October 7, 2019

The Value of Friendship

How much is a great friend worth?

I struck on this question while procrastinating acquiring leads for my tutoring business. We use a simple model to determine which potential customers are worth going after. First, we estimate a customer’s lifetime value (LTV) — the total profit we would accrue if we were to add one more customer — and then work backwards to determine how much we should spend to acquire such a customer (CAC). With a few modifications, this model can be applied to friend-making, and it reveals some unusual insights.

If you’re like most people, you probably find new friends within your existing web of acquaintances. Due to convention or convenience, people rarely look further afield in pursuit of pals.

Some people have pointed out that this seems suboptimal. Applying the lens of lifetime value, it is easy to see why. What is the lifetime value of a great friend? Though friendship often feels priceless, our model cannot handle infinites. To learn anything, we’ll have to make a finite estimate.

Time for some assumptions. Let’s say your income starts at £20,000 and increases by 5% per year. Let’s say you have 60 good years left on this earth. Let’s also say that no matter your disposable income, you want to spend a fixed number of hours with good friends every week.

This assumption is the root of all the craziness that follows, so is worth explaining. The time you spend hanging out with friends could instead be spent earning more money, so an hour hanging out with friends must be at least as valuable to you as your hourly rate. Since your hourly rate changes with income, the value of a great friend scales with your earnings potential over time!

This makes sense, because with friendships, you get out what you put in. The longer you have a friend, the better you know each other, so the better advice they’ll give you. Plus, you have more shared memories to reminisce about. The value a multi-millionaire gets from a catch-up dinner with an old friend is likely to exceed the value they get from a few more hours at work. If we say that a good friend is worth 5% of your income each year, we have all the ingredients needed for our estimate.

Using compound interest, the lifetime value of a great friend comes to over £350,000. This seems like a lot of money, and it is. But our estimate is actually too conservative. We have taken into account fair-weather friendship: hanging out when all is well. But great friends really prove their worth when the shit hits the fan.

When disaster strikes, great friends are those who you know you can rely on. They are the ones who’ll visit you in hospital after the car crash, the ones consoling you after the death of a loved one. And so we’ll work some quarter-life, mid-life, and retirement-age crises into our estimate as well. Let each one of these be worth ~30% of your income in that year.

The new estimate comes to over £430,000, about the same price as the median flat in Islington, a new fully kitted-out Rolls-Royce Phantom, or over 550 iPhone 11s. With all the noise about working hard and sacrificing your social life for your career, this result suggests something non-intuitive: we should spend loads investing in friendships!

We can work out how much to spend by extending the analogy with business. Businesses want a healthy LTV:CAC ratio. Too high and your marketing is unlikely to be reaching high-value customers, while too low and your business is unlikely to be profitable. A good LTV:CAC ratio is about 3-to-1 — this means that the average customer earns you 3 times more money than it cost you to convince her to use your product.

A 3-to-1 ratio implies we should spend over £100,000 acquiring a lifelong friend. This seems ridiculous, until we remember that time is money. If a twenty-something values his time at £20 per hour, then he should spend over 5,000 hours investing in a long-term friendship. Carrying through the maths, you should spend around 1,000 hours per year making friends in your twenties*.

If you buy this argument, around 15% of your waking hours should be devoted to friend-making or friend-keeping. The obvious follow-up question is how to go about doing it. Our model comes in handy here too. Due to compound growth, most of the value you will get from friends will come later in life, so choosing the right friends early on is hugely important. This suggests a two-stage approach.

Step 1 is a sampling phase: spend time getting to know a lot of people. Use the internet, university societies, and friends-of-friends to cast your net as wide as possible.

Step 2 is a focus phase: Wind down your friend-meeting, and double down on friend-keeping. For the slightly introverted like me, this is the fun bit. Less time meeting strangers, more time building relationships with people you already care about.

Focusing on a relationship requires mutual, escalating vulnerability, usually occurring over years of interactions. However, with intensity, focus can be attained in little time. Exercises like the 36 questions that lead to love quickly ramp up intimacy, allowing you to simulate years of interactions in hours. If you put a lot of effort into listening to and sharing yourself with others, you’ll build relationships in a fraction of the normal time, and your returns on friendship will be even higher.

The weighting of step 1 to step 2 depends on your circumstances. How many great friends do you already have? How many acquaintances do you think could become great friends? Consider these questions to work out your own priorities. As you age, shift more effort away from sampling acquaintances towards focusing on friends.

So there it is. It turns out with the right assumptions, you can put a price on friendship.

For some, this impersonal analysis will sit badly. How can you reduce friendship, or love, to a financial value? In my view, the ends of this exercise justify the means. We have a finite amount of life to spend, so it is worth thinking carefully about how best to do so.

Though this model is dispassionate, it suggests actions which are the opposite. If you’re contemplating skipping dinner with friends to put the finishing touches on a work presentation, think twice. Life is short, and friendship matters.

Thanks to Brian Timar for reading a draft of this post.

**Remarkably, this new number is probably still too conservative. I estimated the lifetime value of one friend, and used that to guess the cost of acquisition of many friends. A more accurate figure would rely on the LTV of many friends. The LTV of n great friends will increase with n, but eventually level out at a maximum value. I haven’t run the numbers, but I’d imagine that even for our example person of modest wealth, the LTV of all their friends would exceed a million pounds.*

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