Instrument № 2
Expected Score Calculator
What are my odds? The Elo system answers with one number: your expected score - points per game against this opponent, draws counted as half. Here it is from the official FIDE table and the exact curve.
Expected score (FIDE table 8.1.2)
- Difference D
- −200
- Logistic E
- 0.240
- Per game at K
- +5.2draw
The 400-point ladder
Your odds across the field.
Expected score against opponents from 400 below you to 400 above - the band the 400-point rule was written for. Your current pairing is highlighted.
| Opponent | D | FIDE table | Logistic curve | Points / 100 games |
|---|
The arithmetic
Where the number comes from.
Elo's model treats a rating difference as an odds ratio. Ten to one in your favour means 400 points; one to one means level. Formally, with D = your rating minus your opponent's, the expected score is read from FIDE's Table 8.1.2 - and the smooth curve underneath it is the logistic function[F1, W1]:
Expected score
E = 1 / (1 + 10(Ropp − Ryou)/400)
Worked check: 2000 vs 2200 → D = −200 → E = 0.24 (table) and 0.240 (curve). In 100 such games you'd bank about 24 points - likely a handful of wins cushioned by draws.
The table and the curve disagree only in rounding: FIDE publishes E in 0.01 steps, so at D = 400 the table reads 0.92 while the curve gives 0.909. For a single game the difference is hundredths of a point; over a career they are the same machine. When the gap exceeds 400, remember the guard-rail: for players rated below 2650 the difference is counted as exactly 400 for rating purposes (art. 8.3.1)[F1] - so a 2700-rated opponent is, to your rating, a 2400 one.
Turn this expectation into points: Elo change calculator · a whole cross-table: Performance rating calculator · the long climb: Rating goal planner