How Accurate Are the Predictions?

Our rank predictions are based on statistical sampling and become more accurate as more people submit their data. To understand this, let’s break down three important concepts:

Confidence Level

The confidence level represents how certain we are that the true value lies within our predicted range. A 99% confidence level means that if we repeated this prediction process many times, the true rank would fall inside the predicted interval 99 out of 100 times.

Mathematically, we use a z-score corresponding to the confidence level. For 99% confidence: $$ z = 2.576 $$

Margin of Error

The margin of error (MOE) tells us how far off our prediction could be from the true value due to sampling variability.

It is calculated as: $$ \text{MOE} = z \cdot \sqrt{ \frac{p(1 - p)}{n} } \cdot \sqrt{ \frac{N - n}{N - 1} } $$ where:

• z is the z-score (2.576 for 99% confidence),
• p is the estimated proportion (assumed 0.5 for maximum variability),
• n is the number of samples (i.e., number of students who submitted data),
• N is the total population size (approx. 100,000 JEE candidates).

Confidence Interval

The confidence interval is the range within which we expect the true rank to lie. It's calculated as:

Confidence Interval = Predicted Rank ± MOE

The total width of the interval is 2 × MOE.

More Data = More Precision

As more students enter their data, the sample size n increases. Since the margin of error decreases with increasing n, our confidence interval becomes narrower. In simple terms:

More participants ⇒ Smaller margin of error ⇒ More precise predictions.

For example, in our system:

• With 500 users: margin of error ≈ ±5%
• With 1,000 users: margin of error ≈ ±1.6%
• With 10,000 users: margin of error ≈ ±0.5%

So keep sharing! The more data we gather, the better and sharper the predictions for everyone

Also see them joining the graph live !