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- Jun 7, 2017
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- Original Content
- Greta Roberts, HR analytics, HR data, Metrics, Pasha Roberts, Talent Analytics Corp, Workforce Analytics
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Employee Life Time Value and Cost Modeling – Part 3

By: Pasha Roberts, Chief Scientist, Talent Analytics, Corp.

With a cumulative cost curve in hand, we now turn to evaluate attrition. We hope to illustrate a far more intuitive and useful visualization than the popular business metric, annual attrition. Annual attrition is but a single point on this easy-to-understand business tool.

Employee attrition falls into the same class of “survival” problem as machine failure rates or medical research. This domain has brought us solid statistical innovations, including a visualization known as the “survival curve.” The risk of a particular employee terminating from a job is much the same a figuring when an industrial machine is going to stop working, or how long a patient may live with a given disease. In all cases, we are estimating *when an event will happen* while we’re in the middle of normal operations.

In measuring employee attrition or any survival analytics problem, there is a complication. We don’t know when current employees will terminate – it could be tomorrow or years. Since current employees are a significant part of our sample, we have to compensate.

It is not statistically correct to simply average or regress employment tenures, for this reason. Likewise, it is technically wrong to tally or predict terminations without regard to tenure or staffing level. There is a subtle interplay between tenure and termination that must be handled properly.

This adjustment is done with the Kaplan-Meier Estimator, which mathematically removes current employees from calculations beyond their tenure. Born decades ago from medical research, the Kaplan-Meier calculation is standard in many fields. The function is built into most modern statistical software, such as the “survival” package in R. It can even be done in Excel, with a bit of setup.

Once Kaplan-Meier has been properly adjusted, we can show attrition in at least two ways. The first is called a “Hazard Curve,” which is the chance (hazard) that the event (termination) will occur on any given day in tenure. In *Figure 9* we see hazard curves for two hypothetical locations, Chicago and New York. We see that early termination is more likely in New York.

*Figure 9. Hazard Curves – Daily Probability of Termination*

We will use these Hazard Curve values later for risk-weighting, but it is not the best visual tool.

The best visualization of employee attrition is the Survival Curve. It is a sum of the probabilities in the Hazard Curve, up to each point in tenure. It shows nuances, bulges, trends, and differences far better than any simple attrition figure. We have found that the Survival Curve is accessible for most business users, and hope someday to see it on BI Dashboards everywhere.

*Figure 10. Survival Curves – Probability of Reaching Tenure*

Across the horizontal ‘X’ axis we see tenure, from zero to many years. On the vertical ‘Y’ axis we see the probability of an employee surviving to that tenure. In fact some people don’t show up to their first day of work – but on day 1, survival is near 100%. Statisticians will recognize the Survival Curve as (1 – CDF) of the Hazard Curve.

The business-familiar annual attrition number is here – at the one-year mark, we see 86% survival for the Chicago curve, which subtracts from the top for 14% annual attrition. Likewise, the New York curve shows 58% survival at one year, which subtracts to 42% annual attrition.

But, one year is somewhat arbitrary. Remember that our breakeven point is 2 years – arguably this is a more useful threshold. At this 24-month breakeven point, we see 65% remaining from Chicago, but only 21% from New York.

One of the great strengths of survival curves is that we can compare multiple groupings. On one chart, we can compare geographic regions, as in the chart above. Likewise, we can compare managers, or multiple job roles. In predictive hiring work, we compare survival curves before intervention vs. after intervention.

One important application of these curves is to obtain the lifetime value of an employee in the role.

We can look up the cumulative value at an arbitrary date, say 5 years. The chart shows that an employee at that tenure is worth $78,851. However, not all employees last 5 years – only 18% from Chicago and 0.2% from New York.

Borrowing a technique from finance, we will risk-weight the cost curve to give our answer. A 5% chance of getting $100 is effectively a $5 “expected value.” In a similar manner, we will multiply every probability in the Hazard Curve, *Figure 9*, with the matching dollar value in the Cumulative Value Curve, *Figure 7*.

Then, we sum these expected values into a single number. This is called a dot-product, available in Excel as “DOTPRODUCT” or in R as simple multiplication. This dot-product gives us a proper risk-weighted lifetime value.

