Utility Analysis Calculator
How do you calculate the financial value of a selection method?
The Brogden-Cronbach-Gleser model: N × T × Δr × SDy × Zx − C. On the figures this page opens with — ten hires, three years each, validity of 0.45 replacing 0.20 — the gain is $195,598, about $19,560 per hire. The term that decides it is Zx, which comes from the selection ratio: with ten applicants for ten posts it falls to zero, and a better test is worth nothing whatever its validity.
A better test is worth money only if you are turning people away with it. If you hire everyone who applies, validity is worth nothing.
This is the Brogden-Cronbach-Gleser model, the one the textbooks use, with the term most business cases quietly drop.
Built by Muhammad Shahzeb Anwar, MSc Industrial and Organizational Psychology, who also builds the paid tools in this shop. Most utility figures quoted in business cases leave out the selection ratio, which is the only term that can make the answer zero.
What the better method is worth
Compare a new selection method against the one you use now. Every figure is an estimate; the tool shows you which one it is most sensitive to.
What utility analysis actually does
It converts a correlation into money. A selection method with a validity of 0.45 predicts job performance better than one at 0.20, and utility analysis answers the only question a finance director will ask about that: how much better, in currency.
The model is Brogden's, refined by Cronbach and Gleser in the 1950s, and it is still the one the textbooks teach. It multiplies five things: how many people you hire, how long they stay, how much more accurate the new method is, how much the difference between a good and an average performer is worth, and how selective you can afford to be.
Then it subtracts what the assessment costs. That last step matters more than people expect, because the cost falls on every applicant assessed while the gain falls only on those hired.
The term everyone leaves out
Zx is the average predictor score of the people you actually hire, in standard deviations above the mean. It comes entirely from the selection ratio, and it is the only term that can send the whole answer to zero.
Take the top 10% of applicants and Zx is 1.75. Take the top half and it falls to 0.80. Hire everyone who applies and it is 0 — and the gain is zero no matter how good the test is, because a test only creates value at the moment you use it to reject somebody.
This is why a business case for a new assessment should start with the applicant pool, not the assessment. An employer struggling to fill posts is the employer for whom a better test is worth least.
Why SDy is the weak point
SDy is the standard deviation of job performance expressed in money: roughly what separates an average performer from one a standard deviation above them. Nobody can measure it directly.
The convention, from Schmidt and Hunter, is to estimate it at 40% of salary. Estimates in the literature range from about 40% to 70%, and some authors argue for far less. This tool defaults to 40% because it is the cautious end of the usual range.
Change that one figure from 40% to 70% and the answer nearly doubles without a single fact about your organisation having changed. Treat any utility figure, including this one, as an order of magnitude rather than a forecast — and quote the SDy assumption whenever you quote the result.
What this will not tell you
This is an estimate built on an estimate. SDy cannot be measured, validity figures are usually borrowed from published meta-analyses rather than from your own data, and the model assumes performance and predictor scores are normally distributed and linearly related. It also takes no account of adverse impact: a method can be both more valid and less lawful, and this arithmetic will not tell you so.
Questions people actually ask
What is the Brogden-Cronbach-Gleser utility formula?
Net gain = N x T x dr x SDy x Zx - C. N is the number hired, T the average years they stay, dr the improvement in validity, SDy the standard deviation of job performance in money, Zx the average predictor score of those hired, and C the total assessment cost.
Why does the selection ratio matter so much?
Because a selection method only creates value when it is used to reject somebody. Zx falls as the ratio rises, and at a ratio of 1 - hiring everyone who applies - it reaches zero and the gain disappears whatever the validity of the test.
What should I use for SDy?
The usual convention is 40% of salary, from Schmidt and Hunter. It is an estimate, not a measurement, and moving it to 70% nearly doubles the answer. Quote the assumption alongside the result.
Can utility analysis justify buying an assessment?
It can size the prize, which is worth doing. It cannot settle the decision on its own, because the inputs are estimates and the model ignores adverse impact, candidate experience and whether the validity figure transfers to your roles at all.
Cite this tool
Free to use and free to quote. If a figure here is useful in something you are writing, a link back is all that is asked.
Muhammad Shahzeb Anwar, MSc Industrial and Organizational Psychology. Utility Analysis Calculator. Shahzeb Speaks. https://www.shahzebspeaks.com/utility-analysis-calculator/
The other free tools
Each one answers a single question and refuses the ones it cannot. All free, none asks for an email address.
Want to see who the method actually catches?
The paid Selection Accuracy and Base Rates tool takes the same validity figure and shows you the four groups behind it: the good hires you caught, the poor ones you let through, and the good candidates you rejected without ever finding out. Utility says what it is worth; that one says what it does.
See the paid tool