1 math trick for better predictions

Warning, this is “I watched one YouTube video” level of expertise. Also, some graphs have truncated y-axis.

Predictions are fun. Will a dice roll four or greater? Will it rain tomorrow? Will this company be worth more money tomorrow, next month, next year? An event does or doesn’t happen. We get to predict an outcome.

If an NFL team wins six of their first seven games how many games will they win in total? Well 6/7 is ~85%, and there are seventeen games therefore they’ll win ~14.5 games. But in 2021 there was a team that won six of their first seven games and one math trick could predict it.

Pierre-Simon Laplace gives us the “rule of succession”. That sounds complicated but it’s simple: For any number of outcomes add one to the observed cases and two to the total cases.

Here are four coin flips: heads, heads, tails, heads. The observed rate for heads is 0.75 (3/4). The ‘Laplace’ rate for heads is 0.66 (4/6). Laplace’s addition shifts predictions away from ‘never’ and ‘always’. This is the secret. ‘Never’ and ‘always’ are rare for sequential events.

Here is what the Laplace rate looks like compared to the observed rate for eighteen coin flips.

Here is what the Laplace rate looks like compared to the observed rate for the “six of the first seven” football team, the 2021 Tampa Bay Buccaneers.

Laplace starts at .500. Tampa wins six of their first seven games (.857) but Laplace only increases to .777. Their final winning percentage was .764.

Then there’s the 2021 Detroit Lions, a team that lost their first eight games.

The Laplace rate doesn’t know anything. It doesn’t know coins are 50/50. It doesn’t know about Tom Brady. It doesn’t know the Lions are bad. It’s just a formula that slowly adjusts to extreme events.

Laplace (b. 1749- d. 1827) didn’t have the NFL, so he made predictions about something else, the sunrise. The observed rate is 1.00. The Laplace rate, after 10,000 observed sunrises, is 0.99990002. So you’re saying there’s a chance?

No. That’s a simple wrinkle. Laplace called the sunrise a special “phenomena” which “nothing at present moment can arrest the course of.”

Coin flips, dice rolls, and drawn playing cards are random and have an expected rate.

Sunrises are special phenomena and Laplace’s rate is less helpful.

Football outcomes are a mix. They’re like the sunrise, in that teams have inherent principles. They’re like coin flips in that predictions are difficult, a sign of randomness.

Math helps: relative vs absolute saving rates, people live longer the longer they live, what the mean age means, the vaccine friendship paradox, how many ants long is Central Park?, or how many rolls of toilet paper do the residents of Columbus Ohio use in a week?

Math can be simple. Technique (add one to the numerator, add two to the denominator) and a bit of explanation (extreme events are rare without explanatory phenomena) is all we need.

*Their* restricted action section

One idea around here is that of the restricted action section, and how to unlock it. Broadly the goal is to limit any reduction in the range of choices. For example, the willingness to look stupid is a way to reduce the restricted actions section.

A common cause of restriction are stakeholders. Employees are stakeholders, movie financiers are stakeholders, and institutional investors are stakeholders. In the case of DTC, the most underrated part of the success of companies like Dollar Shave Club, All Birds, or Warby Parker was their competitor’s stakeholders. It wasn’t that Gillette didn’t want to sell their razors for cheap, but that would undermine their retail partners. Stakeholders limit actions. What’s there to do? Tyler Cowen gave a 2022 talk at Yale and advised this:

“Never stop listening while you do this (advocate your position). Don’t make it a crusade, make it a way you are expressing your opinion but trying to learn at the same time. I think especially in university environments you will be more effective that way. If you’re a top line university administrator, the pressures you’re under and the number of constituents you have to cater to is so extreme. Those are frustrated people. A lot of them may be on your side way more than you think but they can’t say so.”

Tyler Cowen

Whenever I find myself flummoxed by someone’s action it’s a sign I don’t understand the incentives. Sometimes the incentives are satisfying the stakeholders. I like Cowen’s approach here: be curious and find the incentives.

Need a louder phantom Tyler Cowen? Here’s more.

JTBD is iteration

The 2012 job-to-be-done at Calm was meditation. But when engineers looked at the usage data they noticed something interesting, there was a lot of Calm usage at night. “When they started productizing around sleep,” explained Vinny Pujji, “that’s when it opened up from being just a meditation focus thing to what they are today, which is mental fitness.”

We’ve looked at a few JTBD ideas: does the bundle of good explain the transaction, as it does with free breakfast? Is there zombie revenue? Even Jazzercise was job-ercised.

With hindsight ‘jobs’ sound easy, but they are iterated solutions. David Packles of Peloton shared (October 2020) two instances where Peloton had to iterate on their first JTBD solution.

First, Packles and his team looked at the largest Peloton Facebook groups. Rather than build for the power users, a no-no, they looked for wider use cases, and thought peole wanted to see when their friends were working out.

“People hated it,” said Packles. While the camaraderie between instructors and peers was important to users, the now-ness was not. So they tinkered. There was almost always at least two people in the same workout at the same time. ‘Friends working out now’ became ‘here now’. This worked, forty percent of daily active users now use this feature.

A second instance was the location field. Rather than where, people used it for what. Packles himself is a ‘Peloton dad’. So Peloton added tags which per Packles, “exploded in popularity” and “became a means of expressing yourself rather than connecting with club.” Half of DAUs have some kind of tag. Rather than people near me, the Peloton users wanted people like me.

That’s interesting moments help us understand how other people see the world. Instagram once had a tool that fought spam by looking for accounts that posted a lot and deleted a lot. During one glance through the data, Mike System noticed that in Indonesia a person was doing that – but in an interesting way. Way back in 2013 she was uploading photos of her store’s products and when they sold she would remove the post. Interesting right?

JTBD feels like a spirit of philosophy as much as it feels like a technique or tactic. It’s a way of regularly reflecting on the world. JTBD isn’t an equation, it’s a long process with a lot of inquiry. But it’s worth the work.


Two cool Peloton stats: they film thirty hours of content a day and their 18 month churn is 14%.

NBA 3s

There’s one honest sport.

When asked if the NBA will soon move back the three point line Mike Zarren said probably not. The reason is probably the business model.

“At the end of the day we are an entertainment and I would want to hear from fans that they are not liking the game as much. That’s not what we are hearing now (2021). You have to listen to the customer and people love the NBA right now…

“You also have a problem with the three-point line corners. The further out you move the crest of the line, the bigger the disparity between the corner-three and the other threes, and we’re not going to make the court wider because that would mean less seats and fewer tickets.”

It’s fun to talk about BIG CHANGES rather than “things are going well, let’s keep working hard and marking small bits of progress every day.” So it’s fun to talk about moving the NBA three-point line further from the basket or having a four-point shot or whatever. But those things won’t happen, chiefly because of incentives. The NBA, like movies, is a business, and like movies, those business incentives dictate the easy and difficult changes.

Creative Operations

Creativity according to John Cleese is “A way of operating.” This smart 1991 YouTube talk, is full of lightbulb jokes and advice on creativity. How many socialists does it take to change a lightbulb?

The problem with creativity is that it seems difficult. It’s like running a 5K for someone who doesn’t run. Like, c’mon, I can’t do that. Cleese nips this complaint right away and offers two helpful pieces of advice.

First, is to be a designer, and we are all designers. We are all designers because designs influence actions. Some designs tightly constrain action, like this Mario 1-1 walkthrough on YouTube. Other designs constrain loosely.

To design for creativity requires two things: space and time. Set the phone to DND. Sit at the desk. As Steven Pressfield notes, put your ass where your heart wants to be. Like a chef ready for the dinner rush Cleese offers his next piece of advice: think.

Rather he says ‘to play’. That’s the second step. Creativity is the subconscious bubbling up and it’s the conscious shutting up.

“As a general rule, when people become absolutely certain that they know what they’re doing, their creativity plummets.” Jon Cleese

Without interruption, think widely.

This will be hard. Most people, says Cleese, don’t like it. It’s hard to just sit or walk or be. It’s hard to just think. Annie Duke faced this. When she coached poker players they wanted to act, to do, to play the hand. But a lot of poker is not playing. Duke’s challenge was to get players to feel like they were poker players while also making good decisions. So, she reframed the actions.

