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Always Struggling With Hard Decisions? This Mathematical Formula Will Help You

Always Struggling With Hard Decisions? This Mathematical Formula Will Help You

Imagine this scenario: you’re a boss with a string of job candidates to choose from. You have to make the final decision on each candidate at the end of each interview. If you make an offer to a candidate, you cannot interview the others; if you don’t make an offer you can never hire that candidate again.

That’s a hard decision to make. With these kinds of constraints, how are you going to maximize your chances of hiring the best candidate?

At what point in the process do you say, “Alright, I’m just going to hire the next candidate that is better than the previous ones?”

This is the “Secretary Problem,” sometimes known as the “Marriage Problem” – and mathematician Martin Gardner solved it in 1960.

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The Solution to the Formula for Making Hard Decisions

Here’s the formula’s solution: after you have interviewed 36.8% of all the candidates, just hire the next candidate that is better than the previous ones.

Essentially, the formula proves that 36.8% is the optimal stopping point. Don’t hire or marry any candidate within the first 36.8% of the group, but after that, simply choose the first one that is better than the first 36.8%.

As a practical example, if you had to interview 50 candidates, starting from the 19th candidate onward, you should hire the next candidate that is better than the first 18 ones.

Note that this doesn’t mean you will always select the absolute best candidate (you may end up with second best if the very best candidate is in the first 36.8%), but this puts the chances of you doing so at 36.8%. Pretty decent odds given the situation, I would say!

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36.8%, by the way, is the value of 1/e, where e is the base of the natural logarithm. You may or may not have recognized that little alphabet from your high school math classes.

For the mathematically-inclined who want to know exactly how the solution was derived, you can read about it here. You can also check out the more reader-friendly Wikipedia page on the Secretary Problem.

How Practical Is the Formula Really?

Like all math problems and formulas, there are always some strict constraints that don’t make it as practical as we would like.

For example, if you were going over a list of job candidates, you could most likely just interview them all and call back the best one after. No need to make a definitive offer at the end of each interview.

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However, since there is always a risk that in the interim the candidate may accept another job offer, it might be wise to follow the 36.8% rule, especially if you know the candidates are in high demand.

Making Hard Romantic Decisions Using the Formula

What about when we try to apply it to the romantic department? Well, since you (probably) can’t date a whole string of people and then go back and select the best one like in the hiring process, the problem now is that you don’t know how many candidates there are in the first place!

How you can you determine 36.8% of a number if you don’t even know what that number is?

Good news, because mathematicians have figured that one out, too, and the answer is still 36.8%! Only now, it’s 36.8% of the total time.

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Here’s how it now works: let’s say you gave yourself a certain period to find a suitable lifelong romantic partner – 5 years for example. After 36.8% of 5 years, which is about 672 days (or 1 year, 10 months, and 3 days), you should just propose to the next romantic partner who was better than the previous ones.

This is known as the unified approach, and was proved in 1984 by German mathematician F. Thomas Bruss. You can read all the mathematical details on how this was derived in his paper here.

Making hard decisions is part and parcel of life; and no mathematical formula will be able to help you with all of them. That said, it is useful to know that in certain scenarios, there is a formula we can use to maximize our chances of obtaining the most favorable outcome.

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Ian Lee

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Last Updated on January 6, 2021

14 Ideas on How to Measure Productivity to Make Progress

14 Ideas on How to Measure Productivity to Make Progress

Everyone has heard the term productivity, and people talk about it in terms of how high it is and how to improve it. But fewer know how to measure productivity, or even what exactly we are talking about when using the term “productivity.”

In its simplest form, the productivity formula looks like this: Output ÷ Input = Productivity.

For example, you have two salespeople each making 10 calls to customers per week. The first one averages 2 sales per week and the second one averages 3 sales per week. By plugging in the numbers we get the following productivity levels for each sales person.

For salesperson one, the output is 2 sales and the input is 10 sales: 2 ÷ 10 = .2 or 20% productivity. For salesperson two, the output is 3 sales and the input is 10 sales: 3 ÷ 10 = .3 or 30% productivity.

Knowing how to measure and interpret productivity is an invaluable asset for any manager or business owner in today’s world. As an example, in the above scenario, salesperson #1 is clearly not doing as well as salesperson #2.

Knowing this information we can now better determine what course of action to take with salesperson #1.

Some possible outcomes might be to require more in-house training for that salesperson, or to have them accompany the more productive salesperson to learn a better technique. It might be that salesperson #1 just isn’t suited for sales and would do a better job in a different position.

How to Measure Productivity With Management Techniques

Knowing how to measure productivity allows you to fine tune your business by minimizing costs and maximizing profits:

1. Identify Long and Short-Term Goals

Having a good understanding of what you (or your company’s) goals are is key to measuring productivity.

For example, if your company’s goal is to maximize market share, you’ll want to measure your team’s productivity by their ability to acquire new customers, not necessarily on actual sales made.

2. Break Down Goals Into Smaller Weekly Objectives

Your long-term goal might be to get 1,000 new customers in a year. That’s going to be 20 new customers per week. If you have 5 people on your team, then each one needs to bring in 4 new customers per week.

Now that you’ve broken it down, you can track each person’s productivity week-by-week just by plugging in the numbers:

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Productivity = number of new customers ÷ number of sales calls made

3. Create a System

Have you ever noticed that whenever you walk into a McDonald’s, the French fry machine is always to your left? 

This is because McDonald’s created a system. They have determined that the most efficient way to set up a kitchen is to always have the French fry machine on the left when you walk in.

You can do the same thing and just adapt it to your business.

Let’s say that you know that your most productive salespeople are making the most sales between the hours of 3 and 7 pm. If the other salespeople are working from 9 am to 4 pm, you can potentially increase productivity through something as simple as adjusting the workday.

Knowing how to measure productivity allows you to set up, monitor, and fine tune systems to maximize output.

4. Evaluate, Evaluate, Evaluate!

We’ve already touched on using these productivity numbers to evaluate and monitor your employees, but don’t forget to evaluate yourself using these same measurements.

If you have set up a system to track and measure employees’ performance, but you’re still not meeting goals, it may be time to look at your management style. After all, your management is a big part of the input side of our equation.

Are you more of a carrot or a stick type of manager? Maybe you can try being more of the opposite type to see if that changes productivity. Are you managing your employees as a group? Perhaps taking a more one-on-one approach would be a better way to utilize each individual’s strengths and weaknesses.

Just remember that you and your management style contribute directly to your employees’ productivity.

5. Use a Ratings Scale

Having clear and concise objectives for individual employees is a crucial part of any attempt to increase workplace productivity. Once you have set the goals or objectives, it’s important that your employees are given regular feedback regarding their progress.

Using a ratings scale is a good way to provide a standardized visual representation of progress. Using a scale of 1-5 or 1-10 is a good way to give clear and concise feedback on an individual basis.

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It’s also a good way to track long-term progress and growth in areas that need improvement.

6. Hire “Mystery Shoppers”

This is especially helpful in retail operations where customer service is critical. A mystery shopper can give feedback based on what a typical customer is likely to experience.

You can hire your own shopper, or there are firms that will provide them for you. No matter which route you choose, it’s important that the mystery shoppers have a standardized checklist for their evaluation.

You can request evaluations for your employees friendliness, how long it took to greet the shopper, employees’ knowledge of the products or services, and just about anything else that’s important to a retail operation.

7. Offer Feedback Forms

Using a feedback form is a great way to get direct input from existing customers. There are just a couple of things to keep in mind when using feedback forms.

First, keep the form short, 2-3 questions max with a space for any additional comments. Asking people to fill out a long form with lots of questions will significantly reduce the amount of information you receive.

Secondly, be aware that customers are much more likely to submit feedback forms when they are unhappy or have a complaint than when they are satisfied.

You can offset this tendency by asking everyone to take the survey at the end of their interaction. This will increase compliance and give you a broader range of customer experiences, which will help as you’re learning how to measure productivity.

8. Track Cost Effectiveness

This is a great metric to have, especially if your employees have some discretion over their budgets. You can track how much each person spends and how they spend it against their productivity.

Again, this one is easy to plug into the equation: Productivity = amount of money brought in ÷ amount of money spent.

Having this information is very useful in forecasting expenses and estimating budgets.

