Voltage distribution between components
Since an LED is a current driven device, if you are using a resistor you won't ever get a very predictable or accurate current draw (variations in process, operating temperature, resistor tolerance, supply variation, etc).
This doesn't matter though as in most cases a +-10% variation won't be a problem. 

If you look in the datasheet for any decent LED you will notice the Vf is given at a nominal current (e.g. 20mA) and (as Jippie mentions) there will also be an I-V curve you can use to graphically predict the Vf at other currents.  

So you could develop a mathematical model and try and calculate the resistor value this way, but I wouldn't bother for two main reasons:


There are already SPICE models that will do this for you, created by the manufacturers themselves so likely to be more accurate than anything you can come up with easily.  
If you want to drive an LED precisely, then use a constant current source. There are hundreds of cheap and accurate driver ICs out there (or an opamp with precision reference can be used) For a random example, the SP7618 has a typical regulation tolerance of 1.5% and a maximum tolerance of 6% from -40&deg;C to +85&deg;C.