Hi
When modelling how the Public wager, one WOULD use the Classification of each race, this is something the Public sees, but in Handicapping you need to use a Statistical description, in the example provided I would classify the race by the average Standard deviation of all runners.

The other important part as you mentioned is the accumulated physical Track bias which is present as we get closer to the finish...in my opinion i would be looking at little closer to the start if i was using going to use performance percentiles