Question About Carroll's Time Per Length Calcs

[PhantomOnTour]

As many of ya'll know, Charles Carroll's 'Handicapping Speed' introduced a Time Per Length concept for making ratings.
In short, he sets the avg length of a horse at 8ft. and determines the amount of time it takes to run that 8ft. (time per length or TPL).

Ex:
A 6f race is run in 22.5-46.0-111.0 (or 71.0 secs)
Our horse was 10 lengths back at the 1/4, the 1/2, and the finish.
6f = 3960ft.
3960ft. / 8ft. = 495 horse lengths in the 6f distance.
Final time (71 secs) / 495 = 0.143 secs
Our horse was beaten 10 lengths, so we determine his actual final time by multiplying his deficit by the TPL (0.143 in this instance).
10 x 0.143 = 1.43...so our horse ran the 6f in 111.0 + 1.43 or 112.43.
He then takes that adj final time and compares it to the world record for 6f and comes up with a rating.

Cool, but what about his actual time for the 1/4 and 1/2? I know Carroll doesn't rate the pace calls (his fig is final time based), but can't we use the same concept to get actual running times for the pace calls?
Well, I'm not sure...follow along.

Using the above race, our horse was 10bl after a 1/4 in 22.5
1/4m = 1320ft
1320ft. / 8ft. = 165 lengths
22.5 / 165 = 0.136 (that's the TPL)
10 x 0.136 = 1.36
22.5 + 1.36 = 23.86 (our horse's actual 2f time).

So...when the race leader hit the 1/2m pole in 22.5 it took our horse 1.36 secs more to get to the same spot.
When our race leader hit the wire in 111.0 it took our horse 1.43 secs more to get to the same spot...allegedly.
Is it true or realistic that our horse only needed 0.07 secs more to cover his deficit at the wire than at the 1/2m pole? They were going much faster at that point. First 1/4 in 22.5 and last 1/4 in 25.0.
If we use his TPL for the last fraction only (i'll spare the calcs here) we get his actual final time at 112.52 instead of 112.43.

Is this a good way to determine a horse's actual running time?
A 6f race in 112.0 has a TPL of 0.145
A 9f race in 151.0 has a TPL of 0.149
If a horse was beaten 10 lengths in each race he would have run a 113.45 and a 152.49...it only takes 0.04 secs more to make up the deficit at 9f than 6f??? Isn't it better to get final time for beaten horses by using the actual winning time plus how long it took the losers to make up their deficit, based on the time for the final fraction?

Help, where is my math and/or logic wrong here?

[maddog42]

As many of ya'll know, Charles Carroll's 'Handicapping Speed' introduced a Time Per Length concept for making ratings.
In short, he sets the avg length of a horse at 8ft. and determines the amount of time it takes to run that 8ft. (time per length or TPL).

Ex:
A 6f race is run in 22.5-46.0-111.0 (or 71.0 secs)
Our horse was 10 lengths back at the 1/4, the 1/2, and the finish.
6f = 3960ft.
3960ft. / 8ft. = 495 horse lengths in the 6f distance.
Final time (71 secs) / 495 = 0.143 secs
Our horse was beaten 10 lengths, so we determine his actual final time by multiplying his deficit by the TPL (0.143 in this instance).
10 x 0.143 = 1.43...so our horse ran the 6f in 111.0 + 1.43 or 112.43.
He then takes that adj final time and compares it to the world record for 6f and comes up with a rating.

Cool, but what about his actual time for the 1/4 and 1/2? I know Carroll doesn't rate the pace calls (his fig is final time based), but can't we use the same concept to get actual running times for the pace calls?
Well, I'm not sure...follow along.

Using the above race, our horse was 10bl after a 1/4 in 22.5
1/4m = 1320ft
1320ft. / 8ft. = 165 lengths
22.5 / 165 = 0.136 (that's the TPL)
10 x 0.136 = 1.36
22.5 + 1.36 = 23.86 (our horse's actual 2f time).

So...when the race leader hit the 1/2m pole in 22.5 it took our horse 1.36 secs more to get to the same spot.
When our race leader hit the wire in 111.0 it took our horse 1.43 secs more to get to the same spot...allegedly.
Is it true or realistic that our horse only needed 0.07 secs more to cover his deficit at the wire than at the 1/2m pole? They were going much faster at that point. First 1/4 in 22.5 and last 1/4 in 25.0.
If we use his TPL for the last fraction only (i'll spare the calcs here) we get his actual final time at 112.52 instead of 112.43.

Is this a good way to determine a horse's actual running time?
A 6f race in 112.0 has a TPL of 0.145
A 9f race in 151.0 has a TPL of 0.149
If a horse was beaten 10 lengths in each race he would have run a 113.45 and a 152.49...it only takes 0.04 secs more to make up the deficit at 9f than 6f??? Isn't it better to get final time for beaten horses by using the actual winning time plus how long it took the losers to make up their deficit, based on the time for the final fraction?

Help, where is my math and/or logic wrong here?

If you are saying why not use the fractional times to compute beaten length times you are correct. This is my main criticism of Carrolls work. He computes an average velocity of the entire race and assumes they are travelling that fast at the end of the race. They are not. His figure does not take into account DECELERATION throughout the race , usually after the first 1/4 mile.
About 99% of horses decelerate after that first 2 furlongs. I usually use the last fraction to compute the lengths per second. I believe Carroll was right about the 8 feet per length and I use his charts to compute that lengths per second.
You can see my thread on Handicapping Magic and another thread for the details.
All that aside I believe Handicapping Speed was a helluva book and it influenced me greatly.
Check out Carrolls Website at Desert Sea. It has some very good articles, probably a books worth.

