Most semi-serious punters look at a race and consider a whole bunch of variables, eg last start finish position, jockey, barrier draw, trainer, different details in past form, etc etc.
They then place a different level of importance on the individual variables and also different variable combinations eg the jockey/trainer combination.
They then crystalise that plethora of information into some type of opinion about the chances of the various runners, and invest on the runner or combination of runners they think will reap a profit.
The models being discussed simply do the same thing in a more systematic and quantifiable way usually using some type of statistical package or techniques.
There's more than one statistical approach that can be taken to do the task, thus the discussion relating to classic regression analysis versus other methods.
Understanding the statistical theory doesn't guarantee a profit. Bill Benter and Alan Woods etc took many many years to develop their methods and previously went broke in the process.
To identify the variables, gather the data, combine them and analyse them in a profitable way is a far more difficult task than grasping the mathematical theory. (Probably more difficult than building a rocket) Thus the discussions about different variables and in particular about to what extent variables are independent.
It's not some mystical voodoo going on here.
The fact is a punter like rad, who claims to have been profitable for many years (and I have no reason to doubt him) has probably developed a capacity to carry out a similar process in his head.
His thinking will obviously be a simpler version and not have the capacity for volume that the methods being discussed have, however those shortfalls are probably balanced by the fact his thinking would be far more flexible in adjusting for the vagaries of the individual race at hand.
Any punter with an academic interest in probability would probably enjoy and benefit from further reading on these subjects. It's not necessary to understand the math in detail, often the premise underlying the exercise is enough to stimulate ideas that will improve your performance on the punt.