mr Garrison,
As I read your original question, I can see that a principle is applied that can give you an idea of performance.
The principle: At half of your take-off roll you should have 2/3
of your lift-off speed (Vr).
The thing is that you need a pre-determined Airspeed Check-point to assess this properly.
Next to that you need to know the point where you can still safely abort the take-off without the danger of an overrun.
Normally that is about half of the TODA but several factors can change that...
Anyhow what we use is, if during a take-off roll we don't get the
2/3 of lift off speed, it is indicating something is wrong,
either not enough engine power, or the softness of the field is a factor and we will abort the take-off if we are before the "Safe Abort-Point"
Indeed this is for short (&soft) field operations.
The danger is when you would continue with not having reached the e.g. 40 kts that you end up in the trees...
For a long tarmac runway there is normally not a problem, but I still use my speed-check to not get airborne with something wrong...
Hope this helps,
Herb