Rather than playing hands as the action, Duke explained that deciding was the action. Thinking through the hands, the outcomes, the pot odds, the base rates and the game-theory-optimal case was what good players did. That was the secret for being a good poker player. This is the secret too, according to Cleese, for operating creatively.

Creative people are comfortable with the lulls. They understand that the time of play is time working on the problem.

There aren’t good metrics for this. There’s no word count. There’s no investment return. There’s no miles or dollars or calls made. There’s nothing to count which means no numbers which means no comparison which implies no value.

Do not fall into this trip says Cleese. Trust that the moments of wide-open thought matter.
After the play it’s time for work.

How many socialists does it take? Five, but they don’t change it and instead insist that it works.

‘Good’ numbers

This summer my kids were not going to watch too much YouTube. But, things changed. My eleven-year-old got into Moriah Elizabeth, a YouTuber into decorating and painting. Her channel is good. It’s interesting and entertaining. It, for me, avoids the overreactions and clickbait present on YouTube. She’s super positive and if not teaching kids how to be creative at least she shows them that it’s okay to mess up, laugh it off, and try again.

She wrote a book, Create this Book where each page is a prompt to draw only with polka dots, or draw a structure, or draw something without lifting your pencil from the page. We bought it. It’s fun. We do a page a day and laugh at or admire our drawings after.

This is to say that not all screen time is equal. But it’s easy to count and present equally. Apple offers a Sunday notification that your screen time was higher/lower than last week. That’s not really helpful. It would be like if a refrigerator displayed the calories consumed but not what exactly someone ate.

It also happens, says Betsey Stevenson, at the macro level during each jobs report. There’s the unemployment number and the initial response is that more workers are better. However it kinda depends on the timescale.

“When we see the ‘quits’ numbers really high that seems bad. In the short run we’re going to see fewer jobs. But it’s actually an optimistic time.” – @BetseyStevenson The Ezra Klein Show

People tend to quit their jobs when times are good and the next job is immediate. As people move about in the economy it follows that wherever they land will probably be a better fit, a win-win for everyone. But that’s hard to quantify.

One way to flip this problem is to restructure the counts. Basketball coach Todd Golden will redraw the lines on a basketball court. If a player shoots from inside the arc it’s worth one point. Shots outside the arch are worth four. That’s clever counting. Restructuring the way a player perceives the points is a way to find the ‘good’ numbers.

Konnikova’s Data

Park of poker’s appeal  is that people balance consequences and rewards. Thoughtfully in the best cases. But the lessons aren’t always obvious.

Nate Silver notes that live poker can be boring because participants don’t play that many hands. Yes, Maria Konnikova replied, that’s one way to look at it.

“There’s a perception that live poker can be boring because if you’re playing well you shouldn’t be playing that many hands. There is a lot of time you are just sitting there. But something I learned from Eric Seidel is that the times you are not in a hand are some of your most valuable opportunities to gather data.”

Konnikova recounts to Silver a time she was disposed as chip leader by an opponent who, after a day of play complimented her on her previous tournament. Why? It was televised. He picked up on her over aggressive style (something Konnikova notes in her book, I highly recommend The Biggest Bluff) in that tournament, and he used that against her in this one.

So rather than play as the thing-to-do, observe and learn are the things to do. Konnikova (and Seidel) reframed poker folds from something passive to something active. This is the same trick Annie Duke used for her poker clients. Duke reframed the action from playing hands to making good decisions.

Barry Ritholtz calls this the don’t just do something, sit there challenge. It’s hard to break the action-progress association. Yet there are situations, beyond poker, where not doing is more important that doing.

The basic level of learning a new thing is the advice to “just do it”. Just exercise/save/invest/read more. That’s difficult, especially without an anchor. A better way might be to substitute something of the same class. In the case of poker, Duke and Konnikova substituted one verb with another, and gave a reason for doing so.

I’m on a big pickleball kick right now and this advice, along with Winning Ugly from Brad Gilbert points in a clear direction: my game isn’t so much about hitting winners first but hitting winners second. A lot of my level is about setting up n+1 shots. Rather than beat an opponent down the line, with varying success, my aim should be to hit feet high down the line, move them, wait for a ‘green light ball’ and then hit winners. 

onward and upward

Why Hank Aaron’s father didn’t want a better house.

