 # Comment ranking algorithms: Hacker News vs. YouTube vs. Reddit

Comments on social sites have to be sorted somehow. How do big platforms do it – is it some complicated mix of recommender systems, learning-to-rank algorithms, Markov decision processes, neural networks, and learning automata? Well, maybe in some cases but often it’s just a simple formula. In this article we put the formulas used by Hacker News, YouTube, and Reddit, along with a few alternatives, to the test, using virtual comment section simulations. Spoiler alert: YouTube does not do well.

## The simulation model

See Python source code for full details.

Of course this is not a perfect model of every comment section. These parameter values will not always be accurate, although I did play around with e.g. the commenter/voter ratio and I got basically the same final conclusions. Realistically the rate of visitors may vary over time. A voter’s probability of leaving after a certain comment conditional on the most recent (non-)vote may also depend on how many comments they’ve already read. Comment threads are not represented here. Vote probabilities may change over time. Et cetera, et cetera.

## The ranking formulas

Here we use the following symbols

• Number of upvotes received so far: $$n_{+}$$
• Number of downvotes received so far: $$n_{-}$$
• Age of comment, in hours: $$h$$

All ranking methods in our analysis rank comments by scoring each comment and sorting in descending order. The scores are determined by the formulas below.

Starting with the basics, we have the ratio $$(n_{+} - n_{-})/(n_{+} + n_{-})$$ and the difference $$n_{+} - n_{-}$$, a.k.a. the number of net upvotes. We don’t expect these to be optimal but they’re useful baselines. Another version of the ratio is $$n_{+}/(n_{+} + n_{-})$$ which performs similarly.

For testing purposes, we have the random ranking which is, well, just random, and the upvote probability ranking which ranks according to the true upvote probability.

Reddit’s algorithm, detailed here, is a frequentist method for estimating the true voting probabilities based on $$n_{+}$$ and $$n_{-}$$. The Bayesian version of this is what we’ll call the Bayesian average: the same as ratio but we imagine that a few extra “phantom” votes have been cast, say 3 downvotes and 3 upvotes.

Hacker News roughly uses the formula $$(n_{+} - n_{-}) / (h+2)^{1.8}$$, which is like ratio, if we interpret the denominator $$(h+2)^{1.8}$$ as an estimate of the number votes cast. In fact, this denominator is probably more naturally thought of as an estimate of the number of votes cast including implicit non-votes. Non-votes (with a value of 0) would not impact the numerator.

To get a sense of how the simulations look, here are the comments as presented to the 240th visitor from one run using the Hacker News scoring formula:

$$h$$ Upvote probability Downvote probability $$n_{+}$$ $$n_{-}$$ HN score
7.9 0.671 0.324 47 5 0.657
14.2 0.671 0.076 82 3 0.515
21.9 0.496 0.14 110 10 0.324
23.3 0.434 0.051 72 12 0.174
8.9 0.162 0.03 8 0 0.094
14.1 0.112 0.054 12 3 0.060
10.9 0.184 0.058 6 0 0.059
5.1 0.151 0.008 2 0 0.058
12.9 0.226 0.049 6 0 0.046
15.0 0.114 0.061 10 6 0.024
7.3 0.021 0.009 1 0 0.017
13.4 0.071 0.008 1 1 0.0
5.2 0.489 0.038 0 0 0.0
3.6 0.151 0.041 1 0 0.0
1.0 0.579 0.087 0 0 0.0
0.7 0.047 0.024 0 0 0.0
21.7 0.158 0.222 19 20 -0.003
20.7 0.048 0.017 1 3 -0.007
10.4 0.055 0.044 1 2 -0.010
11.3 0.041 0.027 0 2 -0.018
19.5 0.104 0.166 5 10 -0.019
5.4 0.045 0.604 1 3 -0.054

YouTube also uses a formula that involves the age of the comment. Their system additionally factors in the user’s lifetime ratio, which for our tests we set to 0 as if all users are new.

Lastly, let’s consider how we might modify the Bayesian average to take time into account. To make new comments more visible we’ll make the phantom votes all upvotes at first, then asymptotically reduce them to non-votes. We’ll also switch to a denominator similar to the Hacker News formula’s in order to estimate non-votes. This yields the modified Bayes formula

$\frac{n_{+} - n_{-} + n_p / (h+1)}{n_p + h},$

where $$n_p$$ is the number of phantom votes. We use the value $$n_p=7$$ in the simulations.

## Ranking the rankings

I did enough simulation runs (1000-20000) with each formula to be pretty confident about how they compare. Without further ado, voila:

Ranking algorithm Average number of upvotes per visitor
Upvote probability 0.978
Modified Bayes 0.916
Hacker News 0.899
Bayesian average 0.878
Difference 0.848
Reddit 0.836
Ratio 0.813