Be careful to use the Hazard Curve, the daily probability of termination, and not the Survival Curve, the cumulative probability of survival. Also, take care to use the entire Hazard Curve, extending far into the future – the sum of probabilities under that curve should equal 1.

*Figure 11. Comparison of Employee Lifetime Value*

In this sample, a Chicago employee’s lifetime value is $31,487, while the New Yorker is a loss with -$9,343. A far cry from the potential $78,851. These groups have the *same* cost curve, but *different* survival curves – which makes a significant difference.

This is more like the lifetime value of a new employee in a given role, than the lifetime value of a specific employee. We are not attempting to predict whether a specific person will someday rise to become President of the company, or if they will take a lateral move to another department. When they enter a new role, they enter a new set of calculations.

The Lifetime Value figure is sensitive to changes in attrition as well as costs or performance. It encompasses most foreseeable financial aspects of employees in that role, and allows fair comparisons of value.

While these numbers may never show up on a financial balance sheet, they are a strong estimate of how a set of employees will play out into the future.

The above approaches assume that all employees are the same, and average performance results. This is not entirely unreasonable, since we often have no prediction of what kind of candidate is joining the company. But, certain roles give us enough data that we can evaluate the many paths to success, and the relative value of each. We can even begin to predict which of several performance paths a new candidate may take.

Rather than building a monolithic example of sales based on averages, we can use large-scale tools like Hadoop or SAP HANA to do better. Consider a sales example, in which we have data for every single transaction sold by every rep for 10 years. Consider that we sort through these millions of transactions, with thousands of sales reps.

Then, we evaluate the sales that each rep made from their first day – how did they do? Instead of one performance curve, we have thousands.

- Did they start strong, and plateau?
- Did they slowly grow and learn to sell over time?
- Did they start strong, fizzle out, and terminate?
- Did they never get it and terminate early?
- Or something else?

We can use clustering algorithms to find groupings of sales rep performance – that is, how different reps ramped up. Now, instead of thousands of performance curves, we may have 3-7 well-traveled clusters or patterns.

In the sections below, we would calculate different breakeven points and different lifetime values, for each of these types of sales reps. Does the business prefer a slow-learner over a strong-start-then-plateau sales rep? The data will tell us – at the simplest level we just need to compare Lifetime Values of each curve type. There are strategic and teamwork considerations as well, and a complete comparison would move into Monte Carlo simulation.

It also moves us far beyond the scope of this chapter. This big data analysis lays the ground for predictive work to identify the propensity for candidates to follow one of these sales performance paths. More advanced applications will span multiple performance variables. This is a simple, single-performance-variable example of what is possible with transactional data and a good amount of effort.

After all of this work, we are left with several useful assets for the role:

- Daily Cost and Performance (The Quantitative Scissors)
- Cumulative Net Value (The Hockey Stick)
- Replacement Cost
- Daily and Cumulative Breakeven points
- The Survival Curve
- Employee Lifetime Value

Here are a variety of business applications of these metrics:

Everyone knows that attrition is expensive, but what is the actual cost? The relevant number is the amount that the business must spend to handle the problem, i.e. the Replacement Cost.

We find the number of attrition-related hires per year – for example, say a role with 1,000 agents that has 40% annual turnover, and a replacement cost of $11,000. This implies 400 agents need to be replaced per year, if the center is holding steady or growing. Simply multiply 400 agents by the Replacement Cost for the annual attrition cost.

In this case, attrition costs $4.4 million a year. If the company halved its attrition rate, they would save $2.2 million.

Employment, and business in general, is not a laboratory environment. We don’t get do-overs for failed scenarios, and our ability to “try things out” is limited. Customer analytics is slightly more amenable to A/B testing, just because the relationship is thinner, and there are many customers.

With this model of lifetime value, we can simulate the impact of programs. What happens if we:

- Increase wages by x%, and assume it will shift survival curves up by y%?
- Reduce wages by x%, and assume it will shift survival curves down by y%?
- Spend $x more on training, and assume it will accelerate learning by y%?
- Spend $x more on coaching, and assume it will help New Yorkers stay y% longer?
- Hire x% more employees in Chicago?

Any of these business changes would impact any or all of the underlying three curves. The outcome of these scenarios can be estimated, compared and prioritized.

