Deep Analysis of Lichess Puzzles

I analysed the 5,524,871 Lichess puzzles for a school project and would like to share the results with you.
If you want to reproduce this analysis, you can follow the instructions here: https://github.com/aKevinM/Lichess-Puzzles-Analysis

To kick things off, here are 10 notable puzzles worth trying:

Yes, your 2000 puzzle rating is impressive. The rating of the puzzles follows a normal distribution, with a slight right skewness (0.28). It is consistent with the Lichess Blitz Players Rating Distribution (https://lichess.org/stat/rating/distribution/blitz) that also has a right skewness. The difference is that here, the frequency for low rated puzzles is quite higher than the rest.

Lichess allows you to train by opening (https://lichess.org/training/openings) and theme (https://lichess.org/training/themes). Only 1,077,989 puzzles (20.3%) have an opening as a theme (only puzzle with less that 20 moves can be categorized as having an opening). The Sicilian Defense is of course the most present opening.

Now, if we look at the most popular themes we see that endgame and mate themes are the most frequent. The figure below presents the rating and number of time played of the 8 most frequent themes.
We see that mate in 1 puzzles are quite easy while long puzzles are harder, which make sense. Forks and discovered attacked are themes that are played a lot. The reason to that is because they are the most common tactical pattern (see how Lichess puzzles are generated: https://github.com/ornicar/lichess-puzzler).

On another note, these are the top 3 most hated puzzle themes:
This podium is no surprise as, in my own experience, these themes are annoying to play, but more importantly: hard (Puzzle Popularity is partly based on the ability of the player to solve the puzzle https://database.lichess.org/#puzzles). Let me know in the comments the theme you hate the most.

If we look at the frequency of the first and last solution moves, we find a very interesting pattern. The first moves are generally 1 piece (probably pawn) move on the king side, while the last moves generally involve major pieces in the middle (queen or rook) moving to last rank. Below is a board diagram to help you visualize it.
In blue, the first moves. These patterns make sense if you think about the tactical motif of Lichess puzzles: first you set up, then you strike. Conclusion: If you’re unsure what move to play in a puzzle, think about that diagram.
The figure above is a scatter plot between the rating of each puzzle and the number of times they've been played. The central mass that you see are the daily puzzles. Since Lichess doesn’t indicate whether a puzzle is a daily puzzle, I've built my own method to detect daily puzzles: keep only puzzles with >50000 times played and popularity <96.

I captured 1,482 daily puzzles (which is about half of the actual amount of daily puzzles). We can see that daily puzzles are on average 488 points harder than the other puzzles and that their scores are more tightly grouped.
Finally, I merged the puzzle database with the standard rated games database to see if puzzles reflect the actual skill level of the players for each opening. The answer is a big no since puzzle with an opening are around 1400-1600 rating while players' Elo using that same opening can vary from 1200 to 2000 Elo (no linear relationship).

Conclusion
So, what can we conclude? At its heart, Lichess puzzles are a story with a consistent structure: it begins with a quiet preparatory move and culminates in a decisive blow, often on the back rank. While your puzzle rating might not directly reflect your opening prowess in live games (please don't look at my profile), the patterns you learn, especially in critical endgames and crushing attacks are universally valuable.

What's next? We could do a positional analysis of Lichess puzzles. Since Lichess provides the FEN for each puzzle, we can examine piece placement, pawn structure, king safety, etc., to uncover patterns beyond tactics. This would allow us to understand not just what moves are played, but why certain positions are more likely to produce puzzles.

Also, I am currently developing a chess website.
It's Lichess puzzles, but with a twist: you have to find the worst moves.
The site also includes fun side games like “Find the Player” and weekly challenges.
Check out the alpha version at: https://crazychess.wtf