Acceleration Index (AI) - Experimental

[jfdinneen]

As already indicated in Secretariat's thread - Quantifying Class - I calculate an Acceleration Index (AI) as an operational definition of class. This index is still experimental (Less than three months live usage) but appears to contribute additional explanatory power to pace and speed ratings for the variation in finishing positions. Obviously, the more measuring points available the more accurate the picture one can draw but the standard first call, second call, and final time values available through sectional timing provide a good starting point. As you know, acceleration is the rate of change of velocity with respect to time so I calculate as follows:


Calls
FC (4f) SC (6f) FT (8.5f)
49.20 114.70 146.10
Fractions
F1 (4f) F2 (2f) F3 (2.5f)
49.20 25.50 31.40
Velocity
D1/F1 D2/F2 D3/F3
53.66 51.76 52.55
Acceleration
V1/F1 V2/F2 V3/F3
60.91 49.26 50.25



Finally, I create a weighted AI based on the values derived from the last three past performances.
In sum:

Eliminate non-contenders;
Rate contenders (3-5) on relevant variables (including AI);
Rank contenders;
Use AI as tie breaker.

Given that I focus exclusively on routes, I would like to receive feedback from anyone who is able to use the approach successfully with sprints or with longshots!

Best wishes,


John

[jfdinneen]

Just a brief update to point out that the Acceleration header should read: (V1-V0)/F1, (V2-V1)/F2, and (V3-V2)/F3 respectively.

Quote:
</B>
Calls
FC (4f) SC (6f) FT (8.5f)
49.20 114.70 146.10
Fractions
F1 (4f) F2 (2f) F3 (2.5f)
49.20 25.50 31.40
Velocity
D1/F1 D2/F2 D3/F3
53.66 51.76 52.55
Acceleration
(V1-V0)/F1 (V2-V1)/F2 (V3-V2)/F3
60.91 49.26 50.25


Best wishes,


John

[Dave Schwartz]

Nifty idea, considering the change in velocity spread over a distance.

Very original.

[chickenhead]

what am I missing here? (V3-V2)/F3 = (52.55-51.76)/31.4=.025....or an acceleration of .025ft/s per sec., no? Where does 50.25 come from?

[Dave Schwartz]

Actually, I think dividing it by distance instead of time might be more meaningful.

I'd be interested in GameTheory's opinion. (You reading this stuff?)


Dave

[jfdinneen]

Chickenhead,


I always scale calculations to avoid negative values - (x * 10) + 50.


Best wishes,


John

[chickenhead]

I've always thought looking at say the sum of the force required, broken out over the fractions, might be useful for form cycles and predicting bounces...

F=ma (everything in meters and kg's)

WAG at M=454kg (make it whatever you think reasonable)

so

F1

F=m(.3325)=151N

F2

F=m(-.023)=-10.3N

F3

F=m(.007)=3.48N

Sum=144.3N

like I said, don't think it would useful for comparing horses per se, but for form cycles it could be interesting.

[GameTheory]

Actually, I think dividing it by distance instead of time might be more meaningful.

I'd be interested in GameTheory's opinion. (You reading this stuff?)
Well, dividing it by time is the correct formula for acceleration (change in "velocity per second" per second). I don't think there is anything real earth-shattering here in terms of originality -- just a standard formula from physics and others have certainly applied it to horses before. We've discussed acceleration here before I think.

What good is it? I have no particular comment about that -- haven't researched it enough.

[TRM]

jfdinneen,

I'm not sure about quantifying class as you suggested, but you may want to look at the hoss velocity figures and look for a gain in numbers or an increase in velocity figures from one fraction to the next. For example, there was a thread discussing the Sun Mil Classic at GP last Sunday. The longshot Musique Toujours won big, but what was the tip-off?

Using the 2nd race back my figs were:

1FC 2FC 3FC
54.68 54.21 55.51

These are adjusted for distance, track variant, and track if necessary. I only look at the 1st, or 2nd back.
Notice the gain from the 2FC->3FC. Sometime this will be the only clue to some of those juicy longshot winners. I look at this as an angle to use, similiar to 1st, 2nd or 3rd start after a layoff. IMO, this is a tip-off of a hoss moving forward in his conditioning and is ready for a good effort next out.

[Tom]

TRM...a particulary good way to find turf winners using velocity is to look for increasing velocity numbers at all three calls. I believe it was GR1 who turned me on to that idea, and it has paid off many times.

[TRM]

Tom,

I have noticed this in the turf races as well.The one I remeber well was the 03' BC where Johar had this huge 3FC move. I almost crapped my pants, but luckily it was a DH. Whew!!

[46zilzal]

to say that nags SLOW down over a piece of ground...Old KGEN graphs show the same thing in half furlong increments....BOTH good ways to compare form particulary as it lessens with lower total energy

[delayjf]

D1/F1 D2/F2 D3/F3
53.66 51.76 52.55
accelleration
(V1-V0)/F1 (V2-V1)/F2 (V3-V2)/F3
60.91 49.26 50.25

I'm no math wiz, but isn't the 3rd fraction acceleration already expressed in the difference in the 2nd and 3rd fraction velocities? (V2=51.76 compared to V3=52.55). To my simplistic way of thinking, that shows a net acceleration of .79 ft per sec in the 3rd call. What am I missing here? :confused:

[jfdinneen]

delayjf,


You are in the right ballpark: 0.78 fps represents the change in speed between the two fractions but acceleration / deceleration also reflects the time interval during which that change in speed takes place and is measured in fps/s (see below).


In Physics, one form of the acceleration equation is:

http://en.wikipedia.org/math/df406be590e89da4fcf9e85662aec1e0.png where

http://en.wikipedia.org/math/8f305c034a04e0c3577654db792c8369.png is the average acceleration (m/s²)

http://en.wikipedia.org/math/25cdaba0e466192c4086c413c442def1.png is the initial velocity (m/s)

http://en.wikipedia.org/math/0aa3ec374bdc0d6a17aecbb6bcda6a89.png is the final velocity (m/s)

http://en.wikipedia.org/math/a124ff74a7d766a6ebbac9f4e7fd0798.png is the time interval (s)



I hope the equation helps clarify the difference.


Best wishes,


John

[46zilzal]

I always promote the idea that you MUST substantiate whatever finding you get with a SECOND line otherwise sample error rears it's ugly head! Many times you find this great line......BUT it is the ONLY ONE!

[46zilzal]

changes in rate of speed over time (I call it deceleration, but we are talking about the same thing) is MUCH less a factor short (5 to 6.5 furlongs) but a major factor long and in the blade runners (grass sodballs)...unkless you are at BELMONT

[delayjf]

John,

I can't believe it (that I understand what your saying) but it does make sence. Anymore examples ??

[Tom]

Perhpas the best contender program Sartin ever wrote. Put in as many lines as you want to and visually see the ones that don't represent the horse. I never hesitated to go back to an older line if the "shape" on the graph matched what I suspected it should run today. If only KGen were available with downloads today......*sigh*

[jfdinneen]

Delayjf,




On further reflection, I think converting the acceleration numbers to standard score format gives a final set of numbers that is more Quirin-Like and intuitive for handicapping purposes:


Quote:
Example 1: 'E' Running Style
Calls
FC (4f) SC (6f) FT (8.5f)
46.30 110.50 147.00
Fractions
F1 (4f) F2 (2f) F3 (2.5f)
46.30 24.20 36.50
Velocity
D1/F1 D2/F2 D3/F3
57.02 54.55 45.21
Acceleration
((V1/F1)*10)+100) ((V2/F2)*10)+100) ((V3/F3)*10)+100)
112-99-97

Example 2: 'P' Running Style
Calls
FC (4f) SC (6f) FT (8.5f)
54.50 117.00 146.40
Fractions
F1 (4f) F2 (2f) F3 (2.5f)
54.50 22.50 29.40
Velocity
D1/F1 D2/F2 D3/F3
48.44 58.67 56.12
Acceleration
((V1/F1)*10)+100) ((V2/F2)*10)+100) ((V3/F3)*10)+100)
109-105-99

Example 3: 'S' Running Style
Calls
FC (4f) SC (6f) FT (8.5f)
50.50 116.80 146.80
Fractions
F1 (4f) F2 (2f) F3 (2.5f)
50.50 26.30 30.00
Velocity
D1/F1 D2/F2 D3/F3
52.28 50.19 55.00
Acceleration
((V1/F1)*10)+100) ((V2/F2)*10)+100) ((V3/F3)*10)+100)
110-99-102



Best Wishes,


John

[jfdinneen]

Note the baseline for comparison is 110-100-100.

So the the previous AIs for the EPS R/S examples should be color-coded as follows:

'E': 112-99-97;
'P': 109-105-99;
'S': 110-99-102

Best wishes,




John

[jfdinneen]

If you would like to reduce the triples to a single number then I advise calculating the geometric mean (average of rates of change) and multiply by 10 to accentuate the differences between the triples.

The AIs for the EPS R/S examples would then be reduced to the following indexes:

'E': 112-99-97 (1025);
'P': 109-105-99 (1043);
'S': 110-99-102 (1036).
Finally, using PAR numbers for the race, you could compare the acceleration profiles of the contenders past performances against the PAR baseline acceleration profile.

Best wishes,


John

[delayjf]

Finally, using PAR numbers for the race, you could compare the acceleration profiles of the contenders past performances against the PAR baseline acceleration profile.

How do you produce your par numbers?

[jfdinneen]

delayjf,


In the previous submissions, I was simply generating hypothetical numbers for the purpose of illustrating the differences between running styles.

In normal day-to-day usage, I use the standard published par times as follows to create an acceleration profile against which to compare contenders running lines.


Quote:
Example: 'SA 9f Dirt CLM-10K PAR'

Calls
FC (4f) SC (6f) FT (8.5f)
47.4 111.9 151.0
Fractions
F1 (4f) F2 (2f) F3 (2.5f)
47.4 24.5 39.1
Velocity
D1/F1 D2/F2 D3/F3
55.70 53.88 50.64
Acceleration
((V1/F1)*10)+100) (((V2-V1)/F2)*10)+100) (((V3-V2)/F3)*10)+100)
112-99-99
AI
(Geomean*10)
1032


Best wishes,


John

[jfdinneen]

Following further experimentation with races in both the US and Hong Kong, I have decided to remove the V1 calculations from the Acceleration Index (AI) - see example below. This updated version adds additional predictive value to speed ratings in both jurisdictions. The baseline for comparison is 100.


Example 1
Calls
FC (4f) SC (6f) FT (8.5f)
46.30 110.50 147.00
Fractions
F2 (2f) F3 (2.5f)
46.30 24.20 36.50
Velocity
D2/F2 D3/F3
54.55 45.21
Acceleration
(((V2-V1)/F2)*10)+100) (((V3-V2)/F3)*10)+100)
99-97 (Quirin-Style)
AI
98


As indicated previously, speed ratings are the primary predictive factor (first derivative of distance over time) with acceleration ratings as a secondary factor (second derivative) and stepwise regression calculations confirm this expectation.

Note I am using AI ratings exclusively for routes (particularly turf) and cannot speak for their value in sprints.


Best Wishes,



John