A chess rating is a number that predicts results. It is not a score you accumulate for showing up — it is an estimate of your strength that gets updated every game, and the update depends entirely on how surprising the result was. The Elo system, designed by the physicist Arpad Elo and adopted by FIDE in 1970, does this with one formula: it converts the rating gap between two players into an expected score, then moves both ratings toward whatever actually happened.

What a Rating Actually Measures

A rating is a prediction, not a reward. If the system says you are 1450 and your opponent is 1450, it claims the two of you will split points roughly evenly over a long match. If it says 1450 against 1850, it claims something more specific: the 1850 should score about 91% of the available points. Everything else — the arithmetic, the K-factor, the deviation numbers — exists to keep that prediction honest.

Two consequences follow immediately, and both surprise people:

  • The absolute number is arbitrary. Elo measures only differences. Re-base a pool so everyone is 500 higher tomorrow and every prediction it makes is identical — which is why a number from one site cannot be compared to a number from another.
  • You cannot farm rating from weak opponents. Beating someone 500 points below you is already predicted, so it is worth almost nothing. Ratings move only on information the system did not already have.

The Elo Formula: Expected Score

Elo's core equation converts a rating difference into an expected score between 0 and 1, where 1 is a win, 0.5 a draw and 0 a loss:

E = 1 / (1 + 10^((Ropponent - Ryou) / 400))

The 400 in the denominator is a scaling choice, and it is why 400 is the number everyone quotes: at that gap the stronger player is expected to score about ten times as many points as the weaker one.

| Rating gap | Stronger player's expected score | | --- | --- | | 0 | 50.0% | | 50 | 57.1% | | 100 | 64.0% | | 200 | 76.0% | | 300 | 84.9% | | 400 | 90.9% | | 600 | 96.9% | | 800 | 99.0% |

Read the 200-point row carefully; it is the one most players misunderstand. A 200-point favourite is expected to score 76% — three points in four, not "wins every game." Losing to someone 200 points below you is not evidence that your rating is fake; it is an event the system already budgeted for.

Note also that expected score is not win probability. A 0.76 expectation could be 76 wins and 24 losses, or 60 wins, 32 draws and 8 losses. The formula does not care which mix produced the total — which is why one scale serves blitz, where draws are rare, and classical, where they are common.

The K-Factor: How Fast Ratings Move

Once you know the expected score, the update is trivial:

New rating = Old rating + K x (Actual score - Expected score)

K is the most a single game can move you — the system's confidence dial. A large K says "we are not sure what you are, react hard to new evidence"; a small K says "we have plenty of data on this player, do not overreact to one bad night."

A worked example: you are 1500, your opponent 1700, your K is 20.

E = 1 / (1 + 10^(200/400)) = 0.24

You win:  1500 + 20 x (1 - 0.24)   = 1500 + 15.2  -> 1515
You draw: 1500 + 20 x (0.5 - 0.24) = 1500 + 5.2   -> 1505
You lose: 1500 + 20 x (0 - 0.24)   = 1500 - 4.8   -> 1495

When both players share a K value, your opponent moves by exactly the same amount in the opposite direction: Elo is zero-sum, points are transferred rather than created. When their K-factors differ — a fast-improving junior against a veteran on the lowest K — the transfer is not symmetric and the pool gains or loses a few points. Over millions of games, that is one mechanism behind the long-running arguments about rating inflation.

FIDE uses a small set of K values: a high one for players new to the rating list until they complete a set number of rated games and for juniors below a rating threshold, a middle one for established players, and the lowest for anyone who has ever crossed a high rating threshold. The exact figures live in the FIDE handbook and have been revised more than once, so check them there rather than trusting any article, this one included. FIDE also caps the rating difference used in the calculation at 400 points, so a huge mismatch is computed as if the gap were exactly 400.

Why Your Gains Shrink as You Approach Your True Strength

This is the part that feels unfair and is actually the system working correctly. Suppose your true strength is 1600 but you are rated 1300. Every game, the formula expects you to score far less than you really do, so almost every result is a positive surprise and your rating climbs fast. As it climbs, the expectations climb with it. Near 1600 the system is right about you, the surprises cancel out, and your rating stops moving.

That is equilibrium, not a plateau in the skill sense. Your rating settles where wins and losses balance and stays there until your actual playing strength changes — so playing more games at a settled rating does nothing. If you are stuck, the fix is diagnostic rather than volumetric; see breaking chess rating plateaus for what typically limits players at each band.

The same mechanism explains the mirror-image complaint, "I lost 200 points in a week." Elo has no memory and no floor of merit: a bad run is treated as new evidence, and if your K is high the correction is fast. It corrects back just as fast when the bad run was noise rather than signal.

Rating Deviation, Glicko and Glicko-2

Elo has a real weakness: it treats every rating as equally trustworthy. A player with 5 games and a player with 5,000 are both just a number, and someone returning after three years away is assumed to be exactly as strong as the day they left.