Consider a change in training:

- More training would increase the first part of the cost curve.
- More training would (hopefully) speed up the ramp-up period on the Performance Curve.
- More training may decrease attrition, moving the Survival Curve up a bit.

The combined effect of these changes would be seen in two ways:

- A different cumulative breakeven date – hopefully lower, if the ramp effect overpowers the increased cost
- An increased lifetime value – with a higher Survival Curve and more ultimate Performance

If the three underlying curves are modeled properly, they will be sensitive to any operational change.

Hiring changes are more complex. Consider a new hiring program to find candidates with lower attrition. This means that the new program would find new candidates with higher Survival Curves. The Cost and Performance curves would remain the same, but the lifetime value of the new hires would be higher, due to a lower risk of attrition.

Two calculable outcomes would bring value to the company:

- Fewer early terminations – fewer of the new hires would terminate while still “in the red” on the Cumulative Value Curve
- More good candidates – the new hires would tend to last longer past the breakeven point, accruing more lifetime value.

These numbers can be calculated and tested. In the first case, of fewer early terminations, the models would estimate a new turnover rate, implying perhaps 40 fewer pre-breakeven terminations. As before, say the Replacement cost is $11,000. So, the company would save 40 times $11,000, or $440,000 in the first year as it transitions to a lower attrition rate.

In the second case, we compare Lifetime Value in the role, before and after the change. We multiply the increase in LTV by the number of new hires, to show an increase in the stock of employee value in the role. Perhaps the LTV increased by $3,100, and we hired 400 agents; therefore we will increase the value of employees in this role by $1.24 million.

Models can be designed to score predictions of future employee attrition or performance, even before someone is hired. Such models are commonly deployed as part of the hiring process to find better candidates. This advanced form of analytics raises employee models from rough averages to a very granular, individual-based view of employment.

All of the above calculations feed directly into such a modeling exercise, and become the method by which we judge the success of a model. If we want to increase performance, we expect to see an increase in the Performance Curve. If we expect to decrease attrition, we would see an increase in the Survival Curve. A successful model will bring higher LTV.

Attrition-based models often use survival curves directly, and aim to shift the curves up. All predictive models create a “score” – your credit score is an example. The Survival Curve becomes the basis for a range of acceptance thresholds for the model. This plot is an example of a survival curve with multiple predictive bands:

*Figure 12. Predictive Thresholds in a Survival Model*

Most of these figures are prime candidates for monitoring in a Business Intelligence framework, particularly interactive dashboards. Imagine a few possibilities:

Consider a dashboard with Survival Curves for every major role in the company. Users could drill in to compare attrition across departments, regions, managers, and roles. Managers could find the areas with the most pain, as measured by turnover. Researchers could identify and discover outliers.

KPIs and alerts could be implemented to keep groups on track. New hires and the results of predictive hiring could be tracked in real time.

Likewise, the single-role Cost Curves and Performance Curves could be combined, drilled into, and split up across the enterprise. Users could compare training costs between geographical regions. Researchers could investigate impact of training or on-boarding changes. Breakeven points and lifetime value could be into directly compared. Scenarios could be tested directly in the BI framework.

We believe that survival curves, along with Cost and Performance curves, are three vital tools that should be produced by every HR or Finance department for every high-traffic role. These three numbers capture the essence of the role’s impact on the company, and are the basis of powerful calculations.

Human Resources is known for having inward-facing metrics, like Cost per Hire or Time to Fill. The metrics that we have introduced here – Cumulative Employee Value, Survival and Employee Lifetime Value – go beyond HR to serve enterprise goals. They are key indicators of how employees – the people that HR hired – are lasting and performing.

These metrics are especially valuable for high-volume, high turnover roles. They are the measuring stick for improvements to hiring selection, engagement efforts, and performance improvements. Is it time for your organization to begin using them?

*Author Bio*

*Pasha Roberts is chief scientist at Talent Analytics Corp., a company that uses data science to model and optimize employee performance in areas such as call center staff, sales organizations and analytics professionals. He wrote the first implementation of the company’s software over a decade ago and continues to drive new features and platforms for the company. He holds a bachelor’s degree in economics and Russian studies from The College of William and Mary, and a master of science degree in financial engineering from the MIT Sloan School of Management.*

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