Surface Variant

[jotb]

Hello All



I was wondering if anyone is familiar with standard deviation and if so, can standard deviation be used for surface variant. I calculated the variant for several racing surfaces over a period of time (about 2 years). The variant was broken down to 3 points of call for sprints. Here were the following results for average and standard deviation for each track.

STANDARD DEVIATION

1/4 1/2 FT

TRACK 1 29.1 57.1 81.9


TRACK 2 28.0 56.4 82.1


TRACK 3 31.2 51.1 78.6


TRACK 4 27.4 52.7 91.1


AVERAGE

1/4 1/2 FT

TRACK 1 1.10 0.61 0.48



TRACK 2 - 0.85 -2.39 -2.47


TRACK 3 0.94 2.03 - 0.76


TRACK 4 1.70 3.59 4.22


Best regards,
Joe

[lousycapper]

Originally posted by jotb
Hello All



I was wondering if anyone is familiar with standard deviation and if so, can standard deviation be used for surface variant. I calculated the variant for several racing surfaces over a period of time (about 2 years). The variant was broken down to 3 points of call for sprints. Here were the following results for average and standard deviation for each track.

STANDARD DEVIATION

1/4 1/2 FT

TRACK 1 29.1 57.1 81.9


TRACK 2 28.0 56.4 82.1


TRACK 3 31.2 51.1 78.6


TRACK 4 27.4 52.7 91.1


Best regards,
Joe

You might want to look at the formula outlined in the thread "Split Times & Different Distances"

Track 4 would give you ratings of:

1/4 - 32, 1/2 - 51

computed this way:

2f x 66 / 27.4 = 4.8175182

4.8175182 - 4.5 = .3175182

.3175182 rounded up = 32
===========================

4f x 66 / 52.7 = 5.0094876

5.0094876 - 4.5 = .5094876

.5094876 rounded up = 51
===========================
I didn't bother to do the final time. I make the distance to be 7f? If it is then the rating would be 57.

I hope this helps you.

-L.C.

[Tom]

Not sure what those numbers you listed are?
What do you want SD to do for you?

[jotb]

Originally posted by Tom@HTR
Not sure what those numbers you listed are?
What do you want SD to do for you?

Hello Tom:

I'm sorry the way that post came out. I was trying to make a chart out of it but when I submited the post it came out rather sloppy. Anyway, I had calculated the variant for 4 different racetracks in NY over a 2 year period. Without making any adjustments to the raw times, I ran a query for each fractional point of call in sprint races. I used the basic calls such as 1/4,1/2 and final time. Just to give you an idea of the type of data , I was working with, I had previously calculated the variant first call for each racetrack and racing date. The first call variant had a range of -100 to +100 or simpy put, 5 lenghts slow or 5 lengths fast. When I ran the query and used the standard deviation calculation the results were similar for each track. I found this result interesting. Track 1 was -29.1, -57.1, -81.9. Track 2 was -28.0, -56.4, -82.1. Track 3 was -31.2, -51.1, -78.6. Track 4 was -27.4, -52.7, -91.1. On the other hand, using the mean for each fractional part of a sprint race, Track 1 was -1.10, -0.61, -0.48. Track 2 was +0.85, +2.39, +2.47. Track 3 was -0.94, -2.03, +0.76. Track 4 was -1.70, -3.59, -4.22. The (-) stands for slow and (+) stands for fast. When I average the variant for each point of call the results basically even out as you can see. For instance, the final time average for Track 4 was -4.22 but the data range for final time was anywhere from -200 to +200 or slow 10 lengths or fast 10 lengths using the .20 as a length. This average for final time -4.22 is telling me that Track 4 final time is slow less than a 1/4 length. The final time variant in sprints for track 4 basically evens out over a long period of time. Actually it even out at each track for each point of call by the results I retrieved. However the standard deviation shows me a different story which I cannot explain. Hopefully you will be able too. One last thing, my variant for each day was not compared to "class pars" but was compared to "surface distance pars".

Thank you,
Joe

[kenwoodall]

Tom- Maybe NY froze over so FC got use to kard surfaces and was better prepared for supr
er fast Churchill. Actually, they slowed the track down 1 second between Friday and Saturday.
Just like 5/4, Mother's day should be deep slow tracks everywhere.