Mark Glickman's Glicko system fixes this by storing a second number alongside the rating: the rating deviation (RD), an uncertainty estimate. A low RD means "we are confident about this number"; a high RD means "this is a guess." Roughly, rating − 2×RD to rating + 2×RD is where the system believes your true strength lies with about 95% confidence. A 1600 with an RD of 45 is genuinely a 1600; a 1600 with an RD of 200 might be anything from 1200 to 2000.

RD then does two jobs:

  • It scales the update. A high RD behaves like a large K — your first games move your rating enormously, then the movement damps down as RD falls. This is why new accounts swing hundreds of points and settled accounts crawl.
  • It grows back during inactivity. Every rating period you sit out, RD increases, because the system is honestly less sure about you than it was. Return after two years and your first few games move you fast again.

Glicko-2 adds a third number, volatility, tracking how erratic your results have been: consistent players get a stable rating, wildly swinging players get a system that adapts faster to them specifically.

Most modern servers use a Glicko-family system rather than plain Elo. Lichess uses Glicko-2, seeds every new account at 1500 with a deliberately large deviation, and marks a rating provisional (with a ?) until the deviation falls below its threshold; Chess.com uses a Glicko-style system of its own. The upshot is the same everywhere: your first ten or twenty games on any site are calibration, not achievement.

Why Online Ratings and FIDE Ratings Differ

Players constantly ask for a conversion — "what is my 1700 rapid in FIDE terms?" There is no honest answer, and the reasons are structural.

Different pools. A rating is only meaningful relative to the population it was earned against. FIDE's pool is people who travel to rated over-the-board tournaments; an online pool includes millions of casual players who never studied an opening. Two differently composed pools assign different numbers to the same strength, and no formula bridges them reliably.

Different anchors. Because Elo measures differences, a pool's absolute level depends on where it was pinned at the start and how it has drifted since. Lichess seeding everyone at 1500 and a federation starting beginners near its rating floor produce scales that were never aligned to begin with.

Different time controls. FIDE maintains separate standard, rapid and blitz lists, and online sites rate bullet, blitz, rapid and classical separately too. A player's bullet and classical strengths can diverge by hundreds of points, and increment versus sudden death changes results again, as our guide to using a chess clock explains.

Different conditions and cadence. Online games have no arbiter, an instant resign button, frequent distraction, and a pool containing some cheating and some sandbagging; over-the-board classical games have tournament conditions, a scoresheet and no escape. FIDE also publishes lists monthly, so your official number lags your form, while online ratings update game by game and feel far more volatile than they are. For how the two big servers compare, see Lichess vs Chess.com.

The only sound statement is a relative one: within a single pool, a higher number reliably predicts a better player. Across pools, it predicts nothing.

What the Numbers Mean: A Skill Ladder You Can Test

Rating bands are usually described in adjectives — "beginner", "club player", "expert" — which tells you nothing you can act on. It is more useful to ask what a player at each level can reliably do at the board. Every position below is playable; use them as self-checks rather than labels.

Roughly under 1000: nothing hangs, and basic mates get delivered

Here the rating measures almost one thing: how often you leave something en prise, and whether you can finish a completely won game. The commonest way a beginner throws a win away is failing to convert king and rook against a lone king.

King and rook against a bare king. If you cannot force mate here inside fifty moves, every won endgame you reach is at risk. Play this position →

The technique is the box: shrink the area the enemy king can occupy, use your own king for opposition, mate on an edge. Our king and rook checkmate walkthrough covers it move by move.

Roughly 1000 to 1400: the standard mating patterns are recognised

Games now stop being decided by one-move blunders and start being decided by short tactics. The back rank is the classic — the mate everyone learns by losing to it twice.

White to move mates in one with Rd8#. The pawns that shelter Black's king also trap it — this is why players give themselves luft. Play this position →

This is also when the f7 square starts to matter. In the Italian Game, White piles two attackers onto Black's weakest point:

1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5
The bishop on c4 and the knight on g5 both hit f7. Black must find 4...d5 rather than the natural-looking developing moves. Play this position →

A 1200 usually knows this position exists; a 1500 knows the answer and why the tempting alternatives fail. That gap — recognition versus understanding — is most of what those 300 points measure, and drilling the standard tactical motifs is the fastest way to close it.

Roughly 1400 to 1800: king and pawn endings are calculated, not guessed

Now the rating starts measuring endgame technique and the ability to calculate a forced line to the end. Opposition is the gateway concept.

Black to move must step aside, and White's king takes the key square — White wins. With White to move, it is a draw. One tempo decides the whole game. Play this position →

If you can explain why the side to move loses here, you understand opposition — and a whole class of pawn endings becomes arithmetic instead of hope.

Roughly 1800 to 2200: theoretical endgames are known by name

At candidate-master strength, players recognise the standard rook endings rather than calculating them from scratch. The Lucena position is the archetype: pawn on the seventh, defending king cut off, and a winning method known for centuries.

