Impact Values Again

[zerosky]

Apologies if its been answered before before but search didn't turn up an answer.

Would it be correct to alter the value of an IV wrt. to the number of runners in today's race?

The reason I ask is that most published IV's are averaged over a variety of field sizes.
For example the highest eps. figure in one study shows an IV of around 1.69
this is derived from approx 30,000 races with an average field size of 7.6. with a win percentage of 22.4%

Now the sample IV equals the sample win percentage divided by 1/7.6 (average sample runners)
Call number of runners in sample n then sample IV = sample win percentage x n
It follows that Actual IV = Sample win percentage x Actual N

Using info from this post.
Prime Power by Field Size

I get the following graph. The calculated figure comes from the mean sample win percentage of 30%
with average sample field size n of 7.9 (sample IV = 2.37)
It's not an exact match but does seem to indicate that adjusting the sample IV for field size may make sense. (Pearson coefficient 0.91)

[Dave Schwartz]

The field size should already be part of the calculation.

This was the error in the original concept as defined by Davis and Quirin back in the 1970s: it ignored field size.

The formula for IV is:

Winners
________________
Expected Winners

Or IV= W/ExW

In the Quirin approach ExW was defined as percentage of starters and W was defined as percentage of winners.

In the approach I defined about 25 years ago it became:

W=Actual Winners
ExW= the sum of 1/FieldSize in each race.

Thus, in a 5-horse field each horse should have: ExW = 0.20.
In a 10-horse field each horse should have: ExW=0.10.


Using this approach, the IVs are automatically adjusted for field size.

[zerosky]

Thanks for the reply.

What I was getting at is that the quoted IV's are usually given for an overall average field size
and that to use them for today's race one needs to adjust them for the particular field size.

As an example from a HTR newsletter a horse with a sharp recent race at the track has an impact value of 1.59
but that IV is for an average of 8 horse fields the win percentage is 20%

So if today's field is 10 then 10 x 0.2 = IV of 2.0
and for a 6 horse field 6 x 0.2 = IV of 1.2
and quite naturally for an 8 horse field 8 x 0.2 =IV of 1.6

clear as mud I know (I'm beginning to confuse myself )

[Overlay]

Originally Posted by zerosky

Thanks for the reply.

What I was getting at is that the quoted IV's are usually given for an overall average field size
and that to use them for today's race one needs to adjust them for the particular field size.

As an example from a HTR newsletter a horse with a sharp recent race at the track has an impact value of 1.59
but that IV is for an average of 8 horse fields the win percentage is 20%

So if today's field is 10 then 10 x 0.2 = IV of 2.0
and for a 6 horse field 6 x 0.2 = IV of 1.2
and quite naturally for an 8 horse field 8 x 0.2 =IV of 1.6

clear as mud I know (I'm beginning to confuse myself )

I've always viewed the major advantage of impact values as being that they were already self-adjusting to field size. Raw percentages are the values that don't translate from one field size to another.

For example, if a factor has an overall winning percentage of 20% over a large sample of races, that doesn't mean that a horse possessing that factor has the same 20% chance of winning in a ten-horse field as it would in an eight-horse field or a twelve-horse field.

By contrast, if a factor has an impact value of 1.50, that means that the horse could reliably be expected to have a 50% greater-than-random (using Davis and Quirin's definition of impact value) chance of winning (for example, a 15% chance in a ten-horse field (1.5 x 10%), or an 18.75% chance in an eight horse field (1.5 x 12.5%)), regardless of the field size. (Dave Schwartz's impact-value definition/calculation is preferable if you have access to the field size for each of the individual races in a given sample. But if you're working second-hand with Davis/Quirin-style aggregate findings rather than compiling raw data yourself, that information may not always be available.)

[zerosky]

In an extremely small sample I have found that using the raw IV (unadjusted for field size)
tends to squash the the odds line at the extremities when combining multiple IV's.
Whereas adjusting the IV's for field size gives a more realistic looking line.

