randomizing piano notes

There are several CAL scripts. HUMANIZE.CAL, RANDTIME.CAL and "Random Time.CAL" are three that I found that vary MIDI data. There could be more, I did not spend much time looking.

Just to put the question into perspective.  I've been playing classical for 55 years (since I was 5) and can get through most of the really difficult technical rep (eg Rach 3, Beethoven pc 4, Bach's WTC, Brahms pc 1 and 2, etc., etc...) 
 
Midi has been a fun thing for me since the early days of Atari, and before that, crude programming on BASIC (we're talking 20 years ago).   I get super-interesting feedback on my own playing using midi technology.  Also, I think any pianist who is honest has to admit that with the most recent piano samples (not so much the earlier attempts), a solo piano recording can be (at least in some cases) virtually indistinguishable from a live recording at the "real thing" (which I do as well).  
 
My question re note positioning really comes from a very narrow concern: I've been taking a closer look at the "midi-trail," so to speak, of my own playing, particularly in respect to the faster preludes and fugues from Bach's WTC (Well-tempered Clavier).  All I'm trying to do, here, is to compare the non-random note timing discrepancy that occurs in playing, say, the second prelude from Bk 1 of the WTC with a "fake" or "midi-generated" discrepancy.   I have the CALS mentioned above, and mea culpa for not experimenting with these first.  I thought, possibly, that there might be a series of quantize parameters that put together might randomly nudge the notes in a chord (or any simultaneous played notes) a few ticks away from each other.  
 
Actual piano playing does this, of course.  But in a non-random way, as folks point out above.  If you examine the midi file of any live piano-playing, you'll often see that the leading or most important note of any chord, or any 2 or more notes sounded together, is a few ticks (let's say milliseconds for the sake of argument) ahead of the less important notes.   Also, it's velocity will be pronounced relative to the other notes in the chord, obviously. 
 
Seems to me that it would be interesting to see how much of this aspect of human playing can be midi-sculpted into an otherwise artificial midi file.
 
That's a tiny bit of where I'm headed here.

Which is pretty close to what we naturally do at the piano.  Just ran the humanize cal, which used in tiny, tiny amounts is not bad.  But it doesn't do what you've described.  I suppose a seasoned programmer could create a CAL for that.  Used to make up CALS, but I'd have to "re-learn" the process!!!