The Lucena position. White wins by building a bridge with the rook on the fourth rank to shelter the king from checks. Play this position →

Our guide to the Lucena position covers the bridge technique, and improving your endgame gives a study order. Above 2200 the ladder meets the formal title system, which has rules of its own.

FIDE Titles: GM, IM, FM, CM and the Women's Titles

FIDE awards lifetime titles that, unlike a rating, can never be lost — once earned, a title is held permanently even if the player's rating falls or they stop playing. The lower titles are rating-only: reach the required number at any point and apply. The top two additionally require norms, certified high-level performances in qualifying tournaments.

| Title | Rating requirement | Norms required | | --- | --- | --- | | Grandmaster (GM) | 2500 | 3 | | International Master (IM) | 2400 | 3 | | FIDE Master (FM) | 2300 | none | | Candidate Master (CM) | 2200 | none | | Woman Grandmaster (WGM) | 2300 | 3 | | Woman International Master (WIM) | 2200 | 3 | | Woman FIDE Master (WFM) | 2100 | none | | Woman Candidate Master (WCM) | 2000 | none |

Two clarifications that come up constantly:

  • The rating does not have to be maintained. A player who touches 2500 once, ever, has satisfied that half of the GM requirement permanently.
  • The women's titles are additional, not a substitute. Women compete for and hold the open titles on exactly the same terms; the WGM/WIM series exists alongside them. Judit Polgár held the GM title.

What a Norm Requires

A norm is a certified performance in a single tournament, and the requirements are deliberately hard to meet by accident. Broadly, a GM norm requires:

  • A qualifying event — usually at least nine rounds, at a slow enough time control, in a FIDE-rated tournament registered for norms in advance.
  • A strong, international field. A minimum proportion of opponents must be titled, a minimum number must be GMs, and they must come from more than one federation. You cannot earn a norm off your clubmates.
  • A performance rating of at least 2600 across the qualifying games. For an IM norm the threshold is 2450.

The exact composition rules — rounds, foreign opponents, titled players, and how the counts change for shorter events — are set out in the FIDE handbook and revised periodically, so anyone actually chasing a norm should read the current regulations rather than any summary, this one included. Three norms plus the rating is the standard route but not the only one: certain championship results confer a title outright, the World Junior Championship winner being awarded the GM title directly.

Performance Rating: the Number a Norm Is Measured In

A tournament performance rating (TPR) answers "what rating would produce this score against this field?" Take the average rating of your opponents and add a bonus or penalty derived from your percentage score, using a table that is essentially the expected-score curve read backwards. Score 50% and your performance equals the field average; score 76% and you performed roughly 200 points above it — exactly the number in the table earlier. A rough informal shortcut is average opponent rating + 400 × (wins − losses) ÷ games; it drifts at extreme scores and is not what FIDE uses for titles, but it is fine for estimating your own weekend.

TPR is also the honest way to read a single event. A 1900 who performs at 2200 in one swiss has not become a 2200 — one tournament is a tiny sample, which is precisely the uncertainty Glicko's rating deviation exists to express.

Where the Grandmaster Title Came From

"Grandmaster" was used informally for the world's strongest players for decades before it meant anything official. A widely repeated story credits Tsar Nicholas II with conferring the title on the five finalists of the 1914 St Petersburg tournament — Lasker, Capablanca, Alekhine, Tarrasch and Marshall — but historians have found no contemporary evidence for it, so treat it as legend.

The title became official in 1950, when FIDE formalised its title system and awarded the GM title to an inaugural group of 27 players. Their number has grown a great deal since, driven by more international tournaments, better training and engine preparation, but still amounts to a tiny fraction of rated players. The youngest ever, Abhimanyu Mishra, earned it at twelve and Magnus Carlsen at thirteen — outliers, not the pattern.

Four Misconceptions Worth Dropping

  1. "My rating is unfair — I lost to a lower-rated player." The formula assigned that outcome a probability, and it was not small. One result is not evidence.
  2. "Playing more games raises my rating." Only if your strength has outgrown your number. At equilibrium, more games produce more variance, not more points.
  3. "1500 here equals 1500 there." Different pools, anchors and populations. The number does not travel.
  4. "Rating measures how much I know." It measures results. Someone who has read ten opening books but hangs a piece every long game rates below someone who has read none and does not. The reliable way up is to analyse your own games, remove the errors you actually make, and play by sound opening principles rather than memorised lines.

Practise the Positions

Reading about a rating system does not move one. The positions above are the concrete checkpoints behind the numbers — the king and rook mate, the back rank, the f7 attack, the opposition, the Lucena bridge — and each has a "Play this position" link that loads it straight onto the free board on LocalChess.

Play them against the engine until the technique is automatic rather than remembered. That is the part that changes your strength; the rating follows on its own.