I was hoping that other folks had larger number of races to look at and whether or not they had faced a similar problem.

thanks for your replies, much appreciated.

[Overlay]

Originally Posted by zerosky

In an extremely small sample I have found that using the raw IV (unadjusted for field size)
tends to squash the the odds line at the extremities when combining multiple IV's.
Whereas adjusting the IV's for field size gives a more realistic looking line.

I was hoping that other folks had larger number of races to look at and whether or not they had faced a similar problem.

thanks for your replies, much appreciated.

In my experience with data I've seen, using raw IV's produces somewhat greater impact-value ranges (slightly higher values on the high end and lower values on the low end) in ranking a field from top to bottom on a given handicapping attribute than using IV's that are adjusted for field size. These differences in the values for individual factors would then be magnified by the process of combining the factors together.

[Dave Schwartz]

Zerosky,

I advocate raising each IV to a power. Thus, the power becomes a weight.

I also recommend using a Fibonacci if you do not know what the weights should be.

Thus, with 3 IVs:


(IV1^1.00)*(IV2^0.62)*(IV3^.38)

[zerosky]

Thanks Dave, I will experiment with that formulae.
To get my line I have been using a formulae derived from Bayes Theorem.
As the IV is a Bayes Factor expressed as probabilities it seems suitable
and allows for the direct multiplication of the Bayes factors (IV) assuming that they are independent.

Its difficult to express it in text so I have attached a pic of it

P = prior probability = 1/N (N= number of runners)
Q = (1-P)
x = number of IV's used
IV = the product of the combined IV's

The sum of the probabilities need to be normalised to a total probability of 1
It seems to produces a fairly good line but I have yet to get a large enough sample with which to test it. (I use 3 IV's)

[cashmachine]

Originally Posted by zerosky

As the IV is a Bayes Factor expressed as probabilities it seems suitable
and allows for the direct multiplication of the Bayes factors (IV) assuming that they are independent.

I am confused: what you are trying to compute by multiplying IVs?

[Robert Goren]

I don't think multiplying impact values works for picking horses. A lot of people have tried to do it and I have not run across anyone that has had success doing it. Certainly nobody is bragging about doing it on this forum. But it does look like it ought to work and they multiply index numbers(which are similar) in certain fields of study. I just wished I knew of someone for whom it work.
The next question is why would you want to multiply IVs when with a good large database you can exactly how often set of criteria when occurring together wins? Then you can use Bayes. This is not the 1970s. Why limit yourself to tools that were the only ones you had back then?

[cashmachine]

Originally Posted by Robert Goren

But it does look like it ought to work and they multiply index numbers(which are similar) in certain fields of study.

How do you define index numbers? What for are they used?

[Dave Schwartz]

Impact Values are the uneducated version of Bayesian analysis.

[Robert Goren]

Originally Posted by cashmachine

How do you define index numbers? What for are they used?

I suppose the common use of index numbers is in making seasonal adjustments to government statistics. As for defining them, most basic stats book devote quite a bit of paper doing just that. I'll trust Google to find you a good definition.

[zerosky]

Originally Posted by cashmachine

I am confused: what you are trying to compute by multiplying IVs?

The posterior probability of a particular horse winning a race given the available evidence.

Posterior odds = Prior odds x Bayes Factor or...
Posterior probability = Prior probability x Impact Value


The initial Prior probability in the absence of any evidence is simply its random probability or 1/number of runners (N)
As each new piece of evidence is considered then successive posterior odds become new prior odds to which the new evidence is added.

[Robert Goren]

Originally Posted by zerosky

The posterior probability of a particular horse winning a race given the available evidence.

Posterior odds = Prior odds x Bayes Factor or...
Posterior probability = Prior probability x Impact Value


The initial Prior probability in the absence of any evidence is simply its random probability or 1/number of runners (N)
As each new piece of evidence is considered then successive posterior odds become new prior odds to which the new evidence is added.

Then the short answer is yes.