“I tried to get my father to move to a house I bought for him. There was one morning he was outside, trying to crank start his car,” Aaron recalls what his father said:

“Listen. I know what you’re trying to do. You’re trying to get your mother and I to move to that house you just bought. But we’re not going anywhere. All these people here, there’s not that many, maybe five or six families, these are friends of mine. I can wake up in the morning. I walk down. I can say hello to Stella, or whatever. These are friends of mine. I’m not going anywhere. So, you can take that money you paid for a house and get a refund.”

Aaron’s estimated net worth was twenty-five million dollars when he passed away, but this comment from his father shows value.

‘Peloton doesn’t offer discounts’

One of the challenges of running a business is seeing a business from the customer’s perspective. Internally your worldview is all website updates and payment processing, employees and benefits, and hiring and HR. Externally the customer wonders: does this do what I want?

Enter jobs-to-be-done.

Job-father Bob Moesta joined Customer Camp to conduct a mock-interview with Amanda about her Peloton purchase. It’s really good. You don’t even need to conduct ‘JOBS’ interviews to get something good from watching. For instance, framing.

Amanda wanted a Peloton. After getting and liking an Oura ring, and hearing her friends talk about Peloton she wanted one. It was better than a treadmill—if she wanted to run she could just run outside. So, Amanda and her husband watched for a Black Friday deal. None came.

A holiday deal? Nope. Is there any discount? No. There’s not really a Peloton discount, and Amanda was hearing about shipping delays (thanks Covid). So Amanda and her husband ordered one, financed with Affirm.

“Finance a stationary bike?!?!?” – Boomer

Well not really, it’s a 0% loan. It’s basically a payment plan. Actually Amanda notes, it’s like a gym membership.

Now here’s the magic trick business model: Peloton pays Affirm a commission for each bike sold and financed. 50M$ in Q3 2020. Peloton doesn’t offer discounts but it does offer 0% financing. And that’s the magic.

This, as regular readers know, is Alchemy. The financial picture is the same for Peloton: they have a retail cost and accept less than that to sell more units. The question is how much less and to who? Having Affirm be the who and the amount be vague creates value. Buyers hold Peloton in higher esteem and it just feels good to finance something at 0%. As one friend told me “it’s free money.”

To the accounting office it’s the same. To the market it’s different.

The JTBD of WINE

A group of investment bankers sat down. It was going to be a good night for Danny Meyer. That was good, it was three-months into his first restaurant.

The man at the head of the table asked for a chardonnay. Meyer delighted. He’d just got in a premier cru Rousseau. It was $45 a bottle. In 2015, Meyer joked, that might buy you half a glass.

Meyer walked out and proudly presented the wine.

“That’s not a chardonnay,” the big banker said.

“What I needed to have done at that very moment, which I trust I’ve done since. When he said, ‘This is not a chardonnay’, I should have said, ‘It sounds like you want a California chardonnay.'”

Danny Meyer, YouTube 2015

Instead, Meyer argued that it was. It went back and forth and the banker brought in the table, each member of which nodded in agreement that it was indeed not a chardonnay.

It was probably less than a minute. Meyer retreated and returned with a cheaper wine from California and that’s the story behind his most important lesson, the irrelevancy of being right.

Wine is odd. People buy wine for all kinds of reasons. The Barefoot founders figured out one way. But there always is a reason. That’s the lesson Danny learned. It’s their reason.

Part of the wine boom from 1980 onward was because wine was presented as doing one job: conveyed in an inaccessible language. Robert Modavi first communicated differently. The Barefoot founders did too. They found out there were other ‘jobs’ of wine.

When I delivered newspapers as a kid I loved the Best Buy ads where I could compare MB and GB and RAM on every new Dell, Compaq, and Gateway computer. But what really mattered was the job: will this play Warcraft II?

Apple figured this out.

Meyer figured this out.

This trips up operators all the time because it’s economic to use shorthand. But shorthand cuts out the magic, the feeling, the job—which is the soul of what a customer hires a product. Don’t be right, do your job.