[Mitch44]

While all these formulas are impressive I seriously doubt 1 in 100 understand them completely, myself included. Algebra etc. was never my forte. Perhaps lone speed you can give some simplistic examples as it all relates to what we do know and use with RDSS basic numbers etc.

There are things in here that are assumptions such as horses accelerate in the 1st Fr and not on the turn. The Doc identified as many as 9 I believe different running patterns that horses run. Some run high 1st & 3rd Fr while decelerating on the turn. Perhaps they can't negotiate the turn or they need a breather but that's their style. Others run poor 1st Fr and great 2nd & 3rd Fr.
Additionally the Doc said it could be as high as 3 to 1 in routes.

Bill Lister brings up an interesting post so I'll enlighten it. While a basic formula is nice it really is dependent on the match up of the race and the actual running styles of the combatants in the race. This has much to do with class but different horses have different deceleration rates. For one horse the ratio can be 4 to 1 while most are probably 2 to 1 . The difference is how fast does that horse decelerates vs. the others and weather its pushed enough to its maximum. If not forced by the match up it'll conserve energy and its deceleration rate will change with it.

Bill your right that horses have different exchange rates and that rate varies by what it must do today by the match up of the horses in the race. Additionally because of cheap class, infirmaries and their inherent style some consistently stop on a dime regardless of the match up. Most are locked into a style that doesn't change much perhaps from poor early training. The race itself can change a horses style, E. g. a strictly E horses has a poor break and comes from off the pace to win.

Mitch44