Bottom line: Don't bother running ANALYZE on InnoDB tables.
Sure, sometimes ANALYZE will improve the "statistics". But sometimes it will make things worse. Hence, a "regular" ANALYZE is probably a waste.
Rolando talks about the "random dives", which is the root of the statistics going bad. ANALYZE simply does the dives.
Percona's Xtradb and Oracles 5.6 have some extra tunables -- none of them really 'solve' the problem of statistics being sometimes bad.
All that said -- When a performance problem is identified, it is only 1 time in 1000 that ANALYZE is the main 'fix'.
MyISAM is a different matter. A table with a lot of churn should probably be OPTIMIZEd monthly. That's more for cleaning up the fragmentation, and secondarily for doing the ANALYZE. (This applies to maybe 1 table in 10,000.)