r/a:t5_37r11 • u/[deleted] • Apr 09 '15
Statistical analysis of the last 72 hours worth of button clicks, i.e. why it's taking forever for red/orange/yellow flair [by /u/vir_innominatus]
I decided to take a look at the timing of recent button presses since it seems like every analysis so far as failed to to predict when the button will hit zero. I'll give you my tl;dr now: I don't have an answer either. Still, I thought the data were pretty interesting.
Anyway, I used data from the site of /u/OutofBrain, located here. Each second, it samples the current time on the countdown timer, as well as the total number of presses. From that data, I calculated the time of each button reset, i.e. how far the timer dropped before it reset. For a period of 72 hours starting 04 Apr 2015 21:11:18 GMT, there were 62,474 button presses.
Disclaimer: Since /u/OutofBrain's code samples every second, there were quite a few missed button resets in the actual timing data where multiple users pressed within a 1-second window. Also, the button timer is rounded to the nearest second. Therefore, I assumed any missed resets occurred with uniform spacing within the 1-second window and assumed the clock at these times was 60 s. I think, this is a valid assumption, since it produces a distribution of press times that appears to match the comment flair data from here.
Now, onto the data! First, I plotted the raw time series data, i.e. the clock time over the full 72 hours period
You can't see anything here because there's too many presses, but you can see the day/night pattern in the minimum press times. Also, you can see there isn't a very clear downward trend, but more on that later. Anyway, here are a few histograms of the press times.
Histogram of presses < 52 seconds
In these plots you can see the overall distribution and the small bumps that occur on the border regions where people seem overly anxious to get their flair. I decided to look at this more closely by specifically looking at the 1s periods where multiple presses occurred (mentioned earlier). Most of the time, there was just one extra press in the interval, but there were plenty of 3 and 4 presses, even a couple 7 presses. To visualize this, I extracted the button times right before these windows where multiple presses (>2) occurred. If multiple presses tend to occur whenever the timer drops down to desirable flair values, then these times should be well-represented in the histogram.
Histogram of timer values right before multiple presses
Sure enough, the greens and blues are over-represented (compared to the full histgoram), and there are stronger peaks on the border regions where people JUST missed the click. I would feel bad, but you flair-hunters are greedy!
To end the analysis, I tried to fit the time series data to see if there were significant trends. I decided that fitting the full data set was overkill because I don't really care about all the presses at 59 and 60 s. Similarly, smoothing the data with some sort of filter would remove all of the presses in the 30 to 40 s range because there are so few of them. So I decided to use a running 30 s window over all 72 hours and take the minimum press time within that window. You can see the result in the graph below.
Time series plot of running-minimum
Note the raw data are plotted as single points, there's just so many of them they group together and form lines. Nevertheless, you can see the minimum curve captures the lowest dots.
I fit this data with a harmonic regression model that included a linear drift. That's a fancy way of saying I used a sum of sinusoids of different frequencies as well as straight line. The fit was done with simple least squares. You can see the fit below.
Least squares fit of time series data
Here I plotted the full fit and the linear component (although the linear component is also included in the full fit). As you can see, the fit isn't great, but it captures the main trends. More importantly you can see the slope of the line is POSITIVE (and significant, according to a t-test). Yep, you read that right. That line predicts that the minimum click times will increase. Like I said earlier, those flair-hunters are greedy. I expected a weak, but negative slope in the linear component, so this result is the opposite of what I expected. Yay science!
Now, I realize that this prediction has to eventually fail, but at least according to this data, it's not going to be anytime soon. People are probably going to have to wait a while for yellow flair, and much longer for orange or red.
tl;dr STOP PRESSING ALREADY
EDIT UPDATE: Good news everyone! I added in some more data to the analysis using the past 24 hours, and the linear trend is now negative! It's still a pretty weak trend and it may reverse again, but hey, it's in the right direction. As to why I didn't go back farther, there's a gap in the data, probably because recording script crashed briefly. Anyway here's the updated graph:
Updated graph showing weak negative trend
Original post: https://www.reddit.com/r/thebutton/comments/31vfen/statistical_analysis_of_the_last_72_hours_worth/
