WS MoreOrLess: Heads Or Tails?

Summary

More or Less: "Heads Or Tails?"

BBC Radio 4, World Service Edition – June 16, 2014
Host: Tim Harford
Main Guests: Steven Levitt, Alex Bellos

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Overview

In this episode, Tim Harford and guests delve into how simple statistics and probability shape our everyday lives—especially big decisions. The episode covers two main topics:

1. The use of coin tosses (chance) in making personal life decisions, featuring Steven Levitt of Freakonomics fame.
2. The math behind the famous "birthday paradox," with author Alex Bellos connecting it to World Cup rosters.

Both stories explore how intuition often clashes with statistical reality, and how leveraging simple mathematical tools can bring unexpected clarity to complex situations.

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Key Discussion Points & Insights

1. Should You Let Chance Decide? (00:19–04:54)

• Steven Levitt's Coin Toss Project

  • Steven Levitt explains a project where people with tough life choices (relationship changes, job quits, etc.) submitted their dilemmas, and when indecision remained, outcomes were decided with a coin toss.
  • Quote:

    “We tried to, through the questions we had, help people think differently about the problem so maybe they could come to some resolution... And then we did the ultimate favor to these folks, which is that we decided to decide for them. We flipped a coin.”
    – Steven Levitt (01:14)

• Demonstration with Producer Laura Gray

  • Laura Gray considers moving in with her boyfriend. Levitt guides her through regret minimization:
    • Think about which choice would leave you with less regret in the worst-case scenario.
    • Laura admits she'd regret not moving in more than moving in, hinting the coin toss is about clarifying inner feelings more than fate.
  • Live Coin Toss:
    • Levitt offers “best 2 out of 3,” referencing his website, but Laura opts for a single toss.
    • Result: Heads (“move in”), which matches her subconscious hope.
  • Quote:

    “This is so embarrassing. On the radio, I was thinking, yes… you’re hoping for heads. It was heads.”
    – Laura Gray & Steven Levitt (03:33-03:42)

• Behavioral Insights

  • Levitt reflects on how people resist change due to cognitive biases:
    • Sunk cost fallacies and the comfort of the status quo.
    • Coin tosses act as “forced constraints”—making the decision immediate and stark.
  • Quote:

    “The biases that humans have suggest that there's not enough quitting going on, changing the path that you're on.”
    – Steven Levitt (04:14)

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2. The Birthday Paradox—World Cup Edition (04:54–08:56)

• Introduction to the Birthday Paradox

  • Tim invites Alex Bellos to explain the paradox:
    • In a group of 23, the odds are better than 50% that two share a birthday—counterintuitive, given 365 days in a year.
  • Quote:

    “The birthday paradox is probably one of math’s greatest hits. It’s something you can say in one line which gives you this kind of wow.”
    – Alex Bellos (05:27, 00:34)

• Illustrating the Paradox with Football

  • World Cup squads, each made of 23 players, provide a real-world test:
    • There are 32 teams, so statistically, about “half” should have at least one shared birthday.
  • Initial finding: 19/32 teams had shared birthdays (from Wikipedia data), but this was an overestimate.
    • Producer interjects: Some data were wrong due to unofficial squad lists—humorous “yellow card” given to Bellos.
  • Corrected result: 16 teams had shared birthdays, aligning almost perfectly with mathematical expectations (~50%).

• Statistical Lesson & Reality Check

  • Even popular statistical curiosities like the birthday paradox can seem unbelievable—until real data reveals the truth.
  • Quote:

    “Sorry ref, my bad. The Revised figures are 16 teams at the World cup have shared birthdays and this is actually really rather good because it's mathematically what you would expect.”
    – Alex Bellos (08:39)

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Notable Quotes & Memorable Moments

• “We would help you decide whether you should get a tattoo or go on a diet or quit your job or break up with your boyfriend. Any question you want. It didn't matter.”
  – Steven Levitt (01:14)

• “Do you want the 2 out of 3 option or you want to go with just 1?”
  – Steven Levitt (03:13)

• “I think I'd have more regret if I didn't move in.”
  – Laura Gray (03:03)

• “There you have it. Their ultimate tool for decision making, flipping a coin.”
  – Tim Harford (03:42)

• “People share birthdays all the time... With 30 people it’s a 70% chance that two people share the same birthday.”
  – Alex Bellos (06:35)

