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Recently the birthday tag has emerged and it quickly has around 100 questions tagged (mainly by one user I suppose).

This is indeed not the first time we have this tag. The last time it was deleted and another tag calendar-computations was introduced.

My concern is probably naive since my understanding in probability/combinatorics are minimal: Is the term "birthday" commonly used? That is, is there a somewhat well-defined sets of questions where people will instinctively add "birthday" as a tag, just like what people do for, e.g. the tag "probability", "combinatorics"?

The term just sounds too layman to me.

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    $\begingroup$ I will add that the tag-creator also created a tag-excerpt: "Birthday problems typically look at probabilities and expectations of a random group of individuals sharing birthdays and how this changes as the numbers of people increases. They often assume that individuals' birthday are independently uniformly distributed across 365 days but similar problems can use other numbers or assumptions. They can be generalised to wider occupancy and collision problems." $\endgroup$ – Martin Sleziak Nov 20 '17 at 8:55
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    $\begingroup$ I wonder whether it would be possible to find a more descriptive tag-name corresponding to the description in the tag-excerpt, for example, birthday problem (or something similar). But it would probably be better to hear opinion from somebody who knows more about this kind of problems. I will also add a link to a related discussion in chat. $\endgroup$ – Martin Sleziak Nov 20 '17 at 8:56
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    $\begingroup$ At least in crypto this is known as the birthday paradox. The small sample I checked seems to indicate that the questions are mostly about that and related themes. Seems awfully specific to me. OTOH somebody could take a special interest in the various applications of this. Meet-in-the-middle-attack might be a better way of phrasing it. If we accept the tag (undecided myself) we should probably come up with a tag name that has less potential for confusion. $\endgroup$ – Jyrki Lahtonen Nov 20 '17 at 10:17
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    $\begingroup$ Anyway, I notified the (probable) tag creator. If only people learned to clear their tag ideas in advance. Sigh. $\endgroup$ – Jyrki Lahtonen Nov 20 '17 at 10:21
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    $\begingroup$ Idea: Use the birthday tag to post problem on your birthday. Doing this will encourage other users to give you an answer as a present. $\endgroup$ – Cure Nov 20 '17 at 16:33
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    $\begingroup$ @Cure I thought the purpose of the site was to give presents all year round. :) $\endgroup$ – Joonas Ilmavirta Nov 20 '17 at 17:13
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    $\begingroup$ For my money, when a single user introduces a tag and then throws over a 100 questions into it within the span of three days... that's either badge gaming for Taxonomist, or just a naive (but nonetheless blatant) ignorance of protocol as to how new tag should be introduced: via some discussion on meta. Especially when the said user has over 80k points. $\endgroup$ – Asaf Karagila Nov 20 '17 at 20:35
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    $\begingroup$ Such a tag might make sense: at least 50% of the questions are about things thoroughly explained in any decent textbook, "birthday" is just the most frequent in probability/statistics. It might help to identify candidates for quick deletion: this site is about specific problems, not about "do my homework, with all details" or "read my textbook to me, slowly". $\endgroup$ – Professor Vector Nov 26 '17 at 17:42
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I introduced the tag because there were several slightly different questions coming up similar to the traditional shared birthday question to which the standard answer is $23$ and to birthday attacks in cryptography to which the standard approximation is $2^{n/2}$. It is not related to calendar calculations such as which day of the week was I born, but is marginally related to coupon-collector's questions which have their own tag.

Since I managed to find over $100$ relevant birthday-related questions in an hour, almost as many as are already tagged with coupon-collector, I feel it is a reasonable tag. It is currently on page $24$ of $53$ of tags listed by popularity.

Indeed any new tag that can be applied to over $50$ questions is rewarded in the system and this tag more than doubles that threshold.

