## Friday, November 16, 2018

### Distribution of paper citations over time

A few weeks ago we had a discussion about citations, and how we can compare the citation impact of papers that were published in different years. Obviously, older papers have an advantage as they have more time to accumulate citations.

To compare papers, just for fun, we ended up opening the profile page of each paper in Google Scholar, and we analyzed the paper citations years by year to find the "winner." (They were both great papers, by great authors, fyi. It was more of a "Lebron vs. Jordan" discussion, as opposed to anything serious.)

This process got me curious though. Can we tell how a paper is doing at any given point in time? How can we compare a 2-year-old article, published in 2016, with 100 citations against a 10-year-old document, published in 2008, with 500 citations?

To settle the question, we started with the profiles of faculty members in the top-10 US universities and downloaded about 1.5M publications, across all fields, and their citation histories over time.

We then analyzed the citation histories of these publications, and, for each year, we ranked the papers based on the number of citations received over time. Finally, we computed the citation numbers corresponding to different percentiles of performance.

Cumulative percentiles

The plot below shows the number of citations that a paper needs to have at different stages to be placed in a given percentile.

A few data points, focusing on certain age milestones: 5-years after publication, 10-years after publication, and lifetime.

• 50% line: The performance of a "median" paper. The median paper gets around 20 citations 5 years after publication, 50 citations within 10 years, and around  100 citations in its lifetime. Milestone scores: 20,50,90
• 75% line: These papers perform "better," citation-wise than 75% of the remaining papers with the same age. Such papers get around 50 citations within 5 years, 100 citations within 10 years of publication, and around 200 citations in their lifetime. Milestone scores: 50,100,200
• 90% line: These papers perform better than 90% of the papers in their cohort. Around 90 citations within 5 years, 200 citations within 10 years, and 500 citations in their lifetime. Milestones scores: 90,200,500

Yearly percentiles and peak years

We also wanted to check at which point papers reach their peak, and start collecting fewer citations. The plot below shows the percentiles based on the yearly numbers of accumulated citations. The vast majority of papers tend to reach their peak 5-10 years after publication; the number of yearly citations starts declining after 5-10 years.

Below is the plot of the peak year for a paper based on the paper percentile:

There is an interesting effect around the 97.5% percentile: After that level, it seems that a 'rich-gets-richer' effect kicks in, and we effectively do not observe a peak year. The number of citations per year keeps increasing. You could call these papers the "classics".

What does it take to be a "classic"? 200 citations at 5 years or 500 citations at 10 years.