Modeling Time to Fill

Introduction

“Time to fill” describes how long it takes a hiring team to fill a newly opened role, and is an important and widely used hiring performance metric. The metric is important for hiring teams because it neatly summarizes how effective the hiring team is at making the needed hire. Shorter time to fill means new employees can get started sooner and fewer total resources are spent on the hiring process. Longer time to fill often means delays, cost overruns, demoralized employees, and can even derail important projects.

While time to fill is widely measured after the fact to gauge the historical performance of the hiring team, comparatively little work has been publicized on how to model expected time to fill, or how to quantify the impact of hiring program features on time to fill. Here, we present a new method for modeling expected time to fill.

Among other interesting uses, our model helps reveal the remarkably large impact that the speed of a hiring process typically has on time to fill. While moving quickly through interviews is widely considered a best practice, it may be surprising just how large the impact can be: Reducing the total length of a screening and interview process modestly can cut weeks or even months from time to fill.

Description of the model

We present a model for time to fill of your search by considering what happens when good candidates apply to your role. Time to fill is defined as the time from receiving the first application to having a candidate accept your offer. A good candidate is one who would eventually receive an offer from you, if they went through your whole hiring process. The model considers the other candidates - those you’d reject - only indirectly.

The model takes 3 simple parameters:

$t$ — hiring latency, the average number of days it takes from a good candidate’s application to your making them an offer, where $t \gt 7$
$c$ — The number of good offers (worthy of serious consideration) your good candidates receive from other companies each day
$a$ — The number of good candidates that apply to your role each day

We discuss the interpretation of these parameters further below.

The model incorporates a few simple assumptions:

If a good candidate receives an offer from another firm, they’ll withdraw from your process unless they receive an offer from you within 7 days. Candidates are also open to receiving competitor offers for 7 days after receiving yours.
If a good candidate receives multiple offers, they have an equal chance of accepting any one of those offers. And if they only receive your offer, they’ll always accept it.
Reflecting the fact that the good candidate’s search is often already in progress at the time they apply to your position, we assume that they could receive an offer on any day, beginning with the day they apply to your position.

The first step in setting up the model is to determine the probability that an individual good candidate would accept your offer, given the time it takes for you to make that offer and the other offers they might receive.

First, consider the case that the good candidate does not receive any offers from competitors between the time they apply to you and 7 days before you make your offer. The probability of this happening is given by:

(1-c)^{t-7}

Now consider that the good candidate might receive one or more competitor offers within 7 days of receiving your offer. If that happens, they’ll need to choose from their multiple offers. The expected total number of offers, including yours, received during the 7 days before and 7 days after your offer is:

1+14 \times c

Under the assumption that the candidate has an equal chance of choosing any of their offers, the total probability of your offer being accepted by a good candidate is simply the product of the above, namely:

\frac{(1-c)^{t-7}}{1+14 \times c}

The probability that the candidate you’ll eventually hire will apply to your position on each day also depends on how often good candidates apply, that is:

\frac{a \times (1-c)^{t-7}}{1+14 \times c}

The expected number of days it will take for your eventual hire to apply is then:

\frac{1+14 \times c}{a \times (1-c)^{t-7}}

Adding the time from application to offer and the 7-day decision period gives us the expected time to an accepted offer:

\frac{1+14 \times c}{a \times (1-c)^{t-7}} + t + 7

Properties of the model and discussion of parameters

Our model is both simple and expressive. One of the three parameters, time to offer, is directly observable, while the other two closely track real-world phenomena.

The $c$ parameter — the number of offers that your good candidates receive each day - tracks the desirability of your candidates, the overall competitiveness of the job market, and the level of effort your good candidates put into applying elsewhere. Consider that:

The more your candidates are in demand on the job market, the higher $c$ will be. Typically, the most skilled candidates are in the most demand - so if you're trying to hire top talent, $c$ is probably on the high side.
The more motivated your candidates are to apply to various jobs, the higher $c$ will be. This motivation varies a lot according to the personality and circumstances of individual applicants. It's also affected by the uniqueness and desirability of your role: If your role is one-of-a-kind and extremely desirable, you might be able to attract special candidates that aren't interested in applying elsewhere. In that case, your $c$ may be very low. However, that situation is certainly more the exception than the rule.

