JoSAA College Predictor 2027

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How the algorithm works (Adaptive Sigmoid)

Our algorithm uses an adaptive sigmoid function with dynamic steepness (K). The steepness scales with the closing rank: tight cutoffs → steep curve, loose cutoffs → wider buffer.

Dynamic Steepness (K) For JEE Advanced (IITs): K = 7 + 5·e^−CR/3000
For JEE Mains (NITs+): K = 5 + 7·e^−CR/15000
At tight cutoffs (IIT Bombay CS, ~100), K≈12 → very steep. At loose cutoffs (GFTI, ~150K), K≈5 → wide buffer.

Sigmoid Score Score = 98 / (1 + e^{K·(ratio−1)}) + 2, where ratio = your rank ÷ closing rank. Ratio < 1 = better than cutoff. Ratio > 1 = worse.

YoY Trend Adjustment Weighted by data confidence. Opening trend → bonus. Tightening → penalty.

Slide Projection When latest data round is behind your target round, closing ranks are projected forward using historical slide multipliers.

📖 Example: Rank 5,000 · IIT Program · Cutoff 3,000

K (adaptive)7 + 5·e⁻¹ = 8.8

Ratio (5000 ÷ 3000)1.67

Sigmoid98/(1+e^8.8×0.67)+2 ≈ 2.3%

Final~3% Reach

📖 Example: Rank 45,000 · NIT Program · Cutoff 50,000

K (adaptive)5 + 7·e^−3.33 = 5.25

Ratio (45k ÷ 50k)0.90

Sigmoid98/(1+e^{5.25×(−0.1)})+2 ≈ 63%

Final~63% Good

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JoSAA College Predictor 2027

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