The power of race times is in knowing the acceleration and deceleration of horses of every age and carrying every weight, with this knowledge one is able to make comparision between horses, based on each horses past performances.
Once you have the comparision it gives you the basis to being able to assign probabilities to each horse.
A hint to using Time & Weight linear regression isn't in looking at the distance of todays race, but the avg distances that all horses have competed over in Todays race.