Expected value math for grant applications

Grant applications are expensive. A typical NIH Phase II or Direct to Phase II application consumes 250 to 400 person hours plus $15,000 to $40,000 in consultant fees, and winning it obligates you to five to eight percent of the award in administrative overhead for reporting, invention disclosures, and closeout if you have no grants office. A small team can afford a handful of serious applications a year. Choosing which handful is the single highest leverage decision in the whole process, and most teams make it by feel.

This is the rubric epiensos uses to make it with numbers. It is calibrated to the evidence in our research on NIH, NSF, DoD, and foundation programs, and it is deliberately simple enough to run on a card.

Step one, a fit score from 0 to 100

Eight factors, each scored 0, 5, or 10 against written anchors, each with a weight. The weights sum to 100.

FitScore = sum(weight_i * score_i) / 10

The range is 0 to 100. The anchors matter more than the weights. A team that argues about whether programmatic fit is a 5 or a 10 is having exactly the conversation the rubric exists to force. Professional capture teams use the same structure under the name bid and no bid matrix (Loopio go or no go template, Instrumentl on decision matrices).

Step two, convert fit to probability without pretending

The mistake most scoring tools make is to treat the fit score as a probability. A fit of 80 does not mean an 80 percent chance of an award. A fit of 80 at an institute that funds 5 percent of applications means something quite different from a fit of 80 at one that funds 28 percent.

So anchor to the base rate and let fit move you around it.

p_win = clamp(base_rate * multiplier(FitScore), 0.01, 0.75)
multiplier(FitScore) = 0.25 + 2.25 * (FitScore / 100)^2

The multiplier is 0.61 at a fit of 40, 1.06 at 60, 1.69 at 80, and 2.5 at 100. A mediocre application at a generous institute still does better than a strong application at a stingy one, which is what the data says. See How to choose an NIH institute for an SBIR application for the FY2024 base rates.

Then apply the documented adjustments:

• Multiply by 1.4 for a resubmission. Resubmissions fund at roughly 20 to 30 percent against about 11 percent for new R01 type applications, per a consultant estimate (Bouvier Grant Group).
• Multiply by 1.3 for a prior SBIR winner. Repeat applicants win at 1.3 to 1.5 times the rate of first timers across agencies (Granted AI).
• Multiply by 0.5 if the stage mismatch factor scored 3 or below. Proposing a feasibility study when you already hold pivotal data is the fastest way to a not discussed outcome.

The clamp between 1 and 75 percent is a humility setting. Nobody has a 90 percent grant.

Step three, expected value

EV = p_win * (Award_total * usable_fraction) - Cost_to_apply - p_win * Cost_of_compliance

• usable_fraction is 1 minus the share of the award that only reimburses overhead you would not otherwise spend, minus any cost share. For a company with real facilities and a 40 percent indirect rate it is usually 0.85 to 0.95.
• Cost_to_apply is internal hours at a loaded rate, plus consultants, plus the opportunity cost of the people who write it instead of doing their jobs.
• Cost_of_compliance is the post award administration: progress reports, financial reports, invention reporting, trial registration, and closeout. About 5 to 8 percent of the award for a small company without a grants office.

Step four, thresholds

• Go if EV is above zero, p_win is at least 0.12, and there is no eligibility blocker.
• Conditional if p_win is between 0.08 and 0.12. Proceed only if the application would be at least 70 percent reusable for another funder.
• No go otherwise.

The probability floor exists because expected value alone will tell you to buy lottery tickets. A 4 percent shot at $30 million has a fine EV and a terrible effect on a twelve person company that spends a quarter on it.

A worked example

A neuromodulation device company with a completed 264 participant randomized trial and a 510(k) pending is considering three routes.

NIH Direct to Phase II, NIDA assignment, HEAL aligned framing. Base rate 21 percent (NIDA SBIR Phase II, FY2024). Fit score 75, which gives a multiplier of about 1.5. Raw probability 0.32, capped by judgment at 0.30. Award $2.15 million, usable fraction 0.9, cost to apply $60,000, compliance $120,000.

EV = 0.30 * 1,935,000 - 60,000 - 0.30 * 120,000
   = 580,500 - 60,000 - 36,000
   = about +485,000

Go.

The same application, NINDS assignment. Base rate 9.7 percent. Fit stays 75, multiplier 1.5, probability about 0.15.

EV = 0.15 * 1,935,000 - 60,000 - 0.15 * 120,000
   = 290,250 - 60,000 - 18,000
   = about +212,000

Still a go, but less than half the value, and the reason is entirely the institute. Our research summary rounds this to plus $185,000 after judgment adjustments to the probability.

NSF SBIR Phase I. Base rate 14 percent. Fit about 45, because NSF funds high technical risk research and a device with pivotal style data is a stage mismatch. Multiplier about 0.71, probability about 0.09. The stage factor scored a 5 here, not low enough to trigger the halving. Award $305,000, usable fraction 0.9, cost to apply $25,000.

EV = 0.09 * 274,500 - 25,000 - 0.09 * 20,000
   = 24,705 - 25,000 - 1,800
   = about 0

No go, and p_win is under the conditional floor anyway. The only reason to write it is if you can carve out a genuinely new technical thrust, for example closed loop parameter optimization, which would move both fit and the stage factor.

What the numbers are for

The rubric is not a forecast. It is a way to make three things explicit and comparable: how well you fit, how crowded the door is, and what it costs to walk through it. When the decision is written down as numbers, the disagreement moves from should we apply to which factor did we score wrong, and that is a disagreement you can resolve with a phone call to a program officer.

It is also a way to learn. Every application in epiensos records the predicted probability at the time of approval. When the outcome comes back, the TALR learn step compares the prediction with the result, tags the reviewer critiques by criterion, and updates the funder model. Once a year the multiplier curve is recalibrated against the actual outcomes. The first two submissions are calibration investments, not failures (Granted AI on repeat applicants).

Where this lives in epiensos

The score endpoint and the match card show every factor score, the base rate used, the multiplier, the adjustments, the clamped probability, and the expected value with each cost input. The strictness slider sets a threshold on fit score and previews how many opportunities would queue, the sum of their ceilings, and the sum of ceiling times probability, which is the likely grant volume at that setting. Approve or decline from the card, and the reason you give when you decline feeds the next calibration.