9. Use Self-Evaluations

Asking your staff to do self evaluations can be a win-win for everyone. Studies have shown that when employees feel that they are involved and their input is taken seriously, morale improves. And as we all know, high employee morale translates into higher productivity.

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Using self-evaluations is also a good way to make sure that the employees and employers goals are in alignment.

10. Monitor Time Management

This is the number one killer of productivity in the workplace. Time spent browsing the internet, playing games, checking email, and making personal calls all contribute to lower productivity[1].

Time Management Tips to Improve Productivity

    The trick is to limit these activities without becoming overbearing and affecting morale. Studies have shown that most people will adhere to rules that they feel are fair and applied to everyone equally.

    While ideally, we may think that none of these activities should be done on company time, employees will almost certainly have a different opinion. From a productivity standpoint, it is best to have policies and rules that are seen as fair to both sides as you’re learning how to measure productivity.

    11. Analyze New Customer Acquisition

    We’ve all heard the phrase that “It’s more expensive to get a new customer than it is to keep an existing one.” And while that is very true, in order for your business to keep growing, you will need to continually add new customers.

    Knowing how to measure productivity via new customer acquisition will make sure that your marketing dollars are being spent in the most efficient way possible. This is another metric that’s easy to plug into the formula: Productivity = number of new customers ÷ amount of money spent to acquire those customers.

    For example, if you run any kind of advertising campaign, you can compare results and base your future spending accordingly.

    Let’s say that your total advertising budget is $3,000. You put $2,000 into television ads, $700 into radio ads, and $300 into print ads. When you track the results, you find that your television ad produced 50 new customers, your radio ad produced 15 new customers, and your print ad produced 9 new customers.

    Let’s plug those numbers into our equation. Television produced 50 new customers at a cost of $2,000 (50 ÷ 2000 = .025, or a productivity rate of 2.5%). The radio ads produced 15 new customers and cost $700 (15 ÷ 700 = .022, or a 2.2% productivity rate). Print ads brought in 9 new customers and cost $300 (9 ÷ 300 = .03, or a 3% return on productivity).

    From this analysis, it is clear that you would be getting the biggest bang for your advertising dollar using print ads.

    12. Utilize Peer Feedback

    This is especially useful when people who work in teams or groups. While self-assessments can be very useful, the average person is notoriously bad at assessing their own abilities.

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    Just ask a room full of people how many consider themselves to be an above average driver and you’ll see 70% of the hands go up[2]! Now we clearly know that in reality about 25% of drivers are below average, 25% are above average, and 50% are average.

    Are all these people lying? No, they just don’t have an accurate assessment of their own abilities.

    It’s the same in the workplace. Using peer feedback will often provide a more accurate assessment of a person’s ability than a self-assessment would.

    13. Encourage Innovation and Don’t Penalize Failure

    When it comes to productivity, encouraging employee input and adopting their ideas can be a great way to boost productivity. Just make sure that any changes you adopt translate into higher productivity.

    Let’s say that someone comes to you requesting an entertainment budget so that they can take potential customers golfing or out to dinner. By utilizing simple productivity metrics, you can easily produce a cost benefit analysis and either expand the program to the rest of the sales team, or terminate it completely.

    Either way, you have gained valuable knowledge and boosted morale by including employees in the decision-making process.

    14. Use an External Evaluator

    Using an external evaluator is the pinnacle of objective evaluations. Firms that provide professional evaluations use highly trained personnel that even specialize in specific industries.

    They will design a complete analysis of your business’ productivity level. In their final report, they will offer suggestions and recommendations on how to improve productivity.

    While the benefits of a professional evaluation are many, their costs make them prohibitive for most businesses.

    Final Thoughts

    These are just a few of the things you can do when learning how to measure productivity. Some may work for your particular situation, and some may not.

    The most important thing to remember when deciding how to track productivity is to choose a method consistent with your goals. Once you’ve decided on that, it’s just a matter of continuously monitoring your progress, making minor adjustments, and analyzing the results of those adjustments.

    The business world is changing fast, and having the right tools to track and monitor your productivity can give you the edge over your competition.

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    Featured photo credit: William Iven via unsplash.com

    Reference

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