Over-round

[mwilding1981]

Hi, I am trying to find a way of scaling down an over-round to 100% using non-linear equations to create a more realistic idea of what the win odds should be. Any help with how to do this would be much appreciated.

[chickenhead]

you have a line that adds to greater than 100%, and you want to scale it to 100%?

just do this: 100*horse percent/total percent

i.e horse at 25% on a 115% line = 100*25/115 = 21.7%

is that what you mean?

[mwilding1981]

hey chickenhead, thats what I am currnetly doing, however I want to make it non-linear. So I want to take into account the fact that an odds-on favourite should not be scaled the same way as a 50/1 shot. Surely without this I am getting a bias result so I am therefore trying to find a way to create the 100% book that fairly represents the hroses chances of winning which I believe will have to be done with an individual equation for each horse.

Any thoughts on this?

[Dave Schwartz]

If I am understanding you correctly, you are saying that you want to exaggerate the scores so that the lower horses come out better.

If that is the case, try raising all of the scores to a power above 1.00.

In our software we call this a "probability power" and it is used to do precisely that.

We also use it on individual factors. The most important factor gets a power of 1.00 and the next most important factor gets a lower power. In this way each factor we add has less power than the one before.

[mwilding1981]

Hi david, thanks for your reply. I believe that is exactly what I want to do. Basically I want to create a 100% book from the odds I am given so that I can get a more accurate representation of the hroses winning probability. However I want to as you say exaggerate in order that they don't give a biased result. Is that what you thought I meant?

So I would change the power that I give each horse based on the odds? So could I for example start with a horse with odds of 1.01 (decimal as on Betfair) and give that a power of 1 and then say for a horse with 1.02 give it a power of .99 etc... almost on a per tick basis. I then raise all the probabilities by there relevant power and create my 100% book as above from these new probabilities?

Did I understand you correctly? The above should then give me the most accurate representation psosible of the horses winning probability based on the given win odds.

[chickenhead]

its not clear to me what you're trying to do. If you are using given odds (only) as your basis, all you can hope to get out of it are the implied win percentages. I don't think there is any other info to be gleaned.

It sounds to me like you think there is a long to short bias you want to correct for. I'm not sure you'll find much of one, but I guess in essence you're asking for the long to short bias correction factor. Based on what I've read around here I don't think it's significant. Maybe someone else can chime in with the actual data.

[mwilding1981]

Maybe that is what I am after, although I thought that I wanted that as well. Let me try and clarify exactly what it is I am doing. As you say I am using the win odds only to get the implied probability of the horse winning. However I then want to make this more accurate by scaling the book to 100%. But if I just use the same factors to scale each horse then surely the results won't be quite right due to each hore compensating a different amount to the over-round? therefore I need to scale each one to a seperate figure based on there odds. Is that right or am I just going nuts!

[GameTheory]

Adjust each horse in parallel by some standard deviation unit amount d (positive or negative depending on whether your current probabilities sum to lower or higher than 1.0) on the inverse normal scale so that when converted back to probabilities they will sum to 1.0. In other words, use the Probit model.

Just don't ask me to explain how to do it, cause I don't think I can...

[mwilding1981]

haha and you know that was exactly what I was going to do!

[GameTheory]

Maybe that is what I am after, although I thought that I wanted that as well. Let me try and clarify exactly what it is I am doing. As you say I am using the win odds only to get the implied probability of the horse winning. However I then want to make this more accurate by scaling the book to 100%. But if I just use the same factors to scale each horse then surely the results won't be quite right due to each hore compensating a different amount to the over-round? therefore I need to scale each one to a seperate figure based on there odds. Is that right or am I just going nuts!
If all you want to do is convert tote odds to probabilities that sum to 100%, just rescale them uniformly and that's fine because the only reason they don't is because of the takeout. Add a little something for breakage and it will slightly more accurate:

convert each horse to a probability
p = 1.0 / (odds+1.05) <--- 0.05 for breakage

and then divide each by the total sum and you will be very very close to what you'd get if you had access to the actual dollar amounts expressed as a percentage. There is no way to get it perfect because of the breakage, but it's close enough.

