How Elo Ratings Work

Why does beating a stronger player earn 15 points while beating a weaker one earns only 5? The answer sits inside one short formula. A 200-point rating gap gives the stronger player an expected score of about 0.76. The Elo system compares that prediction with the real result, then moves both ratings by the surprise.

What Does an Elo Rating Actually Measure?

An Elo rating measures your strength compared with the other players in the same pool. It is not a score of your moves. A rating of 1500 only means something next to the ratings of the people you play.

The system is named after Arpad Elo, a physics professor and chess master. The United States Chess Federation adopted his ideas in 1960, and FIDE, the world chess federation, followed in 1970. His key idea was to treat each game as a test of a prediction.

Before a game, the rating gap predicts how the players should score. After the game, ratings move toward whatever actually happened. Players who keep beating predictions rise, and players who keep falling short drop. Over many games, the numbers settle near each player’s true level.

The system is also zero-sum when both players use the same K-factor. The points one player gains are exactly the points the other player loses.

How Is the Expected Score Calculated?

You find the expected score from the rating gap with E = 1 / (1 + 10^((Rb – Ra)/400)). Here Ra is your rating and Rb is your opponent’s. The result always lands between 0 and 1.

Then the update rule does the rest: R’ = R + K x (S – E). S is your actual score, so a win counts 1, a draw 0.5 and a loss 0. The FIDE rating rules use the same 1, 0.5 and 0 scoring.

The number 400 sets the scale. Each 400 points of advantage makes your expected score 10 times your opponent’s. Equal players each expect 0.5, and a 200-point favorite expects about 0.76.

FIDE rates games from its own lookup table, rounded to two decimals. It matches the formula closely up to 300 points, then drifts slightly, as the 400-point row shows.

Scoring a 1400 vs 1200 Game

Our calculator’s own example pairs a 1400 player with a 1200 opponent at K = 20. Walk through it step by step.

Step 1: The Prediction

The gap is 200 points in your favor. Plug in: E = 1 / (1 + 10^(-200/400)) = 1 / (1 + 0.316) = 0.7597. Your opponent’s expected score is the rest, 0.2403.

Step 2: The Three Possible Results

• You win. Change = 20 x (1 – 0.7597) = +4.8, so you move to 1405.
• You draw. Change = 20 x (0.5 – 0.7597) = -5.2, so you drop to 1395.
• You lose. Change = 20 x (0 – 0.7597) = -15.2, so you fall to 1385.

Only the gap matters, not the rating level. A 1600 player facing a 1400 player gets exactly the same numbers. For the underdog, every change flips sign: an upset win earns +15.2 and a draw earns +5.2.

How Much Does the K-Factor Change Things?

The K-factor is the most points one game can move you. Beating an equal player earns exactly half of K, so 20 points at K = 40, 10 at K = 20 and 5 at K = 10.

FIDE’s Three Values

FIDE rules set K = 40 for new players until they complete 30 games. Juniors also keep 40 through the year they turn 18, while rated under 2300. Most other players use 20 until they reach 2400. After that, K drops to 10 for good, even when the rating later dips below 2400.

Two Less Obvious Rules

FIDE also caps busy months. When K times the number of games in a rating period tops 700, K shrinks to fit. A K = 40 junior with 20 games gets K = 35, since 35 x 20 = 700.

Mixed K-factors also break the zero-sum balance. A K = 40 junior rated 1400 who beats a K = 20 adult rated 1600 gains 30.4 points. The adult loses only 15.2.

Five Common Rating Misreadings

Most rating confusion comes from reading the numbers too literally. These five mix-ups show up again and again.

• Treating E as a pure win chance. Expected score equals your win chance plus half your draw chance. A 0.76 does not mean you win 76 games in 100. Our guide on how probability differs from odds explains the “10 to 1” reading of a 400-point gap.
• Forgetting that draws count. A draw is worth 0.5, so a draw against a stronger player still gains points. The favorite in a draw loses 5.2 at a 200-point gap.
• Expecting big gains from easy wins. At a 400-point gap, a win earns the favorite just 1.8 points at K = 20. Beating much weaker players barely moves you.
• Ignoring the 400-point rule. Since 1 October 2025, FIDE counts any gap over 400 as exactly 400 for players rated below 2650. A 2000 player facing a 1500 player is scored as a 400-point gap.
• Comparing ratings across pools. A 1500 in one league and a 1500 on a website are not the same strength. Each pool sets its own scale.

Where Else Does Elo Work Beyond Chess?

Elo works in almost any head-to-head contest with a clear winner and loser. Versions of it rate players in table tennis, Scrabble, football, basketball, board games and competitive video games.

The core stays the same everywhere: predict a score, compare it with the result, then adjust. Some fields tweak the details. Certain versions also count the margin of victory, such as a big or small win, not only the result.

Where Plain Elo Falls Short

Plain Elo treats every rating as equally reliable. Statistician Mark Glickman notes that a 1700 player who beats another 1700 gains 16 points under the old US Chess Federation system. That happens whether either player is new or has played for years.

His Glicko system adds a ratings deviation that tracks uncertainty. A high deviation means a rating is still unreliable, so it moves faster. Many online sites use Glicko variants for this reason.

The expected score itself is an average outcome, the same idea as in our guide to what expected value means. To check any single game, enter both ratings in our Elo rating change calculator and compare its answer with your official change.

Common Questions About Elo Ratings

References

This article is general games and statistics education. Examples use the classic single-game Elo formula; official bodies and online platforms may apply extra rules. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 27, 2026.