slacker,
The two most common ways to create a market profile are to:
a. use volume * price to create a volume weighted MP
b. use 'price alone' to create a distribution of the price data that is not volume weighted
Ok, let's examine the theory (or my distant memory thereof) first. MP is predicated on examing relative levels of "activity" at discrete price intervals. Bearing in mind that Steidlmeyer conceieved MP specifically for futures and it was back in the early 80's, when Warren Zevon was top of the charts and all futures markets were pit traded. In those days volume came as single figure - a total for the day - and it came the day after. Similarly, an accurate real-time tape (T&S) was a pipe dream. Therefore he had no choice but to use time@price as the basis for measuring "activity".
Wind the clock forward 20 years and I believe we now have a superior basis for measuring "activity" real-time - volume. In the case of electronic markets this is actual contract volume that goes across the tape, and pit contracts we can use tick volume. Incidentally most people don't realise that the volume numbers for pit markets delivered intra-day by data vendors is actually tick volume and not contract volume. Important to bear this in mind.
Instinctively, we all know that activity (there's that word again) is not evenly distrbuted across the session. Activity is U-shaped. There is far more activity at the open and the close. Well guess what, volume is U-shaped also, whereas time is linear.
Now, to answer your question. There is actually only one way of constructing a MP and that is by price. A MP is simply a distribution of TPO's - which is necessarily time@price. But, and this is what I think you were alluding to,
there are NOW two methods available for determining VALUE. Given the premise that more acivity indicates fairer value, then by deduction, you can assess value on the basis of either time or volume, and more importantly, calculate LVA, POC and UVA.
Being a pragmatist I use volume for determining LVA, POC and UVA. See the MP chart below for YM 2/2. I also calculate VWAP (cell DG96) and identify the TOP POC (DE103). Often I arrive at the POC as a consensus between volume POC, TPO POC and VWAP, placing more weighting on the former. The volume based UVA, POC and LVA are cells DE91, DE105, DE113. I actually moved the UVA down to DE97 because I divided the day into two value areas (the division was between rows 92 and 93). To me it is illgoical to have single prints (DE92,3,4) in a value area.Single prints are a sign of price "rejection". And that my firends is how I arrived at the levels I sent Fri morning.
I would encourage all MP newbies to study the the method as the originators intended it, and over time adapt it to suit their personal market philosophy as I have done.