does the explosion process work out mathematically in terms of selecting a horse to bet on? Could I get an example?

#### JesperHP

##### TS Contributor
how does the explosion process work out mathematically in terms of selecting a horse to bet on?
The way I see it it does not. This is not the problem the explosion process is intended to solve. The explosion process the way I read the quoted passage is simply used as a technique - more or less warranted - to get more observations.

Why would you bet on a given horse? With my little knowledge of the gaming industry and conditional logit models my guess is that you predict the probability p of a certain horse A winning and if the market odds are higher than 1/p you should bet on the horse ... just to make a very simple betting strategy.

And also note that the text actually continues with an example:
For example, an explosion from depth one (the
original race) to three can produce two ‘extra races’ by sequentially
eliminating the ‘winner’ from the pared down races (i.e. a race where the
original winner is eliminated and a race where the original winner and second
are eliminated). This is clearly a valuable process as it increases the number of
independent choice sets, which results in more precise parameter estimates.
so perhaps you could explain why you find the example wanting?