Chess puzzle rating explained

A puzzle rating is a classification, not a score. It answers one question: at what difficulty do you solve half of the puzzles? A player rated 1500 is expected to solve about half of the puzzles rated 1500, most of the ones rated 1200 and few of the ones rated 1800. Every solve moves the estimate up, every miss moves it down, and the size of each move depends on how surprising the result was.

The puzzles have ratings too, and they come from the same process run the other way. Each puzzle in the Lichess database has been attempted by thousands of players; every attempt is a game between the player and the puzzle, and the puzzle's rating settles where players of that strength solve it half the time. So a puzzle rated 1400 is not "a 1400 idea": it is a position that 1400-rated players find about half the time, whatever the idea. A one-move back-rank mate may be rated 800; the same mate two moves deeper, behind a deflection, may be rated 1500.

That is also why the number is yours only relative to the pool. Two sites with different puzzles and different players give different numbers to the same person, and both are right.

Almost every puzzle rating uses the Elo formula or a descendant of it. The expected score of a player rated R against a puzzle rated P is 1 / (1 + 10^((P - R) / 400)). Solve it and your rating moves up by K × (1 - expected); miss it and it moves down by K × expected. K is the step size: a K of 20 means a puzzle 400 points above you pays about +18 when you solve it and costs about -2 when you miss it.

The descendants differ in how they choose K. Lichess uses Glicko-2, which keeps a deviation per player: a measure of how sure the system is about your rating. A new account, or one that has not solved in a while, has a large deviation and moves by big steps; a busy account moves by small ones. Chess.com's puzzle rating behaves similarly. Both also rate the puzzles themselves with the same machinery, so a puzzle that turns out to be harder than its rating drifts up over time.

chesstactics uses plain Elo with a step that settles: K = 40 for your first 30 rated attempts, then K = 20, a floor at 400 and a start at 1200. That buys most of what Glicko buys, a fast start and a stable cruise, for one formula that lives in one place: the database function that records the attempt. The gym shows you the two possible deltas before each puzzle for the same reason. There is nothing hidden in the number.

Puzzle ratings run higher than game ratings for most players, sometimes by 500 points or more, and the gap is not a flaw. A puzzle tells you there is something to find and gives you unlimited time to find it. A game does neither. In a game you also have to notice that this is the moment, under a clock, while thinking about a plan, and the tactic is buried among forty positions where there is nothing.

Lichess says this in its own notes: knowing the theme of a puzzle is a hint, and training by theme overestimates your level. The same applies to any puzzle, because the puzzle itself is the hint. A puzzle rating measures pattern recognition when told to look. A game rating measures that plus everything else.

The practical consequence is that the two numbers should be used for different things. The game rating tells you how you play. The puzzle rating tells you which puzzles are worth your time: the ones around it, where you solve about half, are where learning happens, and the ones 400 points below are where you learn nothing.

A new account has no rating, and a system that starts everyone at the same number wastes the first fifty puzzles finding out where you belong. chesstactics instead starts with a calibration: ten puzzles on a staircase from 800 to 2000, one per step, served in order. Each is rated normally, with the large provisional K, so by the end of the ten the estimate is already close, and the staircase has also picked the section of each journey you should start in.

Until the calibration is done, and until the first thirty rated attempts are in, the rating is provisional: it moves fast and it does not appear on the leaderboard. After that the step halves and the number becomes something you can compare with your friends' and with yourself last month.

The diagram is the kind of puzzle that lands in the middle of the staircase. The mate is the same back-rank mate as in the first diagram, but the defender has to be pulled off the back rank first: the queen takes on d8, the queen has to take back, and now the rook comes to e8 with the second rook behind it. One extra move of preparation, three hundred rating points of difference.

A rating is only worth something if it cannot be asserted. On chesstactics the client never holds a solution: when you play a move in the gym, it is sent to the server, checked against the stored line, and the reply comes back. The browser learns the answer only when the puzzle is over. Every rated attempt is the first attempt at that puzzle, so replaying a puzzle you have seen changes nothing, and abandoning a puzzle you have started is settled as a miss the moment you start another, so walking away from a hard one is not free. There is a daily quota of gym starts on the free plan; the Pro plan removes it.

The sprint is built the other way round on purpose. A puzzle rush has to feel instant: sixty puzzles, a three-minute clock, three strikes. A round trip to the server for every move would kill the feel, so the batch ships with its solutions and the browser checks them. That means the sprint is also, in principle, cheatable, which is exactly why it never touches your rating, has no leaderboard, and pays participation XP only, capped per run. The run is re-verified on submit to catch the obvious, but the design does not rely on it. The rating is the one number we will defend, so it is the one number that only the server can move.

Three things move a puzzle rating, in order of how much.

• Solve at your level, and calculate to the end. Most rating is lost on puzzles you could have solved, by playing the first move that looks right. The rating loop is tuned so that puzzles within about a hundred points of you are the ones served; solve those slowly and the number climbs on its own.
• Fix the motifs you miss. A rating is an average over every kind of tactic. If you find forks at 1700 and pins at 1200, your rating sits in between and your games lose pieces to pins. Per-motif statistics are derived from your gym attempts; a motif that lags behind your rating is the journey to do next.
• Bring it back to your games. The rating measures recognition when told to look. The scan of your own games measures the other half: the tactics you walked past when nobody told you. Replaying those, by motif, until you stop missing them is what turns a puzzle rating into a game rating.

What does not move it: volume without attention, easy puzzles for the streak, and reading about tactics instead of finding them. The checklist helps with the last one.