If you've generated your own oddsline, and you want to renormalize after a scratch (for instance), the standard deviation inverse normal thing may be better. The one that I can't explain. :confused:

[mwilding1981]

Well I will look into the inverse thing. I have a book of say 110% on Betfair which doesn't actually have a take-out. I am trying to create extremely accurate probabilities from these win odds, which will surely mean I need to scale as yourself and dave have mentioned.

[GameTheory]

When making my own oddslines, I have found that to get the best accuracy I have to jump through some mathematical hoops when the first estimate adds up to less than 1.0. However, when it is over 1.0, just dividing by the sum seems to do the trick. Note than when you do divide by the sum, you are breaking up that extra 10% (or whatever) proportionally according to the size already allocated to each horse. It sounds as if maybe you don't realize that?

[mwilding1981]

gametheory you are right I completely overlooked that simple fact. May I then ask David exactly what he meant by his 'Probability Power' please?

[GameTheory]

gametheory you are right I completely overlooked that simple fact. May I then ask David exactly what he meant by his 'Probability Power' please?If you, for example, square all the probabilities and then renormalize, it has the effect of exaggerating the estimates at the higher end (above the mean) and lowering the estimates at the lower end (below the mean). So the rich get richer, proportionally, at the expense of the already poor. Raising to a power below 1.0 will have the opposite effect.

[mwilding1981]

Okay and what would be the use of it?

[GameTheory]

Okay and what would be the use of it?We didn't understand what you were asking at the beginning. Dave thought you wanted to exagerate some factors over others based on their odds. Raising to a power will do that. In your case, it is probably not useful -- you just want to renormalize and keep the proportions the same.

[mwilding1981]

Right I understand, that is actually very useful for something else I am working on.

[Dave Schwartz]

May I then ask David exactly what he meant by his 'Probability Power' please?

Like a couple of others in this trhead, I fail to see the value of using the ote odds to do this but...


First, you need to normalize the odds. The absolute easiest way to do this is to simply sum the "booking percentages." That is, 1 / (odds +1)

If you have a horse which is 3.00:1 then the booking percentage = 1/(3+1) or 1/4 or 0.25.

If the horse was 5/2 (i.e. 2.50:1) then the booking percentage is 1/(2.5+1) or 1/3.5 or 0.29.


So, imagine you have this field:

7/1 = 13
5/1 = 17
18/1= 5
8/1 = 11
29/1 = 3
35/1 = 3
22/1 = 4
1/2 = 67

Sums to 123

Normalized to 100% gives us:
7/1 = 10.5%
5/1 = 13.8%
18/1= 4.1%
8/1 = 8.9%
29/1 = 2.4%
35/1 = 2.4%
22/1 = 3.3%
1/2 = 54.5%

You can, of course, get a little more accurate with more decimal places.


So, imagine if one views these as "scores" earned by some factor analysis. If we wished to exagerate these numbers by raising them to a power of 2 (i.e. ^2) then we'd get:

7/1 = 13 =169
5/1 = 17 =289
18/1= 5 = 25
8/1 = 11 =121
29/1 = 3 = 9
35/1 = 3 = 9
22/1 = 4 = 16
1/2 = 67 =4489

sums to 5127

Normalized is:
7/1 = 13 =169 = 3.3%
5/1 = 17 =289 = 5.6%
18/1= 5 = 25 = 0.5%
8/1 = 11 =121 = 2.4%
29/1 = 3 = 9 = 0.2%
35/1 = 3 = 9 = 0.2%
22/1 = 4 = 16 = 0.3%
1/2 = 67 =4489 =87.6%

See how all the probabilities are exagerated?


Dave

[robert99]

Your original question does not explain what evidence had made you think that you can get more accurate by mathematical contrivances rather than adding some more handicapping information that would have to be missing in the given Tote odds.

If you want to favour the favourites in normalising, then in Dave's example you have 23% over-round which can be shared equally between 8 horses, so just take 3% off the basic Tote percentages. So 7/1 becomes 10% and 1/2 becomes 64%.

[Kelso]

I want to as you say exaggerate in order that they don't give a biased result.


I am not at all a stat guy, but isn't an exageration ... to whatever subjective extent one chooses ... itself a bias?





II need to scale each one to a seperate figure based on there odds


Aren't odds, by design, a measure of bias? (This seems, to me, to be an effort to change an apple into an orange.)

[mwilding1981]

Thanks for all the help guys and the detailed example dave.