Does Jon Skeet have mental powers that make us upvote his answers? (The effect of reputation on upvotes)

August 4, 2011
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(This article was first published on Stack Exchange Stats Blog, and kindly contributed to R-bloggers)

Of course since we all know Jon Skeet does have various powers, I will move onto unanswered questions, whether a users reputation makes them receive more upvotes for answers. I’ve seen this theory mentioned in multiple places (see any of the comments to Jon Skeet’s answer that are along the lines of “If this was posted by someone other than Jon Skeet, would this have gotten as many upvotes?”). It is similar to the question we were supposed to address in the currently dormant Polystats project as well.

Examining user and post data from the SO Data Dump, first I looked at the correlation between users reputation and their most recent posts. Below is a scatterplot, with the users current reputation (as of the June-2011 data dump) on the x-axis and the current score on their most recent non community wiki answer on the y-axis.

 

One can discern a very slight correlation between reputation and the score per answer (score = upvotes – downvotes). While consistent with a theory of reputation effects, an obvious alternative explanation is simply those with higher reputation give better answers (I doubt they bought their way to the top!). I’m sure this is true, but I suspect that they always gave higher quality answers, even before they had their high reputation. Hence, a natural comparison group is to assess whether high rep users get more upvotes compared to answers they gave when they did not have as high reputation.

To assess whether this is true, below I have another scatterplot. The x-axis represents the sequential number of the non community wiki answer for a particular user, and the y-axis represents that post minus the mean score of all of the users posts. The scatterplot on the top is all other SO users with a reputation higher than 50,000, and the scatterplot on the bottom is Jon Skeet (he deserves his own simply for the number of posts he has made as of this data-dump, over 14,000 posts!)

In simple terms, if reputation effects existed, you would expect to see a positive correlation between the post order number and the score. For those more statistically savvy, if one were to fit a regression line for this data, it would be referred to as a fixed effects regression model, where one is only assessing score variance within a user (i.e., a user becomes their own counter-factual). Since the above graphic is dominated by a few outlying answers (including one that has over 4,000 up votes!) I made the same graphic as above except restricted the Y axis to between -10 and 25 and increased the transparency level

As one can see, there is not much of a correlation for Jon Skeet (and it appears slightly negative for mortal users). When I fit the actual regression line, it is slightly negative for both mortal users and Jon Skeet. What appears to happen is there are various outlier answers which garner an incredibly high number of upvotes, although these appeared to happened for Jon Skeet (and the other top users) even in their earlier posts. It seems likely these particular posts attract a lot of attention (and hence give the appearance of reputation effects). But it appears on average these high rep users always had a high score per answer, even before they gathered a high reputation. Perhaps future analysis could examine if high rep users are more likely to receive these aberrantly high number of upvotes per answer.

This analysis does come with some caveats. If reputation effects are realized early on (like say within the first 100 posts), it wouldn’t be apparent in this graph. While other factors likely affect upvoting as well (such as views, tags, content), these seem less likely to be directly related to a posters reputation, especially by only examining within score deviations. If you disagree do some analysis yourself!

I suspect I will be doing some more analysis on behavior on the Stack Exchange sites now that I have some working knowledge of the datasets, so if you’ve done some analysis (like what Qiaochu Yuan recently did) let me know in the comments. Hopefully this revives some interest in the Polystats project as well, as their are a host of more things we could be examining (besides doing a better job of explaining reputation effects than I did in this little bit of exploratory data analysis). Examples of other suggested theories for voting behavior are pity upvotes, and sorting effects.

For those interested, the data manipulation was done in SPSS, and the plots were done in R with the ggplot2 package.

To leave a comment for the author, please follow the link and comment on his blog: Stack Exchange Stats Blog.

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