Score
0.46
Kelly
3.5%
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Master's degree
Education / degree · 24-month horizon
Score 0.46 · risk-adjusted return too thin; gather information first (WATCH)
With the resources you committed ($193,100 of equivalent capital) over a 24-month horizon, the prior win rate is 57.0%, the payoff ratio is b=0.80, giving an expected value of EV=$5,351 and a risk-adjusted return of RAROC=0.05. The expected value is positive, but the return is thin relative to the risk you would carry. The Kelly-optimal stake of 3.5% sits inside the 20% risk budget for your Working professional profile.
Two years of in-state public tuition plus two years of forgone bachelor's-level earnings, which dominate everything else. The win rate is FREOPP's share of master's programmes with a positive net lifetime return — the other 43% lose money.
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The three numbers
Win rate, payoff ratio and expected value decide most of the recommendation; Kelly, RAROC and score turn them into an action.
Win rate p
57.0%
Prior probability of success
Payoff ratio b
0.80 ×
b = E[win] / E[loss]
Expected value
$5,351
EV = capital × (p × b − (1 − p))
Kelly
3.5%
(b·p − (1 − p)) / b
RAROC
0.05
EV / (capital × σ)
Score
0.46
score = p × b
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What you are committing
Equivalent capital $193,100, converted from five kinds of resource.
This opportunity carries $193,100 of equivalent capital. The largest single component is opportunity cost, at 85% of the total ($164,100). Opportunity cost is the return on what you gave up, and it is routinely underestimated. If this fails you pay twice: the loss itself, plus the alternative you never ran.
How non-cash resources are priced
One hour of your own time is priced at $38 and one person-month of hired labour at $8,080. These are market shadow prices, not what you personally earn; changing them changes only the scale, not the ranking.
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How this compares with the category
Your assumptions against the Beta(α, β) prior for this kind of decision.
Category mean win rate
56.7%
Beta(α=17, β=13)
Category payoff P50
1.50 ×
P90 4.70×
Your win rate of 57.0% is in line with the category baseline of 56.7%. The payoff ratio of 0.80× is below the baseline median of 1.50×, which typically weighs heavily on the expected value. Baseline source: FREOPP lifetime return by programme (US-EDU-12..17) + BLS CPS earnings by attainment (US-EDU-06..09).
Baseline source: FREOPP lifetime return by programme (US-EDU-12..17) + BLS CPS earnings by attainment (US-EDU-06..09)
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Action plan
Sized to the risk budget of your profile: Working professional.
Recommendation: WATCH — win rate and payoff ratio alone make the expected value positive, but RAROC or Kelly is too low for the risk you are taking. Buy information or shrink the experiment before committing.
- Choosing not to commit today is not the same as missing out. The most expensive decision is usually going all-in on incomplete information.
- This week, write down the two unknowns that matter most (the tornado chart below ranks them) and answer them for under $500 and 20 hours.
- If you can lift RAROC by 50% within four weeks, come back and recompute. Otherwise keep watching.
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Sensitivity analysis
How much the expected value moves when each variable is swung ±20%, ranked by impact. The top two are the ones worth researching before you commit.
- · The tornado analysis identifies Win rate (p) as the variable the conclusion is most sensitive to: a ±20% swing moves the expected value by $79,380. Spend your research budget here first.
- · The second most sensitive variable is Payoff ratio (b) (expected value swings $35,354); the remaining inputs matter markedly less.
- · A quick test for whether to keep researching: buy the information only if it costs less than one fifth of the expected-value swing it would resolve.
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Monte Carlo distribution
10,000 simulated outcomes, seed demo-graduate-school — rerunning with the same inputs gives the same distribution.
P5
-$276,559
Median (P50)
$76,388
P95
$348,872
Probability of a positive outcome
56.5%
Across 10,000 Monte Carlo runs: P5 = -$276,559, P50 = $76,388, P95 = $348,872, and the probability of a positive outcome is 56.5%. The distribution is roughly symmetric — gains and losses are balanced.
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Scenarios
Bull, base and bear, moving win rate and payoff ratio together by ±15%.
Scenario analysis (win rate and payoff ratio moved together by ±15%): bull = $50,365, base = $5,351, bear = -$35,686. The $86,050 gap between bull and bear measures how fragile your assumptions are — the wider it is, the more due diligence pays for itself.
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Counterfactual matrix
What the expected value becomes at other combinations of win rate and payoff ratio — how wrong your assumptions can be before the answer changes.
The counterfactual grid shows that expected value turns non-negative once the win rate reaches 20%, or once the payoff ratio reaches 0.5×. Treat those two lines as the minimum bar any further evidence has to clear.
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Assumptions
Every input behind the numbers above, in one place.
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Reproducibility appendix
Everything needed to recompute this report yourself.
Core formulas
EV = capital × (p × b − (1 − p)) f* = (b·p − (1 − p)) / b RAROC = EV / (capital × σ)Python
from models.feasibility_model import expected_value, kelly_fraction, raroc, go_no_go
p, b, sigma, capital = 0.57, 0.803, 0.6, 193100
ev = expected_value(p, b, capital)
kelly = kelly_fraction(p, b)
rr = raroc(ev, capital, sigma)
print(ev, kelly, rr, go_no_go(ev, kelly, 0.20, rr))TypeScript
import { expectedValue, kellyFraction, raroc, goNoGo } from "decision-lab/lib/feasibility";
const p = 0.57, b = 0.803, sigma = 0.6, capital = 193100;
const ev = expectedValue(p, b, capital);
const kelly = kellyFraction(p, b);
const rr = raroc(ev, capital, sigma);
console.log(ev, kelly, rr, goNoGo(ev, kelly, 0.20, rr));Both implementations are in the repository and are kept in agreement by golden-parity tests: models/feasibility_model.py and lib/feasibility/.
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Sources and disclaimer
- · Kelly J.L. (1956). A New Interpretation of Information Rate. Bell System Technical Journal.
- · Markowitz H. (1952). Portfolio Selection. The Journal of Finance.
- · Sharpe W.F. (1966). Mutual Fund Performance. The Journal of Business.
- · Kahneman D. & Tversky A. (1979). Prospect Theory. Econometrica.
- · Industry baseline: FREOPP lifetime return by programme (US-EDU-12..17) + BLS CPS earnings by attainment (US-EDU-06..09)
- · Decision Lab methodology
- · Full business plan (PDF)