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Any error (or change) in cardinality can have significant side effects in the join order and choice of indexes. Counterintuitively, a change in cardinality from 4 to 3 is much more likely to have a significant impact on an execution plan than a change from 537 to 536. Precision for smaller tables (more specifically, smaller result sets) is very important.
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Glancing through the table of results, it is possible to pick out a couple of patterns. When we use literals, the difference between open (greater than [>], less than [<]) and closed (greater than or equal to [>=], less than or equal to [<=]) is exactly 100. When we go right outside the legal range of values for the columns (user_tab_col_ statistics.low_value, user_tab_col_statistics.high_value), the cardinality seems to fix itself at 100.
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CHAPTER 3 SINGLE TABLE SELECTIVITY
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The values reported for bind variables seem to be rigidly fixed (no difference between open and closed) and have little to do with realistic possibilities (a range returning 60 rows seems unlikely when an individual value returns 100 rows). With a little work (and a few follow-up experiments), we can guess the calculations that the optimizer is probably doing. Taking the second half of the table of results first: Cases 10 through 13 (bind variables with unbounded ranges): The optimizer simply sets the selectivity at 5%. With 1,200 rows (and no nulls), we get 0.05 * 1200 = 60 rows. Cases 14 through 18 (bind variables with bounded ranges): The optimizer simply sets the selectivity at 0.25% (which is actually 5% of 5%). With 1,200 rows (and no nulls), we get 0.0025 * 1200 = 3 rows. Cases 19 and 20 (ranges outside the recorded low/high range): The optimizer detects that the query falls outside the known range, and seems to return a selectivity, hence cardinality that would be correct for column = constant. (There is a nasty boundary case, though, that appears from 9i onwards when every row holds the same value. The script selectivity_one.sql in the online code suite gives an example.)
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BIND VARIABLES AND RANGES
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One oddity with bind variables and ranges: you might expect character_col like :bind to be treated the same way as a between clause, after all, colX like 'A%' looks as if it should be treated like colX >= 'A' and colX < 'B' which it nearly is. In fact (see script like_test.sql in the online code suite), when the optimizer sees this comparison with a bind variable, it uses the same 5% selectivity as it does for an unbounded range with the usual caveat about the effects of bind variable peeking.
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The predicates that use literal values need a little more explanation. The informal, and approximate, version of the optimizer s algorithm reads as follows: Selectivity = required range divided by total available range By looking at (user_tab_col_statistics.high_value user_tab_col_statistics.low_value), we can calculate that the total range in our example is 11. And as soon as you see the number 11, you know that something is going to go wrong with our test case. We know that the test case is about 12 discrete measurements, but the optimizer uses arithmetic that treats the data as if it were continuously variable values with a total range of 11. Anything that the optimizer does with small numbers of distinct values is going to have a critical error built in. (It s a bit like the problem that young children have with fence posts and fence panels why are there 11 posts, but 10 panels Putting it the grown-up way how come there are 11 integers between 30 and 40 when 40 30 = 10 ) But how should we apply the algorithm in each of the slightly different cases
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