How to choose between very good journals in mathematics? I finished preparing a math paper, and am now trying to decide where to submit it.

I read How do you judge the quality of a journal?,
but it seems that the answers there mostly deal with how to judge if a journal is good at all.

The journals I am considering (see list below) are all very good. But how can I know how do very good journals rank?

I know my paper is not at the level of Annals,
so I considered the following journals:
Selecta mathematica,
Duke,
Compositio Mathematica,
American journal of mathematics,
Advances in mathematics,
International mathematical research notices,
and Crelle journal.

How can an author compare the quality very good journals such as these? Is there any reasonable way to use public data in order to sort them from best to worse?

Note: this question is looking for an answer about a general method, not necessarily a particular ranking of those particular journals.
Is there any reasonable way to use public data in order to sort them from best to worse?


Not really.  To start with, there isn't a remotely well-defined notion of ranking.  For example, it depends on the subfield (some journals attract better papers in certain areas than others), it can vary over time, and it depends on the specific goals you have in mind.  More importantly, people just don't always agree: I know some people who would argue that one of the journals you listed is clearly a better choice than the others, but they wouldn't all choose the same one.

The explicit rankings I've seen do a poor job of accounting for these factors.  At best they are mediocre (perhaps valuable as a first cut for distinguishing between journals at very different ranks, but useless for fine distinctions).  At worst they are positively misleading.

Fortunately, choosing between well-known journals like these is not so difficult.  You should look them over and try to gauge which ones look to you like they are publishing the most important papers in your area, while also asking around to get other people's opinions.  (Ask mentors of yours, ask your friends or collaborators, ask colleagues at tea.)  If there's a clear consensus among the people you ask and it's consistent with your own impressions, then you're done.  If there's a clear consensus that disagrees with your impressions, then you need to think and talk a little more.  If there's no clear consensus among several options, then it doesn't really matter which of them you choose.  After all, journal prestige matters only to the extent it is perceived to matter by the community; if the community can't make up its mind, then there is no right choice.

Carrying this out takes a little time, but it's worth it since you learn more about how things are perceived in your research area.