Rating in chess: systems, concepts, and calculations
Rating
Definition
A rating in chess is a numerical estimate of a player’s playing strength relative to other players in the same rating pool. It changes as you play rated games: winning typically increases your rating, losing decreases it, and drawing against stronger opponents can raise it. Ratings are most often computed by statistical systems such as Elo or Glicko, which predict results and adjust ratings based on performance.
How Ratings Are Used
Tournament logistics
Organizers use ratings to seed players and create fair pairings. In Swiss-system events, early rounds pair players with others of similar score and often similar rating. Many events have rating-restricted sections (e.g., U1600, U2000) to group players by strength.
Titles and norms
FIDE titles are connected to ratings. Examples:
- Candidate Master (CM): rating threshold of 2200
- FIDE Master (FM): rating threshold of 2300
- International Master (IM): requires norms and reaching 2400 at some point
- Grandmaster (GM): requires norms and reaching 2500 at some point
Time controls
Most organizations track separate ratings by time control (Classical/Standard, Rapid, Blitz). Online platforms also track Bullet and Chess960 separately. Ratings from different pools are not directly comparable.
Common Rating Systems
Elo
The most widespread system. Each game produces an expected score based on the rating difference; the rating then updates by a factor K times the difference between the actual and expected score.
Glicko and Glicko-2
Enhancements over Elo used by many online sites. Each player has a rating, a rating deviation (RD, indicating uncertainty), and in Glicko-2 a volatility parameter. Ratings of players with high RD change faster, allowing new or inactive players’ ratings to stabilize more quickly.
Federation variations
Federations like FIDE and USCF use Elo-type formulas with their own parameters (K-factors, floors, publication schedules). Exact rules change occasionally; always check the current handbook for specifics.
Key Concepts
Expected score
Under Elo, if player A (rating R_A) faces player B (rating R_B), A’s expected score is E_A = 1 / (1 + 10^((R_B − R_A)/400)). The expected score for B is 1 − E_A.
K-factor
K controls how fast ratings move. Bigger K means faster changes. Typical FIDE values include K=40 for new players (few rated games), K=20 for most established players, and K=10 for long-established players rated 2400+ (subject to periodic updates).
Provisional ratings
New players have high uncertainty. Systems reflect this with higher K or higher RD; early results can produce large swings.
Rating floors and protection
Some systems set minimum floors to prevent severe drops (e.g., USCF rating floors based on past achievements). FIDE currently publishes ratings down to 1000; older floors were higher.
Inflation and deflation
Over long periods, average ratings in a pool can drift. “Inflation” means numbers creep upward; “deflation” means they sink. This complicates direct comparisons across eras or different pools.
Performance rating
A performance rating estimates how strongly you played in an event. If your opponents’ average rating is R_avg and your score percentage is p, a common Elo-consistent approximation is: Rp ≈ R_avg − 400·log10((1 − p)/p). Example: scoring 75% (p = 0.75) against R_avg = 2000 gives Rp ≈ 2000 + 190 = 2190.
Examples and Calculations
Upset expectations
Suppose an 1800 plays a 2000. Rating difference is −200.
- Expected score for 1800: E = 1 / (1 + 10^(200/400)) ≈ 0.240
- With K = 15:
- Win: Δ ≈ 15 × (1 − 0.240) = +11.4
- Draw: Δ ≈ 15 × (0.5 − 0.240) = +3.9
- Loss: Δ ≈ 15 × (0 − 0.240) = −3.6
Swiss seeding by rating
In round 1 of a 32-player Swiss, seed 1 (rating 2450) is typically paired with seed 17 (rating 2050), seed 2 (2400) with seed 18 (2040), and so on—ratings shape these initial pairings, while later rounds pair by score.
Estimating strength from ranges
- ~1000–1400: developing fundamentals; frequent blunders
- ~1500–1800: solid tactics; basic plans; fewer blunders
- ~1900–2100: “expert” level; consistent calculation and endgame technique
- ~2200: master level (national master in some federations)
- 2400+: international master strength and above
Ranges vary by pool; these are rough guides.
Strategy and Practical Advice
Using rating to improve
- Set process goals tied to your rating phase: early on, play many games to stabilize; later, focus on study/play balance.
- Choose opposition wisely: mixing “play up” games for growth with “even” games for confidence and norm chances.
- Track your weak phases by time control—blitz vs classical issues differ.
- Don’t chase numbers: sustainable improvement often outpaces “rating protection.”
Converting between pools
Do not equate numbers from different systems (e.g., FIDE Classical vs. an online Blitz rating). Pools have different opponents, K-factors, and volatility.
Historical Notes
From Harkness to Elo
Arpad Elo’s system replaced earlier methods in the 1960s (USCF) and was adopted by FIDE in 1970, enabling consistent international comparisons.
Famous peaks
- Garry Kasparov reached 2851 FIDE Classical in 1999, long the all-time record.
- Magnus Carlsen set the current FIDE peak at 2882 (2014) and sustained 2800+ for over a decade.
Context matters: pool composition and activity levels influence rating landscapes across eras.
Interesting Facts and Anecdotes
- A single big upset can net fewer points than a string of solid draws if your expected score was already high—K and expectations rule everything.
- “Sandbagging” (intentionally lowering rating to enter lower sections) is policed by federations and organizers; ethics and rules matter.
- Online Glicko-2 with high RD can yield 50+ point swings in a short session; as RD shrinks, ratings stabilize and move more slowly.
- Norm hunters sometimes craft tournament schedules to maximize expected score versus sufficiently high-rated fields to meet norm criteria.
Visualizing Your Progress
Track your rating trends over time to spot plateaus and breakthroughs.
• Peak: