visual clutter

According to TiVo's 2016 report, the average American spends 24 minutes a day searching for content on streaming services and television. Human beings are spending nearly a half hour looking through pages and pages of TV listings, Netflix, Hulu, Amazon Prime Instant Video, Crackle, Sling, Roku, Playstation Vue, YouTube Red, Acorn, Comcast Stream, Plex, HBO Go, Funny or Die, Twitch, VEVO, Seeso, CBS All Access, and DirecTV Now. That's time that should be spent doing literally anything else.
The unfortunate fact is that this type of task is pervasive, so much so that it has its own field of study. Vision researchers investigate visual search, which generalizes the task to any visual scan with the objective of detecting a specific feature. UX designers try to present a visual environment that speeds up average response times.

I'm not concerned with anything scientific today. I'm frustrated with Amazon's UI. It's tortuous. There are so many links to trod through that even on an FHD monitor you can see a screen full of only links. If your task is to find an item by clicking links starting from Amazon's homepage, you will fail.
Bottom of Amazon's Homepage

This made me curious. How many links are there on Is the situation as bad on other popular sites? Clearly, number of links is a proxy for clutter, which itself is just one variable that can be used to predict visual search performance. But regardless of the exact relationship, visual search performance is definitely monotone decreasing in number of links. That is to say, there is no universe in which increasing the number of links, all other things held equal, will speed up your ability to locate the correct link. So I looked at the data, and what I found surprised me.
Bar chart of number of a tags on popular pages

Amazon is far and away the worst American website when it comes to links. However, I will spare them my criticism. Asian internet is a war crime.

Here's some logic behind having a large number of links on the site. Assume that your goal is to have the user interact with the site by clicking the link and nothing else. Also assume that the user interfaces with the site by looking at each link and deciding whether or not to click each link \(i\) with probability \(p_i\) and only stopping when she finds a suitable link. Then the probability that the user clicks a link tends to 1 as number of links increases. But in real life, users don't behave that way. They will balk from long wait times. Increasing the number of links might increase the chance that a desirable link is presented, but will also increase the search time.
Potential relationships between search times and set size

There needs to be a constraint on the number of links. Perhaps testing will construct the relationship between set size and search time, and designers can define an upper bound based on highest acceptable search time. Even an arbitrary budget will force sites to economize and present only the most pertinent information. Screen size and performance factors alone don't seem to be enough of a limitation on Taobao or Amazon.