Originally Posted by Magister Ludi
A race with an infinite number of horses with an equal amount of money bet on each horse is a perfectly competitive race. If all of the money were bet on a single horse, it is a perfectly uncompetitive race. Most races, of course, are somewhere in between these two extremes.

From there we morph into 1st year psychology statistics.

A few tips from "The Master Of The Game" would be appropriate at this point.

I find that very probable. The question is, have your normalized the outcome in this instance?

LG

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The trick isn't finding profitable angles, it's finding ones you will bet through the ups and downs - UB

That's an interesting idea on classifying races. I think this could be extremely useful as its another input to look at to find a profitable angle.

As you can see, the competitiveness index (ci) is a race metric. This is a highly competitive race:

#***o
1***4
2***4
3***4
4***4
ci = .0625

This is a highly uncompetitive race:

#***o
1***1.1
2***21
3***21
4***21
5***21
ci = .1382

Question: does a 7:1 horse (for example) perform differently in a highly competitive race as opposed to a highly uncompetitive race?

1. Calculate the ci for several races.
2. Populate a table with your results. Use the ci for the rows and odds for the columns. The body of the table will be the roi for each combination of ci and odds. I guarantee you that you will be amazed at the results. It should look something like this (several columns omitted):

Return on Investment

****odds range***
****1-2*****8-9
1**********-14.32%
2*-13.70%**-16.89%
3*-14.24%**-19.69%
4*-13.96%**-19.88%
5*-13.39%**-19.57%
6*-13.19%**-25.16%
7*-12.65%**-18.55%
8*-13.39%**-27.85%
9*-10.32%**-37.51%

ci x 100

Thanks for your explanation Magister Ludi. This raises more questions.
Firstly we are adjusting to a 100% market. What odds are we starting with? Our ratings? PP? Open? T Fluc? SP? The key here is to square the normalised odds, hence the more lower odds, along with the sharper they are, load one side of the equation. This is then balanced or mellowed by the number runners.

So what is the effect of a one horse race (Black Caviar) in a field of 15, vs a 2 horse race (say $2.50 and $3) vs a 3 horse race or an even field?

Are we not comparing the value of our selection in comparison to all the other runners?

It is just as well that I can still go outside, pick up the tractor and put it on my shoulders and carry it up to the top paddock.

I look forward to the next instalment. It makes a welcome change from the naysayers and the "I have the holy grail but you have to find yourself" posters that we have had the pleasure (sic) to endure of late.

You can use any public odds that you like to calculate the race's ci.

To reiterate, a maximum entropy/minimum ci race is one where all horses have identical parimutuel probabilities. A minimum entropy/maximum ci race is one which has a uniform distribution of parimutuel probabilities over the interval 0 to 1.

Ceteris paribus, a longer field will yield a lower ci. Conversely, a shorter field will yield a higher ci.

The ci can used to determine the state of the tote board as well as a metric to index the races after the race has been run. It is a metric measuring competitiveness as determined by the bettors. It is also a concentration or dispersion of the odds in a horse race. The ci does not measure the strength of field. It measures the public's perception of the competitiveness of the field.

It is a way to measure more than just the favorite to determine the public's perception of the race's competitiveness.

For lack of a better contribution here; I see that the 'handle' fits, Magister Ludi !

Cheers LG

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The trick isn't finding profitable angles, it's finding ones you will bet through the ups and downs - UB

Thank you for the kind words, milord.

So once the handicapper has finished (please note the handicapping is done before the barrier draw) all horses are equal. However being smarter than the handicapper and with the benefit of the barrier draw, the average punter knows that whilst all horses are equal some horses are more equal than others.

This new found smartness (punters being smarter than handicappers) starts with the PP or punters own (or acquired) odds and goes through to the race's finish. This CI provides a method of measuring the degree of smartness, in each set of odds, vs the handicapper, in each race.

So you can have a CI on the PP, A/odds, open and SP and any other set of odds.

Anyone assessing a race can see that there is one, two or three horses favoured to win a race. This is easily seen in the price or price grouping (1, 2 or 3 horse represent most of the money in a race)

Thus I am assuming here that this CI measures how much a 1 horse race is so that it can be used to compare similar races. I am trying to see where this could be a benefit or is it a distraction.