Grant Success Probability Model
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Calculate the cumulative probability of securing at least one grant based on reviewer score distributions and a fixed number of submissions.
NOTEAbout This Model
## Calculate the cumulative probability of securing at least one grant based on reviewer score distributions and a fixed number of submissions. This model estimates **Cumulative Success Prob** based on uncertain inputs: Reviewer Avg Score, Reviewer Std Dev. Fixed values: Submission Count, Required Score. Run the simulation to see the distribution of possible outcomes.
CONSTANTRequired Score
7
The minimum score required for funding (on a 1-9 scale, lower is often better but here modeled as higher=better).
required_score
VARIABLEReviewer Avg Score
triangular(4.5, 5.5, 6.5)
Average reviewer scores typically center around the midpoint of the scale.
reviewer_avg_score
VARIABLEReviewer Std Dev
triangular(0.5, 1, 1.5)
Standard deviation of scores representing reviewer disagreement or scoring spread.
reviewer_std_dev
CONSTANTSubmission Count
3
Number of grant applications submitted.
submission_count
FORMULAZ Score
(required_score - reviewer_avg_score) / reviewer_std_dev
z-score of the required score relative to the distribution of reviewer scores.
z_score
FORMULAP Success
1 - normal_cdf(z_score)
Probability of a single grant submission being successful based on the score threshold.
normal_cdf
p_success
FORMULACumulative Success Prob
1 - pow(1 - p_success, submission_count)
Probability of getting at least one grant funded across all submissions.
cumulative_success_prob
OUTPUTCumulative Success Prob
cumulative_success_prob
Cumulative probability of receiving at least one grant across multiple submissions. Even with low per-application odds, submitting to several programs significantly improves overall chances.
What is Carlo?
Carlo is a visual tool for Monte Carlo simulation. Model uncertainty by dragging probability distributions, connecting them visually, and running thousands of scenarios instantly.