# Why InnoDB index cardinality varies strangely

This is a very old draft, from early 2007 in fact. At that time I started to look into something interesting with the index cardinality statistics reported by InnoDB tables. The cardinality varies because it’s derived from estimates, and I know a decent amount about that. The interesting thing I wanted to look into was why the cardinality varies in a particular pattern.

Here I’ll grab a bunch of cardinality estimates from sakila.film on MySQL 5.0.45 and put them into a file:

After a while I cancel it and then sort and aggregate them with counts:

Look at the distribution of the counts. The weighted average of these is 1000.53, so it’s close to the truth (1000 rows). But five of the eight distinct estimates are shown about one-half as often as the others; it looks like the random choice of which statistic to use is not evenly distributed.

I mentioned this to Heikki and he pondered it for a bit — but neither of us really figured out what was going on. I know the code superficially, but not as well as he or Yasufumi or others do; and I was not able to find a cause.

More recently I saw that I’m not the only one who notices oddities in the random number generation. I waited. And indeed the fixes for that bug seemed to have fixed the skew in the statistics. Case solved, and all I had to do was wait. Truly, laziness is a virtue.

1. Morgan Tocker says

Excellent! I had a training student ask me this question in San Francisco. It’s great to see such a thorough analysis in Vasil’s post.

The story is much worse than it is sounds. For single-column indexes we get variations. For multi-column indexes we have problems.

Lets consider

CREATE TABLE T (
A int NOT NULL,
B int NOT NULL,
C int NOT NULL,
S varchar(80) NOT NULL,
KEY ix_a_b (A, B),
KEY ix_a_c (A, C)
) ENGINE=InnoDB

Our typical queries are

select S from T where A = ? and B = ?;
select S from T where A = ? and C = ?;

Well, here sampling comes to the play. We will get cardinalities
ix_a_b (1) x1
ix_a_b (2) x2
ix_a_c (3) y1
ix_a_c (4) y2

Because of sampling x1 is never equal to y1. So, for our queries it will always prefer one index over another. It means that one of the queries is always executed using wrong index!!!

I talked to Percona people. In their opinion the behavior is inherent, as sampling of indexes happen independently. I guess, expectations of optimizer are:
1) x1 = y1
2) x1 <= x2 <= rowcount && y1 <= y2 <= rowcount