Gacha Pull Success Rate Calculator
Estimate your success rate for obtaining a desired item or character in a gacha game based on pull rate, number of pulls, pity system strength, and resource availability.
Formulas Used
The Gacha Success Score is calculated using a weighted formula assessing pull rate, number of pulls, pity system strength, and resource availability.
- Base Success Probability:
\\[ P_{\text{base}} = 1 – (1 – \frac{R}{100})^N \\]
Where \\( R \\) is the pull rate (%) and \\( N \\) is the number of pulls. Calculates the probability of at least one success.
- Pull Rate Score:
\\[ R_{\text{score}} = \min\left(5, \frac{R}{2}\right) \\]
Normalizes pull rate to a 1–5 scale, capped at 5 for rates ≥ 10%.
- Pull Count Score:
\\[ N_{\text{score}} = \min\left(5, \frac{N}{100}\right) \\]
Normalizes number of pulls to a 1–5 scale, capped at 5 for ≥ 500 pulls.
- Raw Success Score:
\\[ S_{\text{raw}} = w_1 R_{\text{score}} + w_2 N_{\text{score}} + w_3 P + w_4 A \\]
Where:
- \\( R_{\text{score}} \\): Pull rate score
- \\( N_{\text{score}} \\): Pull count score
- \\( P \\): Pity system strength (1–5)
- \\( A \\): Resource availability (1–5)
- \\( w_1 = 5 \\): Weight for pull rate
- \\( w_2 = 5 \\): Weight for pull count
- \\( w_3 = 5 \\): Weight for pity system
- \\( w_4 = 5 \\): Weight for resources
- Gacha Success Score:
\\[ \text{GSS} = \max\left(0, \min\left(100, \frac{S_{\text{raw}} + 100 \cdot P_{\text{base}}}{2}\right)\right) \\]
Averages raw score and base probability (scaled to 0–100) to balance statistical and practical factors. Ratings: Low (0–25), Moderate (25–50), High (50–75), Very High (75–100).
Example Calculations
Example 1: Typical Gacha Scenario
Inputs: Pull Rate = 0.6%, Number of Pulls = 90, Pity System Strength = 4, Resource Availability = 3
Calculations:
- Base Success Probability: \\[ 1 – \left(1 – \frac{0.6}{100}\right)^{90} = 1 – (0.994)^{90} \approx 0.4173 \\]
- Pull Rate Score: \\[ \min\left(5, \frac{0.6}{2}\right) = 0.3 \\]
- Pull Count Score: \\[ \min\left(5, \frac{90}{100}\right) = 0.9 \\]
- Raw Success Score: \\[ 5 \cdot 0.3 + 5 \cdot 0.9 + 5 \cdot 4 + 5 \cdot 3 = 1.5 + 4.5 + 20 + 15 = 41 \\]
- Gacha Success Score: \\[ \frac{41 + 100 \cdot 0.4173}{2} \approx \frac{41 + 41.73}{2} \approx 41.37 \\]
- Rating: Moderate (25–50)
Result: Gacha Success Score: 41.4 (Moderate), Base Success Probability: 41.7%
Example 2: Low-Budget Player
Inputs: Pull Rate = 1%, Number of Pulls = 20, Pity System Strength = 1, Resource Availability = 1
Calculations:
- Base Success Probability: \\[ 1 – \left(1 – \frac{1}{100}\right)^{20} = 1 – (0.99)^{20} \approx 0.1821 \\]
- Pull Rate Score: \\[ \min\left(5, \frac{1}{2}\right) = 0.5 \\]
- Pull Count Score: \\[ \min\left(5, \frac{20}{100}\right) = 0.2 \\]
- Raw Success Score: \\[ 5 \cdot 0.5 + 5 \cdot 0.2 + 5 \cdot 1 + 5 \cdot 1 = 2.5 + 1 + 5 + 5 = 13.5 \\]
- Gacha Success Score: \\[ \frac{13.5 + 100 \cdot 0.1821}{2} \approx \frac{13.5 + 18.21}{2} \approx 15.86 \\]
- Rating: Low (0–25)
Result: Gacha Success Score: 15.9 (Low), Base Success Probability: 18.2%
Example 3: Whale Player
Inputs: Pull Rate = 2%, Number of Pulls = 200, Pity System Strength = 5, Resource Availability = 5
Calculations:
- Base Success Probability: \\[ 1 – \left(1 – \frac{2}{100}\right)^{200} = 1 – (0.98)^{200} \approx 0.982 \\]
- Pull Rate Score: \\[ \min\left(5, \frac{2}{2}\right) = 1 \\]
- Pull Count Score: \\[ \min\left(5, \frac{200}{100}\right) = 2 \\]
- Raw Success Score: \\[ 5 \cdot 1 + 5 \cdot 2 + 5 \cdot 5 + 5 \cdot 5 = 5 + 10 + 25 + 25 = 65 \\]
- Gacha Success Score: \\[ \frac{65 + 100 \cdot 0.982}{2} \approx \frac{65 + 98.2}{2} \approx 81.6 \\]
- Rating: Very High (75–100)
Result: Gacha Success Score: 81.6 (Very High), Base Success Probability: 98.2%
How to Use the Calculator
Follow these steps to estimate your gacha pull success rate:
- Enter Pull Rate: Input the drop rate (%) for the desired item/character (0.1–10%, e.g., 0.6% for a 5-star).
- Enter Number of Pulls: Input the number of pulls you plan to make (1–500, e.g., 90 for pity).
- Enter Pity System Strength: Rate the game’s pity system (1–5, 1 = weak/no pity, 5 = strong like guaranteed at 90 pulls).
- Enter Resource Availability: Rate your available resources (1–5, 1 = low gems, 5 = high gems).
- Calculate: Click “Calculate Gacha Success Score” to see the result.
- Interpret Result: The result shows a 0–100 score with a rating (Low: 0–25, Moderate: 25–50, High: 50–75, Very High: 75–100) and base success probability (%). If you see “Please fill in all fields,” ensure all inputs are valid.
- Share or Embed: Use the share buttons to post results on social media, copy the result, or get an embed code.
Note: This is a simplified model. Actual gacha outcomes depend on RNG, specific game mechanics, and banner details. Check game data for accurate rates.