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    $\begingroup$ I agree that having the tag is alright; I only think that the name should be somewhat different, my preference would be birthday-paradox, to make it more clear it is not about calendar computation. $\endgroup$ – quid Nov 20 '17 at 14:21
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    $\begingroup$ @quid: though in most cases the results hardly meet the idea of paradox, instead being closer to mildly unexpected. $\endgroup$ – Henry Nov 20 '17 at 14:28
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    $\begingroup$ This is arguably true, but not overly relevant in my opinion. It is a a somewhat common name for this circle of ideas and "make[s] it more clear it is not about calendar computation." If you could propose another name that makes clear it is not about calendar computation we might use that. $\endgroup$ – quid Nov 20 '17 at 14:37
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    $\begingroup$ Another term used here is "collisions". $\endgroup$ – Hurkyl Nov 20 '17 at 16:53
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    $\begingroup$ As a said in the question, all I concern is that the term is not common enough to use. I am asking, as quid suggested, if there is another better terms. (But I have to admit that I am not competent to judge which one is more common. I raised this question merely out of (not so educated) math instinct and the fear that the number of tagged grows too fast). $\endgroup$ – user99914 Nov 20 '17 at 17:07
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    $\begingroup$ I wouldn't worry about renaming the tag now. The name is simple and pretty clear. If we end up feeling like it, we can synonymize or even merge tags later on. I would not be opposed to the other tags mentioned in the comments being created. $\endgroup$ – Joonas Ilmavirta Nov 20 '17 at 17:12
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    $\begingroup$ @Hurkyl good point, maybe bithday-collisions? With both readings "collisions of birthdays" and "birthday (problems) and collision problems" being reasonable. $\endgroup$ – quid Nov 20 '17 at 18:52
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    $\begingroup$ @JoonasIlmavirta: The clarity of the name is in dispute, since it homonymous with a common English word. $\endgroup$ – Hurkyl Nov 20 '17 at 19:12
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    $\begingroup$ Not weighing into whether or not the tag was necessary, I think that at least some of the people that put actual and real effort into the tags on the site, would have appreciated a heads up, in the form of a meta discussion before tagging over a 100 questions. $\endgroup$ – Asaf Karagila Nov 20 '17 at 20:36
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    $\begingroup$ I'm fairly sure I support the idea of renaming this tag. Collisions (or something related) gets my vote so far. After all, the collisions are not nearly always about birthdays. That is just the most widely known example. Aren't algorithms like Pollard $\rho$ based on the same principle? Also, I share the sentiment in Asaf's comment. Reverting a less successful tagging spree is not my idea of fun. $\endgroup$ – Jyrki Lahtonen Nov 20 '17 at 21:19
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    $\begingroup$ @Henry: No. I'm saying that if it turns out that the tag is not a good fit for whatever reason, it's easier and cleaner to remove the tag from two questions (or ideally from none, as discussion should take place prior to tagging any question), than it would be from 100+ questions. $\endgroup$ – Asaf Karagila Nov 20 '17 at 22:17
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    $\begingroup$ Won't "collisions" make some users think, physics problems about billiard balls and such? $\endgroup$ – Gerry Myerson Nov 20 '17 at 22:56
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    $\begingroup$ @JyrkiLahtonen sure, but still "birthday problem/paradox/phenomenon" is used in that context as some kind of technical term. Coupon collector problems are not about somebody actually collecting coupons either, usually at least. Same for billiards. Or coin weighing problems. $\endgroup$ – quid Nov 21 '17 at 0:39
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    $\begingroup$ Anyway, a strongish sentiment is that a useful new tag is one that (eventually) appears on 50 questions without the tag creator adding it their themself. I may admittedly be a bit old-fashioned in my views here. If you only want to keep track of these questions yourself a better way would be to favorite them. But, to reiterate, the jury may still be out thinking whether this is a good tag or not. We have seen much worse suggestions that we could decide to remove more or less on the spot. $\endgroup$ – Jyrki Lahtonen Nov 21 '17 at 19:41
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    $\begingroup$ I'm okay with creating a tag to categorize the problem, but the problem with creating a general/umbrella tag like this is that any user can't subscribe to the specific problem; perhaps they're only interested in "birthday paradox" but not "birthday attack"? And who to guess that "birthday" alone is not about calculating the birth date/day? (hint: new users don't read tag excerpts) $\endgroup$ – Andrew T. Nov 24 '17 at 2:17
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Alternative Idea: Abstract Duplicates

I've sampled from the tag and by-and-large the questions I've looked at look like minor variations on a single question rather than meaningfully different questions that cluster around a single idea. As a result, I suggest that writing a canonical answer that thoroughly answers the abstract question in terms of the number of bins (or months or songs or whatever), $n$, with $n=365$ being treated as a special case.

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