Converting to pounds , surely the only possible reason you would convert anything to do with racing to pounds is to compare to the weight being carried, apart from that converting to pounds must only cause potential inaccuracies.
so horse runs 5 furlongs in 58.00 , par times is 57.60, where is the official conversion to pounds, how many pounds has this horse run slower than par, then does the going or weight carried or pace of race or wind or horse body weight oranything else effect this conversion to pounds. Even if everything is neutral , how many pounds to 2 decimal places has this horse run slower than par. Is there a known mathematical formula to convert race times to pounds.
Yeah
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Outlander this is the sole reason that handicap ratings are in pounds in the first place and goes way back to originators like Dick Whitford a founding member of Timeform. They knew that carried weight had an effect so then attempted to relate beaten margins to the same unit hence - lengths to pounds.
Regarding a universal formula i don't think so but you have to attempt to account for it somehow by making assumptions and then sticking to it. Those assumptions should at least be based on some science.
In the end your results will tell you if your on the right track or not.
So within a running flat population the heaviest horses as a cohort are probably mature sprinters - you could look to HK, Japan & South Africa data for a value - estimate around 1200 lbs (last time i looked at HK think the average weight of a thoroughbred was around 1150 lbs ...don't quote me on that) or you could look to several academic studies that have been done.
Next take the most "common" jockey/handicap top weight impost - in the UK this would be around 10 stone or 140 lbs.
Then you have your running "scale" which is now universal - most of the countries that are part of the Global Handicapping committee have all adopted Whitford's 0-140 lbs scale.
Add in a roughly 15-20 lb average improvement factor over the course of a season for 2 and 3yos which will be a large % of your population your rating in the UK.
All these inputs would be additive so (1200+140+140+20) =1500 lbs which would you then calibrate to your minimum distance.
Hey, that's what John Whitley come up with when he was timefigure manager at Timeform
QED
Calibrating to a minimum of 5f - again in the UK an average time of around 60 seconds given that only around 30% of races are on truly fast ground at least sounds more "right" than wrong.
So then your calibrating it to a racetime (which is how it should be done a la the lengths "thing") you can then say
"im using 1500 lbs per every 60 seconds of racetime"
which also makes the scale variable as racetimes increase as distance gets longer
(1.00sec/60.00sec)*1500 gives a Pounds Per Second value of 25lbs per second
which means (assuming 6 lengths per second) 25/6 = 4.17 lbs per length
So now you have a framework where actual racetime is used to derive the poundage used in both handicap and time figures
A race that goes in 55.60 (Epsom at 5f) will have a value of (1.00/55.60)*1500 = 26.98 lbs per second or 4.50 lbs per length
while
a race that goes in 125.40 (10f at Newmarket) will have a value of (1.00/125.40)*1500=11.96 lbs per second or 1.99lbs per length
As said your results will tell you if your on the right track
Find the baselines of say win % or % of rivals beaten or how much money it loses on Betfair by each rank of rating
Then change that 1500 lbs to a lesser value and test again - does it improve or get worse than the 1500lb baselines ???
Change it to a higher value and test again - does it improve on the 1500lb baselines ???