fractions, z scores and bris prime power figure

[formula_2002]

Here is some stuff I've been doing.
I derived* the z scores using the 4 points of call and came up with a single ranking.

Then I compared my top ranking with the top ranking for the Bris power figure.
6882 races
top bris fig returned a .87 roi.
My top fig returned a .85 roi.

When the horse ran it's previous race at the same track, distance and surface as todays race.

2128 top bris figs returned .89
2091 of my top figs returned .96

These results are for all odds>=.1

*It's a bit quirky.
4th call -((4th call -3rd call)+(3rd call -2nd call)+(2nd call-1st call))
all calls are adusted for beaten lenths, (lenths x .20 = seconds).
Any other suggestions!

[Tom]

Yeah, use .167 instead of .20 for beaten lengths.

[formula_2002]

Thanks, I give it a try.

Have been getting some interesting results when the play is kept close to the tail of the curve.

results for 3000 + plays
Dec 05 1.24 roi
Jan 06 .57 roi
feb 06 1.00 roi

aug 06 1.37 roi
sep 06 1.15 roi
oct 06 1.02 roi
nov 06 .94 roi

for a total of 1.04 roi.


Additionally, I just ran march 06
.87 roi

[formula_2002]

Yeah, use .167 instead of .20 for beaten lengths.
using .167 vs .20 improved the March roi by 1 percentage point.
So then I tried .15;) , and it lowered the roi by 2+ percentage points.

I'll re-run every thing tomorrow and let you know the results.

[singunner]

In the end, a beaten length as a unit shouldn't make a difference in this equation as to how many seconds you judge it as being. The difference you're noting should just be random variance.

That is, within the equation you defined, such should be the case. Assumedly you have other factors involved which could favor a specific definition of lengths. In such a case, it should become apparent rather quickly what your ideal definition of a length would be.

[michiken]

I also have used this formula as it defines a horses internal fractions:

a. It shows what 'hidden moves' within a race. I like to see an increasing pattern of these figures.

b. Favorites are most often the average pace runners i,e the horses with the highest speed or pace figures. This method allows you to identify the pace attackers who may (at a better price) pass these type or complete a good per or tri.

c. This formula also can show how the horse will distribute its energy.

d. Like anything else, I have seen this formula have its good days and bad.

e. Is there a typo here? Should the highlighted red minus sign below actually be a plus sign?

4th call - ((4th call -3rd call)+(3rd call -2nd call)+(2nd call-1st call))

Here are some older threads I posted pdf's showing something similar to what you are trying to do:

http://www.paceadvantage.com/forum/showthread.php?t=23930

http://www.paceadvantage.com/forum/showthread.php?t=21442

http://www.paceadvantage.com/forum/showthread.php?t=19592

http://www.paceadvantage.com/forum/showthread.php?t=19455

http://www.paceadvantage.com/forum/showthread.php?t=23514

[formula_2002]

In the end, a beaten length as a unit shouldn't make a difference in this equation as to how many seconds you judge it as being. The difference you're noting should just be random variance.

That is, within the equation you defined, such should be the case. Assumedly you have other factors involved which could favor a specific definition of lengths. In such a case, it should become apparent rather quickly what your ideal definition of a length would be.

We must be talking about different thing, because I find it to make a difference (to the raw score).
I have attached an excel file to better explain the results of the formula.
Just right click each cell to see the formula within the cell

[garyoz]

In the end, a beaten length as a unit shouldn't make a difference in this equation as to how many seconds you judge it as being. The difference you're noting should just be random variance.

That is, within the equation you defined, such should be the case. Assumedly you have other factors involved which could favor a specific definition of lengths. In such a case, it should become apparent rather quickly what your ideal definition of a length would be.

Excellent point. You need to have "theory" somehow tied to the physical world as a basis of the modeling. Otherwise, you could be correlating unrelated events and trying to attach meaning. Not sure what the underlying relationships are in your Z score. Is it most closely related to speed figures or what? Bris Prime Power is a compound variable consisting of several factors (personally I don't like Power numbers--don't find them terribly insightful--too highly correlated with past class and speed figures--pointing out the obvious)

As has been stated many times on this board, correlation is not causation. The relationship will usually break down over time if its is correlational. This also gets us into the well worn discussion of backfitting, etc.

[formula_2002]

I also have used this formula as it defines a horses internal fractions:

c. This formula also can show how the horse will distribute its energy.

e. Is there a typo here? Should the highlighted red minus sign below actually be a plus sign?

