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Taylor-Russell Calculator: Success Ratio from Validity, Selection Ratio and Base Rate

How do Taylor-Russell tables work?

They give the success ratio, the share of people hired who turn out successful, from three numbers: the test's validity, the selection ratio (hires divided by applicants) and the base rate (the share who would succeed anyway). For example, validity .50, selection ratio .10 and base rate .50 give a success ratio of .84: the test lifts success from 50% to 84%. This calculator computes the value exactly instead of reading a printed table.

Taylor and Russell published their tables in 1939 to answer a manager's question a correlation cannot: how many more of the people we hire will work out? Printed tables only cover a few values; this calculator handles any combination and shows the whole 2x2 outcome.

Enter the validity, selection ratio and base rate; the calculator gives the success ratio, the gain over chance, the Naylor-Shine mean performance of those hired, and a full table for your base rate.

Use the calculator All free tools

Built by Muhammad Shahzeb Anwar, MSc Industrial and Organizational Psychology. It sits beside his Selection Accuracy and Utility Analysis calculators: Taylor-Russell answers what share succeed, utility analysis what that is worth.

The calculator

Your selection

Runs in your browser. Nothing you type is stored or sent anywhere.

The correlation between test scores and job performance, from -1 to 1.
Hires / applicants (20 hired from 100 = 0.20).
The share of applicants who would succeed if hired at random.

How it is computed

Test scores and performance are treated as bivariate normal with correlation equal to the validity. The cut-off on the test is the score above which the top share of applicants falls (the selection ratio), and success is performance above the point the base rate implies. The success ratio is the probability of being above both lines divided by the selection ratio. The calculator evaluates that bivariate normal probability with Genz's (2004) algorithm, which reproduces the printed tables (validity .50, SR .10, base rate .50 gives .84; validity .30, SR .20, base rate .50 gives .67).

Naylor-Shine answers a different question: instead of a success/fail split, the average standardised performance of the people hired, which is validity x the normal ordinate at the cut-off / selection ratio. With validity .50 and SR .10, hires average .88 standard deviations above the applicant mean.

What the numbers teach

Three lessons come out of every Taylor-Russell table. A modest validity is worth far more when the selection ratio is low. A test adds the most when the base rate is near 50%: if almost everyone would succeed, there is little to improve, and if almost no one would, even a good test finds few successes. And when you hire nearly every applicant, no test helps at all.

Before you rely on this

What this will not tell you

The model assumes a linear, bivariate normal relationship and a success/fail criterion, and it uses the validity you enter, which should be corrected for range restriction if it came from your own hires. It says nothing about fairness between groups (see the adverse impact calculator). Nothing you type leaves your browser.

Questions

Questions people actually ask

What is a selection ratio?

The number of people hired divided by the number of applicants. Hiring 20 from 100 applicants is a selection ratio of .20. Lower ratios mean more choice and more benefit from a valid test.

What is the base rate in Taylor-Russell?

The proportion of applicants who would be successful if hired without the test, for example at random or with the current method.

What is the difference between Taylor-Russell and Naylor-Shine?

Taylor-Russell gives the proportion of hires who succeed, which needs a success/fail cut on the criterion. Naylor-Shine gives the average standardised performance of the people hired, with no cut on the criterion.

Does a validity of .30 matter?

Yes, more than the number suggests. With a base rate of 50% and a selection ratio of .20, validity .30 raises the success rate from 50% to about 67%.

Why does a test help less when the base rate is high?

If 90% of applicants would succeed anyway, there is little room to improve; the test can at most lift success from 90% toward 100%.

The papers behind the method

Sources

The method and algorithm come from these papers; each reference was checked against its DOI record on 17 October 2026. Naylor and Shine (1965, Journal of Industrial Psychology, 3, 33-42) has no DOI.

  1. Taylor, H. C., & Russell, J. T. (1939). The relationship of validity coefficients to the practical effectiveness of tests in selection. Journal of Applied Psychology, 23(5), 565-578: https://doi.org/10.1037/h0057079
  2. Genz, A. (2004). Numerical computation of rectangular bivariate and trivariate normal and t probabilities. Statistics and Computing, 14(3), 251-260: https://doi.org/10.1023/B:STCO.0000035304.20635.31
Citation

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. Taylor-Russell Calculator. Shahzeb Speaks. https://www.shahzebspeaks.com/taylor-russell-calculator/

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Turn the success ratio into money

The free Utility Analysis Calculator puts a value on a better selection method using the Brogden-Cronbach-Gleser model, per hire and in total.

Open the Utility Analysis Calculator