The Metrics of Success: 8 Ways Math Can Help You Win at Work

The days of the abacus are far behind us, but sometimes, mathematics and algebra still seem more like far-out theoretical physics than something that can have concrete influence on our lives. But did you know that the very rules of reality are governed by mathematics?

In a certain light, our daily lives are simply the product of a perpetually extending mathematical equation. Your life is littered with maths and stats, and if you learn a little bit about them, you’ll be able to use them to your benefit in business and in your private life.

So, how can we use mathematical and statistical tools to turn them to our advantage? In between finishing up my dissertation in mathematics and pondering the nuances of string theory, I combed through the Blinkist archives and found mathematical concepts that you can actually put to work. Let’s start with a seemingly simple mathematical concept: the average.

1. Know your averages.

All averages are not created equal. There are actually three different types of averages: the mean, the median, and the mode, and each is distinct.

The mean, also known as the “arithmetic average,” is probably the average you are most familiar with. It is found by adding up all the variables and then dividing the total by the number of samples.

The median describes the middle point in a sample. For example, the median of {1, 2, 6, 12, 23} is 6, because half of the values are above 6 and half are below.

The mode describes the most common variable in the sample, the number that appears most. In the sequence {1, 2, 2, 4, 10}, 2 is the mode.

As you can see, the word “average” isn’t as straightforward as we might think, so it’s always worth asking exactly which “average” people are talking about.

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2. Boost your decision-making with randomized testing.

Use randomized testing — a mathematical tool masquerading as a “growth hacking” tool! — to make decisions about marketing strategies. Randomized testing is a very effective tool which is already reshaping business research.

If you run a small business, you can use randomized testing to determine your marketing strategy. For example, how do you know if one webpage design attracts more customers than another? The company Offermatica offers randomized testing software to help answer that by randomly displaying one design or another when users visit your page. This is commonly known as A/B testing.

There are lots of different programs out there that can tell you in real time which page design is getting more click-throughs and which is generating more purchases. This kind of systematic random testing can enhance your site’s performance and help you determine which marketing strategies work best.

Fact: Ian Ayres himself made use of randomized testing to determine the title for his book. He was choosing between “Super Crunchers” and “The End of Intuition.” He set up a randomized Google ad campaign, and based on user interaction, found that random viewers were 63 percent more likely to click through on the Super Crunchers ad.

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3.Use data to build your startup faster and avoid self delusion.

Sometimes entrepreneurs lie to themselves a bit when assessing their success. After all, they often need to convince other people (like investors!) of their ideas without having any hard evidence that these ideas will actually work. A small amount of this can be called confidence, a large amount — delusion.

Happily, data is the antidote to self-delusion. By allowing you to soberly measure your success, it keeps you on track: you’ll know exactly where you stand as you work toward your goal.

However, you can’t just decide to “focus on the data” and be done with it. No, you have to understand which metric is most important for your business.

At any given time, you should always know the most important metric for your current stage of growth. As a startup founder, you’ll have to keep track of multiple data metrics, all of which will seem important. Revenue per customer, pageviews, clickthrough rate, and customer satisfaction can all be measured. Depending on how developed your startup is, one or another will be crucial for that growth phase.

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4. Understand your success on social media by using a unified engagement metric.

What exactly does success look like on social media? Believe it or not, this is a problem for a stealth math solution! You can quantify success by examining several different data metrics.

First, success can be measured by audience, or the individual users who’ve elected to have your posts show up in their newsfeed. Different platforms have different ways of identifying audience. On Twitter, audience is measured by followers, for whom your tweets appear on their timeline.

Success can also be measured by engagement, or the amount of audience interaction with a brand’s content. On Twitter, engagement is measured in terms offavorites, essentially the equivalent of the “like” button on Facebook, where the audience shows its support for a tweet as well as the number of replies your tweet receives.

Finally, you can look to your shares to gauge your success. Getting the audience to share your social media posts means that your content not only connected with your customers but also was good enough for them to attach it to their own personal profile. On Twitter, shares can be measured by retweets, which cause your tweets to show up on the timelines of those who follow that particular user who retweeted your post.

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5.Use probability to know what to expect from a bet.

In any situation where we’re uncertain about an outcome, probability can help us. Probability can’t tell us exactly what will happen in the future, but it can tell us what we should most likely expect.

For example, probability theory can tell us what’s likely to happen if we place a bet on something. We can use probability to know what might happen when we buy a lottery ticket by determining the ticket’sexpected value — the sum of all the different outcomes, each weighted by its probability and payoff, for a given event.

To calculate the expected value of a lottery ticket, we have to consider each possible outcome of the situation. We multiply the chance of each outcome by the ticket’s value given that outcome. Then we add up the results.

Let’s look at an example. Imagine a lottery with only two possible outcomes, losing or winning. A ticket costs $1; there are 10 million tickets; the winning ticket is worth $6 million. Here, the expected value of the ticket is 60 cents. That means that on average, we should expect a loss of 40 cents every time we play the lottery.

Fun fact: A real lottery has much, much worse odds, and a correspondingly lower expected value. So what’s the lesson here? Whether you’re playing Megabucks or betting your company’s entire future on one potential product, a little math can save you a lot of misery.

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6. Make better decisions in tricky situations with four simple mathematical strategies.

Many business contexts involve uncertainty or risk, so decision making needs to be approached with caution — but how exactly?

Consider this example. Assume you run a restaurant and you’re planning on opening a new location. Should you open a large or small location? From your experience you know that a big locale generates $500,000 in profit if popular, but incurs a $300,000 loss if not.

Likewise, a small drive-through can generate $275,000 in profit or incur an $80,000 loss. Now, if you are unsure what to expect from the new market, here are four possible approaches for you.

One decision-making technique is to choose the highest possible payoff. So, if you’re optimistic about the market, you aim for the maximum profit. You build a large restaurant that if popular will bring a $500,000 return.

Another technique is to choose the lowest potential loss. In this case, even though doing nothing has zero potential payoff, it cannot generate any losses either. So, if you’re rather pessimistic, you do nothing.

A third technique is to pick the best return on average. You choose this technique assuming that favorable markets and poor markets are equally likely.

You calculate the average return for each restaurant, beginning with the large one — ($500,000 — $300,000) × 50% = $100,000 — followed by the small one — ($275,000 — $80,000) × 50% = $97,500. You decide to open a large restaurant, since its average return is marginally higher.

One final technique is to weight the average return. You might estimate that there is a 30 percent chance of a good market and a 70 percent chance of a bad market.

You weight the average return by multiplying the potential profits and losses by their respective probability, and then subtract the potential losses from the potential gains. So, (0.3 × $500,000) — (0.7 × $300,000) = $60,000 in losses for the large restaurant, and (0.3 × $275,000) — (0.7 × $80,000) = $26,500 in profit for the small one.

In the fourth case, you decide to open a small restaurant since of the two, it is the only option whose weighted average return produces a profit.

Combining statistics and probability in this way can help inform your business decisions and allow you to minimize loss and grow responsibly.

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Math: more than just a college class

It turns out your teachers were right — math is important in adult life. And while you might be able to skate by knowing just the bare minimum, we’ve seen that math can also confer concrete benefits to those who take the time to apply it to their daily lives. So take a minute, put two and two together, and see what you get (hopefully it’s four).

Intrigued? Blinkist has blinks for all of these books and thousands more available right now. Try one out — it’ll only take you fifteen minutes!