Ranking intersections and Squares

If you're doing a sudoku puzzle and you're trying to work quickly or efficiently, you want to concentrate your efforts where you're most likely to get results.  Sets with only one or two empty spaces, for example, are guaranteed to give you hits or pairs respectively.   But with sets that have three, four, or five empty spaces we're less likely to get hits, although we might get twoshares or the occasional pair.  And sets with six or more empty spaces are unlikely to pay off at all.

Similarly when we were looking at the abbreviated arrays, we saw that the more data we had intersecting on a square without a known, the better chance we had of getting a hit or a pair in that square.

We can infer then, that our search for results will be dependent on the interaction of how crowded the sets are and how much intersecting data is coming in.

To try to quantify this effect, we need to rank things.  Since my abbreviated arrays only work with squares, we're going to only rank the squares for the sake of this analysis, not the columns or rows.  We'll need to rank them for crowdedness, and also for intersecting data.

Crowdedness is easy.  We'll use Roman numerals, I to IX, for the number of empty spaces in the square, and reserve the X for squares that are completely filled in, because there isn't a zero in that number system.

For intersecting data we only need five ratings,  We'll use A when there are four data influences, B for three, C for two, D for one, and E for none.  The K stands for a known.  Like so:

K|K|A
B|K|K
C|B|K  

K|K|K
D|D|D
D|D|D              

K|K|B
D|D|D
C|C|K  

K|K|C
C|K|D
D|C|E

There's one more factor to take into account, but it will have to wait for another day.