Circle Rating Calculator
Calculate how circle ratings are determined based on performance metrics, difficulty, and accuracy.
Calculation Results
How Are Circle Ratings Calculated? A Comprehensive Guide
Circle ratings in rhythm games like osu! are complex calculations that determine a player’s performance on a given beatmap. These ratings consider multiple factors including accuracy, combo, misses, difficulty modifiers, and the inherent challenge of the map itself. Understanding how these ratings are calculated can help players improve their scores and strategize their gameplay.
The Core Components of Circle Rating Calculation
The circle rating system primarily consists of these key components:
- Base Performance Value: Determined by the star difficulty of the map
- Accuracy Multiplier: Rewards higher accuracy with exponential scaling
- Combo Multiplier: Bonuses for maintaining high combos relative to the map’s maximum
- Miss Penalty: Significant deductions for missed notes
- Mod Multipliers: Adjustments based on gameplay modifiers
- Score Version: Different calculation methods between legacy and current systems
1. Base Performance Value
The foundation of any circle rating calculation is the base performance value, which is directly tied to the star difficulty of the beatmap. This value follows an exponential scale:
| Star Difficulty Range | Base Performance Value | Growth Factor |
|---|---|---|
| 0 – 2 stars | Linear growth (1:1) | 1.0x |
| 2 – 5 stars | Exponential growth begins | 1.05x – 1.2x |
| 5 – 7 stars | Steep exponential growth | 1.2x – 1.5x |
| 7+ stars | Very steep exponential growth | 1.5x – 2.0x |
For example, a 4-star map might have a base value of approximately 400, while an 8-star map could have a base value exceeding 2,000 due to the exponential scaling. This system rewards players for successfully completing more challenging maps.
2. Accuracy Multiplier
Accuracy plays a crucial role in circle rating calculations, with the multiplier following a non-linear scale that heavily rewards near-perfect performance:
| Accuracy Range | Multiplier (ScoreV2) | Effective Bonus |
|---|---|---|
| 90.00% – 94.99% | 0.5x – 0.8x | Minimal bonus |
| 95.00% – 97.99% | 0.8x – 1.1x | Moderate bonus |
| 98.00% – 99.49% | 1.1x – 1.4x | Significant bonus |
| 99.50% – 100.00% | 1.4x – 1.5x | Maximum bonus |
The accuracy multiplier is calculated using the formula:
AccuracyMultiplier = 1 + (0.5 * (Accuracy - 95) / 5) ^ 1.5 // For accuracies above 95%, with diminishing returns near 100%
3. Combo Multiplier
The combo system rewards players for maintaining long combos relative to the map’s maximum possible combo. The multiplier is calculated as:
ComboMultiplier = (PlayerCombo / MaxCombo) ^ 0.8 // The 0.8 exponent creates diminishing returns for very high combos
For example, achieving 90% of the maximum combo would give approximately a 0.93 multiplier (0.9^0.8 ≈ 0.93), while a full combo would provide the full 1.0x multiplier.
4. Miss Penalty System
Misses have a severe impact on circle ratings through two mechanisms:
- Direct Score Reduction: Each miss reduces the maximum possible score by a fixed percentage (typically 6-10% per miss depending on the scoring system)
- Combo Breaker: Misses reset the combo to zero, dramatically reducing the combo multiplier
The miss penalty formula in ScoreV2 is:
MissPenalty = 0.97 ^ NumberOfMisses // Each miss applies a 3% multiplicative penalty
5. Mod Multipliers
Gameplay modifiers (mods) adjust the final rating through multiplicative factors:
| Mod | Multiplier | Effect on Gameplay |
|---|---|---|
| NoFail | 0.90x | Prevents failing but reduces score potential |
| Easy | 0.50x | Larger circles, more forgiving timing |
| Hidden | 1.06x | Notes fade out before hitting |
| HardRock | 1.14x | Smaller circles, faster approach rate |
| DoubleTime | 1.30x | 30% faster song speed |
Mod multipliers are applied multiplicatively to the final score. For example, using HardRock and Hidden together would apply a 1.14 × 1.06 = 1.2084 multiplier.
6. Score Version Differences
The calculation method changed significantly between ScoreV1 (legacy) and ScoreV2 (current):
ScoreV1 Characteristics
- Linear accuracy scaling
- Less combo emphasis
- Harsher miss penalties
- Simpler mod interactions
- Max rating capped at ~500pp
ScoreV2 Characteristics
- Exponential accuracy scaling
- Strong combo rewards
- Diminishing returns on perfection
- Complex mod interactions
- No theoretical maximum
Practical Example Calculation
Let’s calculate a sample circle rating for:
- 6-star map (base value: ~1,200)
- 98.5% accuracy
- 95% max combo (1,900/2,000)
- 1 miss
- HardRock mod (1.14x)
- ScoreV2 system
Step-by-step calculation:
- Base value: 1,200
- Accuracy multiplier: 1 + (0.5 × (98.5 – 95)/5)^1.5 ≈ 1.32
- Combo multiplier: (1900/2000)^0.8 ≈ 0.97
- Miss penalty: 0.97^1 ≈ 0.97
- Mod multiplier: 1.14
- Final calculation: 1200 × 1.32 × 0.97 × 0.97 × 1.14 ≈ 1,650
Advanced Considerations
Several nuanced factors can further influence circle ratings:
- Aim vs. Tap Difficulty: Maps with complex slider patterns may receive additional hidden bonuses in certain scoring systems
- Approach Rate: Higher AR maps can slightly increase the base performance value
- Map Length: Longer maps tend to have higher maximum potential ratings due to sustained performance requirements
- Object Density: Maps with higher note density (notes per second) receive additional weighting
- Player Rank: Some systems apply small bonuses for top global rankings on a map
Common Misconceptions About Circle Ratings
Despite the transparency of the calculation system, several myths persist:
- “Full combo always gives maximum rating”: While full combos are important, accuracy and difficulty modifiers often have greater impact at higher levels
- “Higher star rating always means better score”: A 99% accuracy on a 5-star map can outscore a 95% accuracy on a 6-star map
- “Mods always increase your score”: Some mods like Easy significantly reduce potential ratings despite making the map easier
- “The system is completely objective”: While mostly mathematical, some subjective elements exist in difficulty rating maps
Strategies for Maximizing Circle Ratings
Players looking to optimize their ratings should consider these strategies:
- Focus on accuracy: The exponential scaling means improving from 98% to 99% can be worth more than playing a slightly harder map
- Prioritize combo maintenance: Even one miss can cost 10-15% of your potential score
- Choose mods wisely: HardRock and DoubleTime offer the best risk/reward ratios for skilled players
- Play to your strengths: Some players excel at high-speed maps while others perform better on technical patterns
- Practice consistency: The rating system heavily rewards consistent high performance across multiple plays
The Mathematics Behind the System
The complete ScoreV2 formula can be expressed as:
FinalRating = BaseValue × AccuracyMultiplier × ComboMultiplier × MissPenalty × ModMultiplier Where: AccuracyMultiplier = 1 + (0.5 × (Accuracy - 95) / 5) ^ 1.5 ComboMultiplier = (PlayerCombo / MaxCombo) ^ 0.8 MissPenalty = 0.97 ^ NumberOfMisses ModMultiplier = Product of all individual mod multipliers
For those interested in the complete technical implementation, the official osu! wiki provides detailed documentation on the performance points system, including edge cases and special calculations for different game modes.