Most experienced bike riders have a well defined riding position, usually the result of years of fine-tuning and the help of a professional fitter.
When considering a new frame, the first thing you should check is the ability to correctly replicate your riding position. This is not a trivial task if you don't have the new frame in your hands.
VeloSizer does just that: it tells you the setup (i.e. exposed seatpost, saddle offset, stem length and stem spacers) you need to replicate your current position on the new frame. Once you know this, you (or an experienced professional) can then judge if that particular frame has the potential to become a well-riding bike.
A note on forks: if you specify the frame geometry in terms of top tube or front center, you must also specify fork length and offset.
This is generally not an issue for road bikes as fork length and offset are usually included in geometry charts.
On the other hand MTB charts often omit these values and only tell you the brand/model/travel they refer to. VeloSizer includes a list of forks, so that you can pick the model even if you don't know these parameters.
It is important to select the fork that your geometry chart refers to (or at least a similar model with the same travel). If you intend do use a different fork keep in mind that you are altering the actual frame geometry and VeloSizer won't give you correct results.
VeloSizer itself is very accurate, i.e. for a given input it produces a very accurate output. However, there are some factors that usually cause small differences between the model and reality: in particular frame and position are difficult to measure down to the millimeter. Additionally saddle shapes vary quite a lot and geometry charts published by manufacturers sometimes contain mistakes or imprecisions.
That's why you should only use this tool to get a rough idea. If you are making a purchase, please check the bike in person before spending the cash!
I obviously won't hold any liability for any losses or damages caused by the use of this tool.
Note: in case this wasn't clear, VeloSizer does absolutely no guess work nor uses any empirical formula. Given a frame geometry (and the components), there is exactly one and only one setup that puts the rider in a given position -and it can be accurately computed.
If you need a powerful tool to play with bike parameters, I encourage you to take a look at Bike CAD. VeloSizer has only the humble goal of helping you replicate your position from bike to bike, while Bike CAD is a full blown bike-specific CAD application, arguably the best on the market.