Analysis is a means to an end, not an end by itself.
Instead, we must perform analysis with an eye toward what we want to accomplish. Don't say, "we'd like to understand behavior X". Instead say, "the customer is seeing behavior X and wants behavior Y. Let's figure out how those two behaviors are different under the covers."
Don't say, "that unexpected performance improvement should be analyzed." Instead say, "we'd like to make sure that the performance increase we're seeing isn't due to measurement error, some change in system input we haven't noticed, or caused by some transient state."
In other words, don't simply set analysis or even understanding as a goal. Instead, set a goal of what you will do with that analysis and that understanding. That way you know when to stop analyzing and when to start doing.