Statistically, how does question length relate to community response?

Question

It is obvious that a question which is too short will almost certainly lack context, and that a question which is too long may run the risk of readers never finding out what the question actually is (Some may not want to read the full question).

Therefore, I was wondering: What is the optimal length in characters for a question? I would like to evaluate this statistically, using the Site Analytics (Data.SE) by Stack Exchange.

To evaluate the community response, I suggest using the following metric:

$$\text{Percentage of upvotes}=\frac{\text{Total number of upvotes}}{\text{Total number of votes}}\cdot 100$$

From experience, I think there would be a global maximum around $3000$ characters.

According to this post, the maximum amount of characters per question is $30000$ characters (with spacing). Since most questions seem to be approximately $500$ characters, I suggest that we represent the data on two different bar charts. One going from $0$ to $2500$ characters on intervals of $50$ characters, the other going from $0$ to $30000$ characters on intervals of $500$. Here is an example of what I mean by "intervals" (Except that here I represented it on a table instead of a bar chart). Obviously, this data is made up:

$$\small\begin{array}{c|c}\text{number of characters}&\text{Percentage of Upvotes}\\\hline1-50&10\%\\51-100&15\%\\101-150&25\%\\ \vdots&\vdots\\2451-2500&90\% \end{array} \qquad \begin{array}{c|c}\text{number of characters}&\text{Percentage of Upvotes}\\\hline1-500&30\%\\501-1000&60\%\\1001-1500&77.5\%\\ \vdots&\vdots\\29501-30000&85\% \end{array}$$

I suggest that we let the Number of characters (with spacing) be on the horizontal axis and the Percentage of upvotes to be on the vertical axis on the bar chart.

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Of course, if you can think of a better way of representing this (Rather than a bar chart), feel free to write an answer. Similarly, if you can think of a better metric to evaluate community response, feel free to suggest one in the comments or write an answer using that metric.

Since I lack experience in programming and I have not seen any query which does this, I would appreciate it if you could show us the statistics and conclude with an optimal length.

Answer 1

TL;DR: the longer, the better.

Based on the current data, longer questions tend to get a higher ratio of upvotes than shorter questions. There is not enough data to determine an 'optimal' question length.

Full version

I constructed a SEDE query which lets you play a bit with the interval length, and the maximum considered length. Feel free to fork it to play around yourself.

_{(note that the vertical axis does not start at zero, because of how SEDE works and reasons)}

We see that shorter questions definitely score worse, but after 2500 characters the trend seems to halt, or at least it's hard to see the trend because of the 'noise' caused by the fact that there aren't that many questions in that range.

For reference, here is the complete SEDE query:

DECLARE @IntervalLength INT; SET @IntervalLength = ##IntervalLength:int##;
DECLARE @MaximumLength INT; SET @MaximumLength = ##MaximumLength:int##;

SELECT (LEN(p.Body) / @IntervalLength) * @IntervalLength AS 'Post length',
  100.0 * SUM(CASE v.VoteTypeId WHEN 2 THEN 1 ELSE 0 END) / COUNT(*) AS 'Upvote %'
  FROM Votes AS v
  INNER JOIN Posts AS p
    ON v.PostId = p.Id
  WHERE p.PostTypeId = 1 -- questions
    AND v.VoteTypeId IN (2, 3) -- up/downvotes
    AND LEN(p.Body) < @MaximumLength
  GROUP BY (LEN(p.Body) / @IntervalLength) * @IntervalLength
  ORDER BY (LEN(p.Body) / @IntervalLength) * @IntervalLength