4th call - ((4th call -3rd call)+(3rd call -2nd call)+(2nd call-1st call))



I have a problem thinking of this formula as energy distribution. Since energy is the ability to do work (in the direction of the force) and work is the force (pounds) x distance (feet), this formula only looks at time.
But power=work/time.
The problem I have in determing power is, how do you determine the force.
One thing I have calculated is, when knowing the force, it is better to run slower with a heavy load.
You will use less power over the same distance than someone runing faster with the same load.

There is no typo. I'm looking for the best statistically proven roi, so I can change the "-" to a "+" and see what it does to the roi.

Thanks for the thread references. They look interesting.

Joe M

[formula_2002]

Yeah, use .167 instead of .20 for beaten lengths.

In about 3500 plays, a .167 returned a .99 roi. The 8 month study returned a stdev of .157
A .20 returned a 1.01 roi. The same 8 month study returned a stdev of .23.

I'm not a Statistician, but I gather the .157 indicates less risk than the .23

We continue..

[michiken]

1. I did not realize that your equation is calculated in time based units. Therefore the minus sign is probably correct.

2. Here is a work energy equation for Force (http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Energy/WorkEnergyEqn.html)

Since a horse's mass (= Weight/Gravitational Constant) should be a constant, the formula 1/2 m portion should cancel and should resolve to:

[FV2 - IV2] where:

FV2 = Final Velocity Squared
IV2 = Initial Velocity Sqared

You could then calculate the force used during each incremental call?

Total Work Force = (4V2 - 3V2) + (3V2 - 2V2) + (2V2 + 1V2)

[formula_2002]

Do you have some results (roi) I can look at using these formulas.

Thanks
Joe M

The following are the results for my formula, using .162 for lenghts to seconds time conversion, when the previous track, surface and distance is the same as todays and the z-scores fall within a defined area of the curve.

rounded odds to roi
1odds .95 roi
2 .86
3 1.08
4 .85
5 1.00
6 .98
7 .95
8 1.33
9 1.26
10 1.16
>10 <=20 .94
>20 odds 1.25 roi

overall performance for 2348 races =1.0 roi and 21% winners.

I'll be comparing these results against another independent section of my data base.

1.0 roi in a 7% rebate world is not too shabby.

[GameTheory]

Tom says .167 (1/6 sec), whereas I've always had the best results at something around .183...

[Tom]

I vary between .16 and .17 depending on the track. I use .24 for harness and am getting really good results wsicne I switched to that.

[formula_2002]

Tom says .167 (1/6 sec), whereas I've always had the best results at something around .183...

Just ran it through the current data base.
While it cut down the number of plays to about half, the roi was 1.05
I'll look at to at it closer tomorrow..

Happy New Year To All.
(next year I'lll be 70!! :jump: )

Ps at .2 the roi was 1.01
at .162 it was .99

[formula_2002]

1. Since a horse's mass (= Weight/Gravitational Constant) should be a constant, the formula 1/2 m portion should cancel and should resolve to:


There appears to be no allowance for other induced loads such as the surface of the track, slope of the track, wind resistance.
Since I can not get a handle on these loads, my first approach is to leave them out and see what results are obtained without them.

[rrbauer]

Without getting into specifics, a model that I worked on using BRIS prime figs where there was at least 8 points separation between #1 and #2 ranked horses produced better results for better quality races as measured by purse value and race type than for lower quality races. This may not have any bearing on the work that you are doing but it was something that I came across casually that seems to have held up over time. I have not done exhaustive testing on it.

[andicap]

Joe,
why not just bet horses 3-1 and up? That improves your ROI a couple of points.

[formula_2002]

Thanks, I give it a try.

Have been getting some interesting results when the play is kept close to the tail of the curve.

results for 3000 + plays
Dec 05 1.24 roi
Jan 06 .57 roi
feb 06 1.00 roi

aug 06 1.37 roi
sep 06 1.15 roi
oct 06 1.02 roi
nov 06 .94 roi

for a total of 1.04 roi.


Additionally, I just ran march 06
.87 roi

Just ran races for 2005
LIFE GOES BACK TO NORMAL.

jan 05 1.22 roi
feb 05 .80
mar 05 1.0
apr 05 .91
may 05 .70
june 05 .81
july 05 .77
aug 05 .82
sept 05 .78
oct 05 .50

2269 races returned an roi of only .84.

How come?

[Tom]

Take out = 0.16?

[formula_2002]

Take out = 0.16?

I have been using .183 length to seconds conversion.

The standard deviation of the 1st samlpe (1.05 roi) was .15. The average was 1.02.
1 deviation could produce roi's of (1.02+.15) = 1.17 or (1.02-.15)=.87

So the answer could be..the standard deviation was the "cause" ;)
Next time someone tells you that they have an overall roi of 1.20, ask him what the standard deviation was!! It could help to determine risk.

[GameTheory]

I have been using .183 length to seconds conversion.

The standard deviation of the 1st samlpe (1.05 roi) was .15. The average was 1.02.
1 deviation could produce roi's of (1.02+.15) = 1.17 or (1.02-.15)=.87

So the answer could be..the standard deviation was the "cause" ;)
Next time someone tells you that they have an overall roi of 1.20, ask him what the standard deviation was!! It could help to determine risk.It is not appropriate to look at SDs for ROI because ROIs do not occur normally distributed because the individual payoffs are not normally distributed either. However, if the average mutuel for all these samples is about the same and it is only the win percentage that is fluctuating, which may or may not be the case, then you can look at the SDs for win percentage (which does tend to be normally distributed around the mean) and calculate ROIs based on those and the average mutuel and you'll get pretty much the same results you are seeing. But if the payoffs are fluctuating also, it is likely the positive results you are seeing in some of the samples is just due to a few longshots.

So calculate the average win percentage and average mutuel for each sample. Also look at short odds vs long.

[formula_2002]

TO ALL
The attached file indicates the results for the SYSTEM PLAYS and the PUBLIC PLAYS for 2005 and 2006.
The only difference between the two is, the system plays use ranking and z score qualifiers, everything else is the same.

As you will see, the public's performance in 2005 and 2006 is quite similar.
The question is how come there is a "big" difference between the sytem plays for 2005 and 2006?

Thanks
Joe M

[formula_2002]

Tightened up the plays a bit to the tail end of the curve and established a new qualifier. Previous race must have had a field of 10 or more.
This cuts the number of plays down by 2/3’s , but now 2005 and 2006 both show good flat bet roi’s(1.10 to 1.2)

Unfortunately the two changes make’s all these races a sample.
Now I have to re-write the programs to accept the All-Ways .alw files.
(the previous files were Bris .drf files)

[singunner]

It sounds very interesting. Your ethic is admirable, but I worry that you might be inadvertently narrowing your predictions down to the point where your formula is becoming fitted to your dataset. Of course, as you say, a larger dataset will certainly help clarify this.

What's your SD for 05 and 06 with your new method? And what about your ROI and SD over the 2-year period?

[formula_2002]

It sounds very interesting. Your ethic is admirable, but I worry that you might be inadvertently narrowing your predictions down to the point where your formula is becoming fitted to your dataset. Of course, as you say, a larger dataset will certainly help clarify this.

What's your SD for 05 and 06 with your new method? And what about your ROI and SD over the 2-year period?
I have not done that analysis just yet.
I have done an incremental odds review.
Most of the plays are in the rounded odds segements of 1,2 and 3. There is profit in each segement.

There were 171 plays in the three segments returning a flat bet profit of 1.28 . There were 76 actual winners and 60 expected winners for an a/e roi of 1.27.
These are very good numbers even with the slight back fitting .

[singunner]

It certainly seems like you're on to something, but that is a fairly low number of plays. I'd be interested to see your final results, but if those numbers hold, I tend to think you might keep them under your hat. ;)

[PriceAnProbability]

Tightened up the plays a bit to the tail end of the curve and established a new qualifier. Previous race must have had a field of 10 or more.
This cuts the number of plays down by 2/3’s , but now 2005 and 2006 both show good flat bet roi’s(1.10 to 1.2)

Unfortunately the two changes make’s all these races a sample.
Now I have to re-write the programs to accept the All-Ways .alw files.
(the previous files were Bris .drf files)

You're backfitting.

What's the rationale behind only considering this factor? If you can't find one, don't trust the results so quick.

[formula_2002]

You're backfitting.

What's the rationale behind only considering this factor? If you can't find one, don't trust the results so quick.

I know. That's what I said. Changing one qualifier compromises the entire data base.

It was a hard lesson learned but not forgotten ;)