[MV McKee]

Joe,

Your "average" variant should come out very close to zero (as it did).

I am not certain exactly what it is you are trying to do with the standard deviation formula however.

Standard deviation is generally used to determine the confidence interval for your mean, and to identify "outliers".

Combined with your sample size, you can use StDev to determine with some precision how accurate your average is (Confidence Interval). In other words, an example would be that I can say with 95% certainty that for an infinite number of racing days at track A the average variant is -4.22 +-1.03.

The other (general) use of Standard Deviation is to determine if there are any outliers within your set of observations. If your set of observations (variants) form a normal distribution, then you will generally want to exclude any values that are > |3*StDev| from the mean. The simplest way to do this is to paste all your values into a single column on an Excel spreadsheet, and use the Data Analysis function titled "Descriptive Statistics". This will give you most of the important characteristics that you need to get started with some simple analysis of your data. Look at the following:

1) Kurtosis and Skewness - If these are both >-1 and < 1, Standard Deviation can be used to determine if you have any "outliers" or unusual values that may be pulling your average one way or the other. Actually, you may want to be wary if the Skewness is < -.7 or > .7.

2) Confidence Level - Basically the number you will want to use to determine if your average is of any use to you in actual practice. If you feel that the range is to wide, you will either have to increase your sample size or decrease the StDev. Best to do the former.

[jotb]

Originally posted by MV McKee
Joe,

Your "average" variant should come out very close to zero (as it did).

I am not certain exactly what it is you are trying to do with the standard deviation formula however.

Standard deviation is generally used to determine the confidence interval for your mean, and to identify "outliers".

Combined with your sample size, you can use StDev to determine with some precision how accurate your average is (Confidence Interval). In other words, an example would be that I can say with 95% certainty that for an infinite number of racing days at track A the average variant is -4.22 +-1.03.

The other (general) use of Standard Deviation is to determine if there are any outliers within your set of observations. If your set of observations (variants) form a normal distribution, then you will generally want to exclude any values that are > |3*StDev| from the mean. The simplest way to do this is to paste all your values into a single column on an Excel spreadsheet, and use the Data Analysis function titled "Descriptive Statistics". This will give you most of the important characteristics that you need to get started with some simple analysis of your data. Look at the following:

1) Kurtosis and Skewness - If these are both >-1 and < 1, Standard Deviation can be used to determine if you have any "outliers" or unusual values that may be pulling your average one way or the other. Actually, you may want to be wary if the Skewness is < -.7 or > .7.

2) Confidence Level - Basically the number you will want to use to determine if your average is of any use to you in actual practice. If you feel that the range is to wide, you will either have to increase your sample size or decrease the StDev. Best to do the former.


Hello MV MCKEE

At this point, I'm not sure if I want or need the stdev. to work for me. I just found it interesting that each of the 4 tracks were similiar in regard to the numbers. I'm happy to hear that my "average" for each track should be around "0" which it is.

My ulitmate goal is to create "condition pars" for each condition and distance for the racing circuit. Using "raw times" to create "condition pars" had me confronting many obstacles. I thought it might be best to first create "surface pars" calculate the variant compared to the "surface pars" and finally to adjust the raw times. I felt the "condition pars" could now be created with accuracy.

I was wondering why it's important for the "average" to be "zero" over a length of time. Granted the average is close to zero according to my results but the standard deviations produced different results but similiar to each track which I thought was a postitive sign. From the track 1 example why or what does it mean when the numbers come back -29.1, -59.1 and -81.9. By the way, those numbers were for the 1st call, 2nd call, and final time. If track 1 produced an overall average of -1.10, -0.61 and -0.48 are we saying that over the course of time the variant for each call "even out" and if this is the case, then why is the standard deviation minus 29.1, minus 59.1 and minus 81.9. Using the (.20) as a length, why is the standard deviation result informing me that the 1st call is about a length and a half slow, almost 3 lenghts slow for the half and final time is a tad over 4 lengths slow? If you look at all my examples from the stdev result you will see that each track is almost identical. Why did this result occur?

I'm desperately trying to figure out what you meant by the examples you provided me in regard to using the stdev. I'm sorry but I'm having some difficulty understanding stdev. What is 3*stdev? What are outliers? Please write back!

Thank you and best regards,
Joe