How the Secret Formula Behind Social Media Actually Works

Ever wondered how social media platforms decide how to fill our feeds? They use algorithms, of course, but how do these algorithms work? A series of corporate leaks over the past few years provides a remarkable window in the hidden engines powering social media.

In January 2021, a few Facebook employees posted an article on the company’s engineering blog purporting to explain the news feed algorithm that determines which of the countless posts available each user will see and the order in which they will see them. The article includes a fancy-looking formula central to the algorithm, but the formula is nearly impossible to decipher since the authors didn’t bother to explain half the symbols in it. 

When I first read that blog post, I felt like the cave dwellers in Plato’s famous allegory seeing shadows dance upon the wall— flat, colorless projections of a richer world existing out of sight. I knew the obfuscated formula was not the full story, I just didn’t know how to get outside the cave and find the real math behind it. 

Eight months later, Facebook was rocked by one of the biggest scandals ever to strike the tech industry. Frances Haugen, a Facebook product manager turned whistleblower, snuck over ten thousand pages of documents and internal messages out of Facebook headquarters. She leaked these to a handful of media outlets.

A barrage of stories soon ran, largely focusing on the most alarming, attention-grabbing revelations. Internal studies documented Instagram’s harmful impact on the mental health of vulnerable teen girls. A secret whitelist program exempted VIP users from the moderation system the rest of us face. Mark Zuckerberg and other executives were allegedly unwilling to stem the flood of dangerous extremist content propagated on the platform.

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Will Oremus, a tech writer for The Washington Post, called me and explained that he had something else in his sights. He wanted to lift the veil on the formula in the engineering blog post, and he realized that Haugen’s documents were the key to doing so. 

It turns out Facebook engineers have assigned a point value to each type of engagement users can perform on a post (liking, commenting, resharing, etc.). For each post you could be shown, these point values are multiplied by the probability that the algorithm thinks you’ll perform that form of engagement. These multiplied pairs of numbers are added up, and the total is the post’s personalized score for you. There’s a bit more to it than this, but in broad strokes your feed is created by sorting posts according to these scores, from highest to lowest.

Here’s what this looks like in symbols. Suppose we have a specific user and a specific post in mind, and we write P_like for the probability that the user likes the post, P_love for the probability that they tap the heart emoji, P_angry for the probability that they tap the angry emoji, P_comment for the probability that they comment on the post, and P_share for the probability that they share it. (There are other forms of engagement, but let’s just focus on these for now.) And let’s write V_like, V_love, and so on for the point values assigned to these engagements. Then the magic formula is:

Score = V_like × P_like + V_love × P_love + V_angry × P_angry + V_comment × P_comment + V_share × P_share

The idea is that the algorithm wants to surface the posts you’re most likely to engage with—but there are several forms of engagement, not just one. It wouldn’t make sense to treat all forms of engagement equally; a reshare really does seem like stronger engagement than a like. So the different forms of engagement are weighted differently, and a weighted sum combines them into an overall measure of anticipated engagement.

Let’s try this with some concrete numbers. Suppose a like is worth one point, a heart emoji is worth five points, and a comment is worth thirty points. And suppose one of your friends posts a picture of the puppy they just adopted, while another friend writes a post about a new job they landed. You’re fond of both friends, but let’s be real: you’re more excited about the puppy than the job. If there’s a 50% chance you’ll like the puppy pic, a 20% chance you’ll love it, and a 10% chance you’ll comment on it, then the puppy post scores 1 × 0.5 + 5 × 0.2 + 30 × 0.1 = 4.5. If there’s a 20% chance you’ll like the job announcement post, a 10% chance you’ll love it, and a 5% chance you’ll comment on it, then its score is 1 × 0.2 + 5 × 0.1 + 30 × 0.05 = 2.2. The puppy pic wins and is placed higher in your feed than the job announcement.

Now suppose there’s also a post by your uncle falsely claiming that COVID was caused by 5G towers. Let’s go ahead and give a 0% chance of you liking or loving this post. But you are tempted to write a comment telling your uncle he’s full of s–t, or at least politely explaining why he’s wrong. Let’s put your probability of commenting on this post at, say, 20%. Then its score is 1 × 0 + 5 × 0 + 30 × 0.2 = 6, greater than 4.5. So before you come to the puppy post that makes you happy and the job post that makes you mildly envious, you’re going to see a COVID conspiracy post that boils your blood. Facebook doesn’t try to make you angry, but the algorithm has figured out what kinds of posts will keep you engaged.

The Vs in the formula, the engagement point values, are out of your control. But you can influence the Ps, the estimates of your engagement probabilities. If you tend to engage with posts about food, then over time the algorithm will bump up your estimated engagement probabilities on food posts. If you want more food content in your feed, go ahead and like, love, comment, and share away. If you don’t want food content, don’t engage with it.

