Sport & fitness
Elo rating change model
Explore expected scores and updates with your own scale and K factor.
A clear answer. Here’s how.
Expected score=1/[1+10^((opponent−your rating)/scale)]. Change=K×(score−expected), with scores 0, 0.5 or 1. Period mode uses one baseline for all expectations; sequential mode uses the latest model rating. Opponent ratings remain supplied values. No rating floors, federation rules, provisional treatment or official rating update is applied.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Starting rating
- 1500
- K factor
- 20
- Rating scale divisor
- 400
- Update timing
- One period: expected scores use starting rating
- CSV: Opponent rating,Score
Opponent rating,Score 1500,1 1600,0.5 1400,0
Example result
| Opponent rating | Score | Expected score | Model change | Cumulative model rating |
|---|---|---|---|---|
| 1,500 | 1 | 0.5 | 10 | 1,510 |
| 1,600 | 0.5 | 0.359935000197 | 2.80129999606 | 1,512.8013 |
| 1,400 | 0 | 0.640064999803 | -12.8012999961 | 1,500 |
Change 0. All expectations use the starting rating. No official rating rules applied.