• “Foul by Alex Bellos for getting his birthdays from Wikipedia, which you won’t be surprised to hear, weren’t all correct.”
  – BBC Producer/Editor (08:12, humorous aside)

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Useful Timestamps

• 00:19 – Tim introduces the main topics.
• 01:14 – Steven Levitt explains the coin-flipping decision project.
• 02:03 – Live example: Laura Gray’s move-in dilemma and Levitt’s regret-minimization advice.
• 03:12 – The coin toss for Laura Gray.
• 04:14 – Levitt discusses people’s resistance to change.
• 05:27 – Alex Bellos explains the birthday paradox.
• 07:16 – Using World Cup squads as real-world data for the paradox.
• 08:12 – BBC editor corrects Alex Bellos’ earlier stats; final tally matches the paradox.
• 08:56 – Episode closes.

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Summary

This short and witty episode demonstrates real-world applications of probability in both personal choice and world events. Steven Levitt shows that sometimes a coin flip is as valuable for clarifying your heart as it is for moving fate, while Alex Bellos brings statistics alive through football’s irresistible numbers game. Whether deciding on major life changes or marveling at “impossible” birthday facts, the episode celebrates how mathematics reveals surprising truths about our daily lives.

Transcript

[Laura Gray]

This is the short edition of More

[Tim Harford]

or Less, first broadcast on the BBC World Service.

[BBC Announcer]

Thank you for downloading from the BBC. For details of our complete range of podcasts and our terms of use, go to bbcworldservice.com podcasts

[Tim Harford]

hello, and welcome to More or Less on the BBC World Service. You can insert your own statistical pun here. Hi, I'm Tim Harford. A little later, we'll be investigating what we can learn by examining the birthdays of World cup footballers.

[Alex Bellos]

The birthday paradox is probably one of math's greatest hits. It's something you can say in one line which gives you this kind of wow.

[Tim Harford]

But first, I'd like to claim that the world's most popular economics writer is me. But sadly, we don't live in a just universe. Instead, it's Steve Levitt, prize winning professor of economics at Chicago, famous data detective, and with the journalist Stephen Dubner, the author of Freakonomics, and more recently, Think Like a Freak. Levitt and Dubner say they want to help people make better decisions. So I sat down with Steve Levitt and asked him about a very unusual project he and Dubner have been working on.

[Steven Levitt]

Essentially, we put out the word that if you had a big problem that you were trying to solve, you could come and we would help you. We would help you decide whether you should get a tattoo or go on a diet or quit your job or break up with your boyfriend. Any question you want. It didn't matter. And we tried to, through the questions we had, help people think differently about the problem so maybe they could come to some resolution. Many people, even after having done that, still couldn't decide what they should do. And then we did the ultimate favor to these folks, which is that we decided to decided for them. We flipped a coin.

[Tim Harford]

Now, Steve, there is actually someone in the studio with us, my producer, Laura Gray, who's putting her head in her hands. I'm going to take a coin out. Laura, would you mind coming on the mic? Steve, I'm going to give you a coin. Now, Laura has a decision, so tell Steve all about it.

[Laura Gray]

Okay, so my decision is should I or should I not move in with my boyfriend?

[Steven Levitt]

Okay, so if you had, if you had to decide today, which way are you leaning?

[Laura Gray]

No.

[Steven Levitt]

You're leaning no. Okay. And have you in the recent past been leaning yes or you've been leaning no the whole time?

[Laura Gray]

Been leaning yes.

[Steven Levitt]

Okay. One thing I think that's helpful in decision making is to first think about if you move in and the worst case scenario and think about how Bad, that is. And how much regret you'll have. Okay. And then think about if you don't move in the worst case scenario and kind of what you what, how much regret you have. Because I think that that's not a crazy way to make decisions is to say, I'm going to take the path where in the worst case, I will have the least regret. So is there one path or the other? Which feels incredible, like we would have the most regret.

[Laura Gray]

I think I'd have more regret if I didn't move in.

[Steven Levitt]

Okay, so heads is going to be move in, tails is going to be not moving. You ready?

[Laura Gray]

Yeah.

[Steven Levitt]

We also do a very important option on the website which is to offer best 2 out of 3 if you really want to make sure the gods don't make a mistake. Do you want the 2 out of 3 option or you want to go with just 1? 1?

[Laura Gray]

Cause just the one.

[Steven Levitt]

Okay, here we go. Heads you move in, tails you don't. Here we. What were you hoping for?

