DOC: Remove old versions from doc dropdown
- [X] closes #53286

The version switcher in the docs is currently missing for <= v1.3 and broken for 1.4. I had a look at the views for the older versions, and I don't think it's worth to keep the old versions in the dropdown:

![version_switcher_views](https://github.com/pandas-dev/pandas/assets/10058240/c47fbd17-a0ec-4bf4-a1d3-6180f22c9c09)

Note that this only affects the dropdown for the documentation of pandas 1.5+. The documentation of the old versions will continue to exist, and accessible from links on the internet, bookmarks or typing the url. And the dropdown in these old versions will continue to be broken. But from the main documentation it won't the possible to select 1.4 in the dropdown, and then get an error when trying to go back to the stable documentation.

The data in the screenshot is from Google analytics, from the first half of last year. @jorisvandenbossche can you add the url and credentials of Plausible to our credentials, so anyone can access the latest stats?

CC: @lithomas1 
I made a small edit to the 1.4.4 files on the server, and the 404 error should be fixed now. 

Personally, given that we are keeping those files on the server anyway, I would also keep them in the dropdown. Seems like low effort to keep them. 
(I think for me the main reason to remove old versions at some point is to reduce the visual noise if the dropdown gets too long, but not sure if that's already an issue right now)

For example for 1.5, if you look at download statistics from PyPI, 1.5 is still "used" (downloaded) almost as much as 2.0, and those two are half of 2.1. 

(will ask about adding an additional account for plausible) Thanks for the fix to 1.4, that's nice.

To be clear, 1.5 is still kept in this PR (it's the last of the 1 series, so I'd leave it for long).

I'd personally still move forward with this PR, as you say, to reduce noise and make it easier to find the relevant versions. If there is significant interest in these older versions (1.3 and 1.4 in particular) after merging this, I'm surely happy to add them back. But I think leaving from 1.5 onwards is what almost any user would need.

Of course just my opinion, and if people think that people are actually using the dropdown for 1.0 to 1.4 I'm happy to close this and leave things as they are for now. Again going on download stats (with all its disclaimers and limitations), pandas 1.3 is actually downloaded more than 1.4, 1.5, or 2.0. 

> Of course just my opinion, and if people think that people are actually using the dropdown for 1.0 to 1.4 I'm happy to close this and leave things as they are for now.

I have no idea how many people use this (and the site analytics don't track that AFAIK ;), there are entry/exit pages, but I am not sure you can see that per individual page), but even if it's a small group of people using it, I think it's worth keeping it for them since it doesn't cost us much. 
Personally I don't find the current list already too long to make it distracting from the version you might want to select (especially because we intentionally leave out all bug-fix releases. In comparison, the scipy docs has all and there the dropdown even falls of the bottom of screen ;))

Anyway, I don't see the value in removing them already now. But I also won't keep discussing, it's small enough of an issue to not be worth spending too much time on. The 1.3 version results seems consistent with analytics, it's interesting that many users stayed there.

Closing here, we can revisit in the future. > I have no idea how many people use this (and the site analytics don't track that AFAIK ;), there are entry/exit pages, but I am not sure you can see that per individual page)

One more ;) I quickly took a look at our google analytics dashboard, and as I mentioned I not sure you can derive any information about this exactly (people using the dropdown), but just to have an idea how many of the page views are for specific versions: querying the pages on having "pandas-docs/version", and downloading the results of that for the last 28 days:

```
In [32]: df.head()
Out[32]: 
                          Page path and screen class  Views  Users  Views per user  Average engagement time  Event count  Conversions  Total revenue version
0  /pandas-docs/version/1.4/reference/api/pandas....  17779  12113        1.467762                 0.000165        32840            0              0     1.4
1  /pandas-docs/version/1.4/reference/api/pandas....   7729   6310        1.224881                 0.000000         8332            0              0     1.4
2  /pandas-docs/version/1.3/reference/api/pandas....   2818   1903        1.480820                 0.000000         5186            0              0     1.3
3  /pandas-docs/version/1.5/reference/api/pandas....   2522   2040        1.236275                12.276961         6918            0              0     1.5
4  /pandas-docs/version/1.1/reference/api/pandas....   2257   1255        1.798406                 0.000000         4358            0              0     1.1

In [33]: df["Views"].sum()
Out[33]: 119728

In [34]: df.groupby("version")["Views"].sum().sort_values(ascending=False).head(10)
Out[34]: 
version
1.4      36033
1.5      25432
1.3      14039
1.1       8460
2.0       8281
1.0       4148
1.2       3427
1.5.3     3050
1.3.5     1728
2.1.4     1662
Name: Views, dtype: int64
```

So that are a bit more than 100k page views in total (which is a lot in absolute numbers, but luckily also only around 2% of all page views). 
And here it is actually 1.4 that has more views, while in downloads that's much smaller.

Now, I assume that most of those page views are people getting there from clicking a link or from a search giving an old page  > The 1.3 version results seems consistent with analytics, it's interesting that many users stayed there.

My guess is that there is somewhere a package that has an (potentially unnecessary) pin on that pandas version. I would also be surprised if that many users actually did that intentionally.