The $a$ parameter — the number of good applicants you receive each day - tracks the volume and quality of your sourcing program relative to your hiring standard. Consider that:

Your hiring standard ultimately determines which of your applicants are good candidates. High standards will result in a relatively low value for $a$ - that is, few candidates meet your bar - while low standards will result in a relatively high value for $a$ - that is, many candidates meet your bar.
Doubling your applicant volume will double $a$ , provided that quality is held constant.
Making your role more desirable for good candidates - for example by investing in your employer brand or increasing advertised compensation - will increase $a$ by increasing the quality of your applicant pool.

Extending the model

Another feature of our model is that it can be extended easily to cover more ground. Perhaps most importantly, our model provides a clear path to robust cost to hire estimates, because time to hire is typically the most important unknown in that estimation. With a few additions, our model can also provide ancillary metrics like the expected number of candidates required to hire and the expected number of good candidates lost.

Additionally, it’s straightforward to replace expected values with distributions in the model. Representing time to hire as a distribution allows for more nuanced planning and estimation compared to using simple expected value.

We are actively working on these items and will post updates here as we complete them.

Implications of the model: Discussion

Our model clearly demonstrates the remarkable importance of reducing hiring latency. For example, in a moderately soft hiring scenario where a good candidate applies every 10 days and those candidates receive an offer every 14 days on average:

Companies with a 2-week hiring latency will make a hire in about 8 weeks on average
Companies with a 4-week hiring latency will make a hire in about 19 weeks on average
Companies with a 6-week hiring latency will make a hire in about 45 weeks on average

As you can see, not only is the impact of hiring latency extremely large - it also follows an exponential curve which begins to explode upward as latency extends beyond a few weeks.

This immediately calls into question “industry standard” practices of taking one week (or longer) to review initial applications, and then allowing the subsequent interview process to run two to four weeks afterward. You can expect every week of hiring latency to directly add multiple weeks - or even multiple months - to your time to fill.

The impact of hiring latency is no less pronounced in other scenarios. Say you have a great candidate pool and see good applicants every 5 days - twice as often as above. Here’s the chart:

Having a 5-week interview process will still cause more than 5 weeks of delay vs having a 2-week process.

Or, say it’s a tough market for job seekers, so even your good candidates can only expect to get an offer every 3 weeks. Though that is a much more favorable situation for hiring teams, having a 5-week interview process will still add 2 months to the time to fill vs having a 2-week interview process.

Hot markets for job seekers elevate the importance of reducing hiring latency. Below is the scenario where you get a good candidate every 14 days, and they get an offer every 10 days. In this case, if your hiring latency is 4 weeks, it will take an average of one year to complete your hire!

Meanwhile, if you have a fast 2-week process, you can expect a hire in just 3 months, even in this ultra-competitive environment.

We can also ask which is more impactful: getting more good candidates into your pipeline, or reducing hiring latency?

Starting from our baseline of good candidates applying every 10 days and receiving an another offer every 14 days, and 28-day hiring latency, here is the remarkable result:

Doubling applicant quality so that good candidates apply every 5 days will result in a hire 7 weeks sooner, but halving hiring latency to 2 weeks results in a hire 11 weeks sooner - without changing the candidate pool!

To help illustrate this point more generally, the following chart compares the impact of changing hiring latency (dark blue) vs changing applicant quality (light blue) from the baseline described just above.

Notice that the hiring latency curve is steeper than the applicant quality curve throughout. This shows that the impact of improving hiring latency by a given percent is always greater than the impact of improving candidate quality by the same percent from the baseline.

Furthermore, since it would be unusual to double your candidate quality without increasing your overall candidate volume, that doubling of good candidates could easily result in a longer hiring latency: You need more time to deal with the additional application volume. What happens in that case?

It turns out that letting your interview process extend just 8 days longer to handle that extra volume (from 28 to 36 days) completely negates the benefit of getting a good candidate every single week instead of every 2 weeks!

Bottom line - minimizing your hiring latency is incredibly important. It’s likely your biggest opportunity to increase the success of your hiring program and reduce your time to fill.