[Laura Gray]

This is so embarrassing. On the radio, I was thinking, yes,

[Steven Levitt]

you're hoping for heads. It was heads.

[Tim Harford]

There you have it. Their ultimate tool for decision making, flipping a coin. What's incredible is that more than 40,000 people have used this site to make decisions. Leavitt admits that even with 8,000 people changing their minds on the toss of a coin, he doesn't have statistically robust results to tell us that. For example, if in doubt, we should change direction in life. But he argues that other evidence from economics and psychology suggests that we do tend to be too stuck in our ways.

[Steven Levitt]

I think the biases that humans have suggest that there's not enough quitting going on, changing the path that you're on. Even though today I feel like I should change, I think to myself, okay, I could change today, or I could stick with it for one more day and I could quit tomorrow. And one of the benefits, if you want to call it, of this little coin toss experiment is that the coin toss is actually. This is a case where I think you could argue from a behavioral economics perspective that imposing a constraint, forcing someone to actually decide, today I'm either going to quit or I'm not going to quit, has a real benefit to the person.

[Tim Harford]

Steven Levitt. So if you have a big life decision to make, why not try flipping a coin? You're listening to More or Less now. We've learned this series that if there's one thing more or less listeners love, it's birthdays. We're still getting emails about the problem we posed A few weeks ago about the chances of having a major round number birthday on a weekend. So we thought why not challenge one of our favourite mathematical authors to find a birthday related twist on on a big story that everyone's watching.

[Alex Bellos]

I'm Alex Bellos, the author of Alex through the Looking Glass, How Life I'm with a tongue twisting title. I'm Alex Bellos, author of Alex through the Looking Glass. How Life Reflects Numbers and Numbers Reflect Life.

[Tim Harford]

Such a good title. You're overwhelmed as you try to say it. So Alex, you're here to tell us about the birthday paradox and loyal more or less listeners may know about the birthday paradox, but just remind us.

[Alex Bellos]

Well, the birthday paradox is probably one of math's greatest hits. It's something you can say in one line which gives you this kind of wow. And what it is is that you only need 23 people for it to be more likely than not that two of them share the same birthday. And this is not a logical paradox, there's nothing self contradictory about it. But it goes so against sort of intuition because you know there are 365 days of the year, so surely you'd need more than 23 people for it to be more likely than not that two share the same birthday.

[Tim Harford]

What's the most persuasive way you found to convince people that this is at least a plausible statement?

[Alex Bellos]

The theoretical way to explain it using probabilities, which is not difficult but quite tricky on the radio you can see it very clearly. It's not difficult, but actually I think you need to just look at the world. People share birthdays all the time and think, oh, it's an amazing coincidence that two people in my class of 30 share the same birthday. Actually, with 30 people it's 70% chance that two people share the same birthday.

[Tim Harford]

Now it would be great if we had some convenient real world data set where we gathered together groups of 23 people again and again and again and were able to examine shared birthdays. But I can't think of an example

[Alex Bellos]

that really works well, I thought long and hard and then all of a sudden I realized that the World cup is a brilliant, brilliant example because the squads for the World cup are each made of 23 players. So you have, you know, 32 examples to test this out.

[Tim Harford]

There are 32 teams. We should expect about half of them to contain a shared birthday. And if we're a long way away from half, either on either side, then something's going on or we've been unlucky.

[Alex Bellos]

Expect 50.7% of them. But when you look at the figures, which I did, you will find that there are 19 out of the 32 teams have shared birthdays, including five of the team have two shared birthdays. So four players share birthdays and this is about 60%.

[BBC Producer/Editor]

Afraid we're going to have to stop the interview there. Foul by Alex Bellos for getting his birthdays from Wikipedia, which you won't be surprised to hear, weren't all correct. Normally that would be an automatic red card and a sending off, but as we had to record this interview before the official FIFA squads were released because Alex was about to leave for Brazil, I'm going to give him a yellow card and the chance to retake the answer all the way from Sao Paulo.

[Alex Bellos]

Sorry ref, my bad. The Revised figures are 16 teams at the World cup have shared birthdays and this is actually really rather good because it's mathematically what you would expect. So actually it's all turned out rather well.

[Tim Harford]

Alex Bellos. Well, that's all we have time for today. Please keep your questions and your comments coming. We're at more or lessbc.co.uk and as always, there's further information and a downloadable edition of the show [e-mail] more or less. We'll be back next week. Until then, goodbye.

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