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I rarely use MSE and so I don't have a good feel for what it's like overall. I was slightly surprised by a recent comment by Christian Remling which characterizes MSE as a "homework factory with noise/content ratio $\approx \infty$" that is no longer even a "moderately reasonable site." Seeing this comment made me wonder whether the common practice on MO of suggesting that a question be migrated to MSE needs to be re-thought. If MSE is a complete mess of a site (I'm not sure it is, but let's suppose for the sake of argument that it is), then directing people to it seems like a bad practice.

I would be somewhat reassured if someone could show me some statistics, demonstrating that a high percentage of questions that are migrated from MO to MSE receive answers that are subsequently accepted by the person asking the question. Are there any such statistics available?

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    $\begingroup$ Maybe the tag (statistics) would be suitable here? $\endgroup$
    – Martin Sleziak
    Commented Jan 10 at 5:26
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    $\begingroup$ You mentioned "common practice on MO of suggesting that a question be migrated to MSE". My impression is that closing a question of MSE level is more common than directly migrating it. One of the frequent close reasons mentions Mathematics - but it also includes a link to some site guidelines - see here: Revamping the closure reasons in 2022. One thing to consider could be mentioning list of suitable sites rather than only Mathematics - similarly as in the FAQ and ... $\endgroup$
    – Martin Sleziak
    Commented Jan 10 at 7:36
  • $\begingroup$ ... in the modal window. (But perhaps the text of close reason would become more clumsy. Moreover, for somebody who already posted here - in the SE network - recommending another SE site feels more natural.) $\endgroup$
    – Martin Sleziak
    Commented Jan 10 at 7:36
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    $\begingroup$ My current knowledge of MathSE is mostly concentrated on some tags (group theory and a few more specific). While the overall quality is not high, it certainly not as bad as suggested — the content/noise ratio is low but I'd not call it not "close to zero". The community tendancy at MathSE (for the last 5-6 years) is indeed to reject brief questions regardless of their contents if they are not presented as homework, showing efforts etc. This is indeed somewhat discouraging. (Well, this doesn't address OP's question.) $\endgroup$
    – YCor
    Commented Jan 10 at 9:40
  • $\begingroup$ I guess it's worth pointing out that the question mentions two different (albeit related) things. One of them is migration - this happens after several close voters choose to move a question to MSE But "directing people to MSE" could be reasonably interpreted as mentioning MSE in comments. For the latter, it would be next to impossible to get some reasonable statistics. (If a question was migrated to Mathematics, you can still see that in the question's timeline. But you won't find out whether somebody suggested MSE to the OP in some post on MO - especially if the MO post is now deleted.) $\endgroup$
    – Martin Sleziak
    Commented Jan 10 at 12:57

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As mentioned in the migration tag-info, users with sufficient reputation have access to some statistics about recent migrations (in the last 90 days). In the same place you can find a list of questions migrated from MO. Here is a link for MathOverflow and for Mathematics.

I understand that by successfully migrated you do not mean just that the migration is not rejected - but here is at least something you can easily access.

I do not have access to those stats on MO, but on Mathematics this link says about the migrations MO $\to$ Math.SE in the last 90 days: 61 migrations, 24% rejected.

Screenshot

Asaf Karagila's answer says that he sees 61 migrations and 14% rejected here on MO (as opposed to 24%). Naturally, it would be reasonable to expect the numbers to be the same. This was reported as a bug here: Migration stats not consistent between sites. One of the answers suggests as a possible explanation that: "I assume it's a bug that counts question closed as duplicates "rejected" on the destination site, but not on the source site."

It is quite possible that I might have easily missed something, but when I went manually through the list, I found 7 rejected migrations: MSE4802240 (MO457868), MSE4803113 (MO458012), MSE4808291 (MO458545), MSE4814211 (MO459141), MSE4825567 (MO460233), MSE4823712 (MO460072) and MSE4839414 (MO461654). (This one was migrated on October 3 - so it is more than 90 days: MSE4780067 (MO455711).)

Merged or closed as duplicates: MSE4785546 (MO456321), MSE4792175 (MO457164), MSE4794364 (MO457164), MSE4798902 (MO457583), MSE4818747 (MO459598), MSE4825567 (MO460233), MSE4834554 (MO461146) and MSE4839685 (MO461643). (This one is older - migrated on October 5: MSE4781319 (MO455916).)

You might find older stats here on meta, for example, the answer here mentions statistics in June 2015: Migrating to Math.SE: too many close reasons.

One should be able to find migrated questions from SEDE. But not the deleted ones - so you won't find here rejected migrations, with the exception with the ones which are still not deleted.

See also: Migration notes in schema at Data.SE and How can I track for rejected migrations in the SEDE? For migrations we should look in the PostHistory table, which is described in detail here: Database schema documentation for the public data dump and SEDE.

Keep in mind that SEDE is only updated once a week.

For example: this query and a similar query with some information about the post.

The above queries show migrations from all sites to Mathematics - but the Comment field in the PostHistory table could help to restrict this specifically to MO: https://data.stackexchange.com/math/query/1813983. (Unlike the previous two queries, in this case I list only migrated questions, not the answers migrated together with the questions.) And from that you can get various stats - e.g. numbers per month, percentage of questions with at least one answer, questions with accepted answer etc.

For example, this query shows: number of all migrated questions, number of questions with at least one answer, number of questions with an accepted answer (per year). Naturally, looking at accepted answers can be somewhat misleading - many users do not bother accepting an answer. (And one should keep in mind that in some cases one or more answers was posted already on MO - before the migration.)

In the graphs below I have excluded 2024 - we're in January, the stats for such short period are not comparable with previous years. (But the queries can be used for any period)

Graph

And this query shows percentages rather than absolute numbers.

Graph

Another outcome, which can IMO be considered a success is when the migrated question was closed as a duplicated. After all, this means that the OP was directed to a place where their question is already answered. Here is a query where also duplicate closures are included.

Graph

And again, a query showing percentages rather than counts.

Graph

In case it might be interesting for somebody, it is possible to look at the migrated questions in a specific tag (on the target site).

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From the moderator tools I can reveal that in the past 90 days there had been 61 migration attempts from MathOverflow to MSE and only 14% were sent back, which should be about 9 (I'm not sure about the rounding, so possible 8, although unlikely).

Let me add that we also sent 4 questions to Cross Validated and 1 of those was sent back.

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