Where things get subtle is with unpleasant posts, especially ones that anger or offend you. Think of it this way. When you argue with your uncle, you are giving his COVID conspiracy posts 30 points for each comment you leave—no matter how critical your comment is—and these points drive all his other COVID conspiracy posts up in your feed. In fact, these points drive his COVID conspiracy posts up in everyone’s feed, because the algorithm is smart enough to realize that if you’re inclined to comment on these posts, so are his other friends. Worse still, the algorithm associates COVID conspiracy content with other conspiratorial content, so when your uncle posts a flat-Earth link, the algorithm in essence thinks: “They commented on the other conspiracy posts, so I bet they’ll comment on this one, too.”

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It doesn’t end there. The algorithm correctly deduces that if you’re likely to comment on your uncle’s conspiratorial content, you’re likely to comment on other users’ conspiratorial content as well. In the end, your laudable effort to educate your uncle with a choicely worded comment backfires and tells the algorithm to elevate all conspiratorial content in your feed and, to a lesser but non-negligible extent, in the feeds of other users. Oops. 

TikTok also uses an algorithm to determine which of the billions of videos on the platform to show to each of its one billion users. How does it work? The New York Times hunted for answers and got hold of an internal document labeled “TikTok Algo 101” written by a TikTok engineering team. In a December 2021 article, The New YorkTimes wrote that this document includes a “rough equation for how videos are scored . . . : Plike × Vlike + Pcomment × Vcomment + Eplaytime × Vplaytime + Pplay × Vplay.” While the article didn’t really explain this formula or the symbols in, it is similar enough to Facebook’s that we can figure it out.

Surely, Plike is the estimated probability that the user clicks the heart-shaped like button on the video, while Vlike is the point value engineers have assigned to this form of engagement. Same story for Pcomment, commenting on a video, and Pplay, playing a video. Eplaytime I’m rather certain is the number of seconds the algorithm expects the user will watch the video for, and Vplaytime is the point score indicating how many points each second of play time is worth. If, hypothetically, a comment is worth twenty points and a second of play time is worth two points, then a 50% chance of commenting would count for the same amount of engagement as an expected five seconds of play time. 

The secret TikTok document goes on to explain that “the recommender system gives scores to all the videos based on this equation, and returns to users videos with the highest scores.” Sound familiar? Yes, TikTok’s mind-reading algorithm is, at its mathematical core, nearly identical to Facebook’s algorithm. Both rank posts/videos according to a weighted sum of the amount of engagement they are expected to elicit from the user. 

Have you ever seen a TikTok video with overlaid text saying something like “Wait for it,” “You won’t believe what happens,” or “You’ve gotta watch till the end lol”? These phrases tend to bump up the expected play time for most users, so it’s a cheap trick to boost the video’s score. Some people post videos where literally nothing happens, but they trick you into watching multiple times, thereby racking up even more expected seconds. The math is simple: if the algorithm thinks you’ll watch a ten-second video three times, that’s thirty seconds of expected play time. 

If you don’t like a video for whatever reason, limit your play time. Importantly, resist the urge to rewatch it out of frustration or disgust. And don’t give in to the temptation to comment. Comments and seconds watched, no matter what quality and kind, tell TikTok’s algorithm one thing: “Give me more videos like this.”

In March 2023, Elon Musk had a big chunk of the source code for X (then Twitter) posted online. Would you be surprised to hear that the platform ranks posts by using a weighted sum of estimated engagement probabilities? For all the jousting by the tech giants, for all the competition to build the best social media platform, it turns out that Facebook, TikTok, and Twitter all run on essentially the same simple math formula. I think it’s a safe bet that all the other platforms driven by user engagement do too. The weighted sum of engagement probabilities is the formula driving social media.

My biggest takeaway from this formula and its ubiquity is that users can develop healthier social media feeds, but doing so takes restraint and intentionality.

Imagine there’s a KFC in your town, and one time after a stressful day at work you give in to temptation and head there for an easy dinner. The next day, the KFC has mysteriously moved one block closer to your house. Now the convenience and the allure are even greater, so you find yourself visiting it more often. But each time you do, the KFC moves even closer to your house. Soon it’s down the block from you and is part of your weekly routine. Eventually the KFC is next door, and you’re eating fried chicken more often than any reasonable human being should. You’re not proud of it, but how can you resist when KFC is the first thing you see (and smell) in the morning and the last thing before bed at night? 

This is how social media algorithms work. They bring the things we engage with closer and closer. Once we start clicking the social media equivalent of junk food, we’re going to be served up a lot more of it—which makes it harder to resist. So we click it more and the algorithm promotes it even more highly in our feeds. It’s a vicious cycle that can quickly turn our feeds into endless streams of digital dreck. Knowing how and why this cycle happens is the first step to stopping it. Just remember: the tech companies choose the Vs in the social media formula, but the Ps are shaped by your actions online.