[speculus]

As many of ya'll know, Charles Carroll's 'Handicapping Speed' introduced a Time Per Length concept for making ratings.
In short, he sets the avg length of a horse at 8ft. and determines the amount of time it takes to run that 8ft. (time per length or TPL).

Ex:
A 6f race is run in 22.5-46.0-111.0 (or 71.0 secs)
Our horse was 10 lengths back at the 1/4, the 1/2, and the finish.
6f = 3960ft.
3960ft. / 8ft. = 495 horse lengths in the 6f distance.
Final time (71 secs) / 495 = 0.143 secs
Our horse was beaten 10 lengths, so we determine his actual final time by multiplying his deficit by the TPL (0.143 in this instance).
10 x 0.143 = 1.43...so our horse ran the 6f in 111.0 + 1.43 or 112.43.
He then takes that adj final time and compares it to the world record for 6f and comes up with a rating.

Cool, but what about his actual time for the 1/4 and 1/2? I know Carroll doesn't rate the pace calls (his fig is final time based), but can't we use the same concept to get actual running times for the pace calls?
Well, I'm not sure...follow along.

Using the above race, our horse was 10bl after a 1/4 in 22.5
1/4m = 1320ft
1320ft. / 8ft. = 165 lengths
22.5 / 165 = 0.136 (that's the TPL)
10 x 0.136 = 1.36
22.5 + 1.36 = 23.86 (our horse's actual 2f time).

So...when the race leader hit the 1/2m pole in 22.5 it took our horse 1.36 secs more to get to the same spot.
When our race leader hit the wire in 111.0 it took our horse 1.43 secs more to get to the same spot...allegedly.
Is it true or realistic that our horse only needed 0.07 secs more to cover his deficit at the wire than at the 1/2m pole? They were going much faster at that point. First 1/4 in 22.5 and last 1/4 in 25.0.
If we use his TPL for the last fraction only (i'll spare the calcs here) we get his actual final time at 112.52 instead of 112.43.

Is this a good way to determine a horse's actual running time?
A 6f race in 112.0 has a TPL of 0.145
A 9f race in 151.0 has a TPL of 0.149
If a horse was beaten 10 lengths in each race he would have run a 113.45 and a 152.49...it only takes 0.04 secs more to make up the deficit at 9f than 6f??? Isn't it better to get final time for beaten horses by using the actual winning time plus how long it took the losers to make up their deficit, based on the time for the final fraction?

Help, where is my math and/or logic wrong here?

Here (http://www.paceadvantage.com/forum/showpost.php?p=204940&postcount=22) is another viewpoint on the measure of a length, and here (http://www.paceadvantage.com/forum/showpost.php?p=204992&postcount=35) is the formula that gives near-accurate time (up to 1/100th of a second) for various distances, if that helps.

[maddog42]

Here (http://www.paceadvantage.com/forum/showpost.php?p=204940&postcount=22) is another viewpoint on the measure of a length, and here (http://www.paceadvantage.com/forum/showpost.php?p=204992&postcount=35) is the formula that gives near-accurate time (up to 1/100th of a second) for various distances, if that helps.

Am I missing something here? This formula seems to assume that there is a constant deceleration for a given Distance. This Is not so. If horses did decelerate at a constant rate (they are not machines) It would make things much easier. If that formula uses a fractional time and then calculates deceleration, it would be better.

[maddog42]

Here (http://www.paceadvantage.com/forum/showpost.php?p=204940&postcount=22) is another viewpoint on the measure of a length, and here (http://www.paceadvantage.com/forum/showpost.php?p=204992&postcount=35) is the formula that gives near-accurate time (up to 1/100th of a second) for various distances, if that helps.

I just went back over the formula and I see there is a place for the fractional time( I think). The small t is the 3rd fraction? This might work. Now I have a problem with using 9ft+ as a length. Carroll claims that the value of a length
in his formula is not 7.5 or 8.5, because they have been tried. I believe his formula though flawed worked as good as it did because of the averaging of the speed across the entire race and the acceleration and deceleration approximated but did not accurately portray the 3rd fraction. The 8 ft /length
works very well for me and I have also hand timed races off of video tape, to verify this With Mixed but close results.
Now Speculus you seem very serious and I respect this. Could there be another reason for our discrepancy. Do the Chart makers in your country do things differently? Sometimes the value of a length can compensate for other inaccuracies, and do it well. I am also skeptical that you could get within .01
of a second. I damn sure couldn't.
I will give your formula a try.

[speculus]

I just went back over the formula and I see there is a place for the fractional time( I think). The small t is the 3rd fraction? This might work. Now I have a problem with using 9ft+ as a length. Carroll claims that the value of a length
in his formula is not 7.5 or 8.5, because they have been tried. I believe his formula though flawed worked as good as it did because of the averaging of the speed across the entire race and the acceleration and deceleration approximated but did not accurately portray the 3rd fraction. The 8 ft /length
works very well for me and I have also hand timed races off of video tape, to verify this With Mixed but close results.
Now Speculus you seem very serious and I respect this. Could there be another reason for our discrepancy. Do the Chart makers in your country do things differently? Sometimes the value of a length can compensate for other inaccuracies, and do it well. I am also skeptical that you could get within .01
of a second. I damn sure couldn't.
I will give your formula a try.

The verdict, in terms of lengths, at the finish is a completely different affair as compared to the verdict at various calls. At the calls, it was (before we got the the new photo finish camera) the race caller's version, prone to error, whereas at the finish, it was a print on a strip of photographic paper, so even the acceleration/deceleration error was nullified as each horse would get on the print precisely at the instant (in time) when it physically crossed the finish line.

Having said that, I would be curious to know your findings after you give my formula a try. Thanks.