DNA Inheritance- Math vs. Biology
So, at core (it seems) you are interested in the rate of recombination events and the magnitud of their occurrences. This would be the only source I can think of that would give you information about the 'composition' of one chromosome (other than brute-force sequencing). 

As you seem to know, recombination is an important factor that 'shuffles' some specific areas of the chromosomal DNA during meiosis (process needed to produce gametes). There is a technique developed by T. H. Morgan almost a century ago, that measures the rate of this 'recombination' events by comparing how two (or/and more) particular loci co-ocurr across generations (when recombination occurs, it is more likely to break co-occurrences of distant loci, as opposed to close loci). Thus, we can use this distance measure as a measure of recombination. In fact, in honor of Morgan, the units used to measure recombination rates are called 'centiMorgans', and abbreviated cM. A cM is the probability for a particular loci (it can be a gene or a smaller sequence) to co-occurr with another loci (to be 'linked' to). Thus, is a relational measure: every particular sequence is related to another, and by transitivity (if A and B are close, and B and C are also close, then A and C will probably be close -this is a generalization-). When done in chromosomal or genomic scale, we can build linkage maps.

In modern times, there's quite more resolution, from whole genome studies at gene/chromosome resolution, and even higher resolutions (remember that a 'loci' can be any unit of your interest in the DNA).

Being all that said, recombination rates, and thus the probability of inheriting certain DNA features from parents/ancestors based on recombination, vary quite a lot. There are many 'hot-spots' and other regions seem to be 'protected' from recombination (for instance, regulatory DNA). According to the work I cite here, the probabilities of recombination can vary within about an order of magnitude (the most likely recombination occurring at 10 times higher probability than the less likely), but this varies a lot.

I hope this helps a bit. I am still not sure what do you mean by "biological factors", but for sure recombination is one of the important factors influencing the identity of each chromosome across generations (others are, of course, point and chromosomal mutations).