# questions vs. time graph

SO just hit 250K questions... congratulations! Is there a # of questions vs. time graph? Just curious. (is it O(t) or O(t log t) or O(t3/2)? ;)

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Just to clarify, you mean number of questions as a function of time the site has existed, right? Because I've seen numerous graphs of number of questions per hour of day and day of week, but i don't think i've seen one showing the whole time the site has been around. – Kip Aug 7 '09 at 13:45
@Kip: Yes, you are correct in your interpretation. – Jason S Aug 7 '09 at 13:51
The graph is mostly linear, actually. I got the data for a question ages ago for a question about when we would hit 1,000,000 but I never actually graphed it. – Ian Elliott Aug 7 '09 at 14:04
Here's the post if you're curious, a bit old now but should still give you an idea meta.stackexchange.com/questions/4608/… – Ian Elliott Aug 7 '09 at 14:07
ok i've updated my answer with a cumulative posts chart – Kip Aug 8 '09 at 2:27

Here's one I just made, plotting posts per day vs. age of site. Actually looks more like O(log(n)) to me, or somewhere between O(n) and O(log(n)), but I'm no statistician. The big spike is the public launch. The dips correspond to American holidays: Thanksgiving around 120, Christmas around 150, Easter around 250, Memorial Day around 300. See a higher-res version here.

I started with this query:

SELECT DATEDIFF(FROM_UNIXTIME(creationdate), '2008-07-31') AS age
, COUNT(*) as num
FROM posts
GROUP BY age
ORDER BY age


Then I separated weekends from weekdays, since they were clearly two separate trends.

Update: As requested in the comments, here is a chart showing total number of posts vs. age of site. I'll give you that this looks like it could be O(n2), with a very small constant factor (and an anomalous bump around the public launch). Unfortunately I don't remember enough about statistics to tell you which function is a better approximation. I know you need to use r-squared and rho and standard deviations, but I don't remember the significance of any of those things. One of them is supposed to be less than 1.0 I think. Anyway. A higher res version is available here.

Okay, just for fun, here's one plotting posts per day, grouped by day of week. I'm surprised Monday is consistently lower than other days of the week. Higher res here.

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that's per day? looks like O(n) growth so far (except the launch spike), on a per day basis, which would be O(n^2) growth for cumulative # posts. (could you plot cumulative?) – Jason S Aug 7 '09 at 14:53
yeah, that's posts per day. i'll work on cumulative posts this evening, but i'm busy at work right now. :-/ – Kip Aug 7 '09 at 15:22
I don't get the last graph, shouldn't age be by weeks not days? – Ian Elliott Aug 9 '09 at 3:27
@Ian: it's a graph with each of the weekdays separated out to a separate trace. The dark blue line, for example, is thursdays. – Jason S Aug 9 '09 at 14:20
@Kip: cool graphs. Yes, that's the kind of stuff I was looking for. I guess my question was more to the site maintainers, e.g. is this something that they could post, say, once per month. – Jason S Aug 9 '09 at 14:21
@Ian it wouldn't really matter, it would look the same except that the values on the x axis would be divided by 7, and monday would be shifted left by 1 unit, tuesday by 2, etc. The graph was just easier to draw this way with the data i had already collected. – Kip Aug 9 '09 at 18:39
Image links are all broken. – Jason S Feb 14 '15 at 20:16
@JasonS looks like imageshack has run out of money and is making a desperate attempt to stay on the internet by charging people to view images which no one will do. I don't have the original images, and even if I did they would be images of 4.5-year-old data... – Kip Feb 14 '15 at 23:56
5.5 year old data. :-) yah. – Jason S Feb 15 '15 at 1:54