Tag: mean reversion

1 math trick for better predictions

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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.

Does the bundle explain it?

MIKE4 Comments

Defaults are a design tool to frame thinking. One designed-default is mean reversion. For most situations, said Cade Massey, “Try regression to the mean on for size and see if that can explain it.” Another is to start with the base rate: what typically happens in situations like this? During the Summer of 2021 there were many comparisons of vaccinated and unvaccinated Covid infection rates. This was a case of base rate neglect.

Mean reversion and base rates are good starting ideas because they prevent our Narrative Spin Drives from jumping into high-output mode. For instance, there’s an annual NFL video game known as Madden NFL. There’s also a Madden curse. If someone appears on the cover they have a terrible season after. It’s happened to eighty-two percent of the athletes!

Or it is base rates and mean reversion. To earn the cover rights, a player must have an excellent season, and their “success equation” benefited from a few lucky bounces. That happens. But bad luck happens too.

To add to the value of starting with base rates and mean reversion we can add “The Bundle”: the idea that a JTBD is a collection of things.

Marc Andreessen talked about the bundle of education: a dating scene, knowledge, social interactions, signaling, potential professional connections, cheap financing, and so on. Part-of-the-reason education innovation hasn’t gained distribution is that online only addresses parts of the bundle. It’s hard to date or build friendships on a video call.

Another bundle is the meal. Every meal is a combo meal: social interactions, nutrients, calories, taste, and so on. We can see bundles further yet. Food is more than the sum of its vitamins and nutrients. Eating an orange is more than theVitamin C, fiber, and sugar.

Work is a bundle too. Economist Tyler Cowen often notes that part-of-the-problem with Universal Basic Income is that it doesn’t address The Bundle. From NPR:

“Companies, like those in the tech industry such as Google and Apple, built enormous offices and put them all right next to each other in Silicon Valley and the office expanded what it was in people’s lives. They became like a second home. They had fancy food, concerts, dry cleaning, free meals.” – Stacey Vanek Smith, Planet Money, August 2021

Okay, a confession. I love Ted Lasso. It’s my favorite show since Parks and Rec. What I admire about Lasso is that he sets a tone (assuming for a moment it’s a real football club but this ethos may exist in the real production). Players begin the day and “Believe”. That’s what starting with base rates, mean reversion, and the bundle does too. Starting with those prompts prevents the Narrative Spin Drive from generating primarily palatable explanations.

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One thing I’ve changed my mind on is reading fiction. Fiction, like Ted Lasso, appeals to us because it is a fake premise sharing a human truth.
Also, the idea of online education needing distribution is from Alex Rampell, a colleague of Andreessen, who asks: Will disruptors gain innovation before innovators gain disruption? This is the “TiVo Problem.”

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April 2022 update. Taylor Pearson highlights Kris Abdelmessih’s post.

Base rate and mean reversion structure

MIKE1 Comment

One decision making suggestion is to start with the base rate, to find a set of comparable circumstances and ask, ‘what typically happens?’

In investing it is to find the price of, say Amazon, and ask how often a company of those characteristics grew at an expected percentage. Rather than start with the idea that Amazon is a great company that does a bunch of things well and so on – we can ask, for companies like this how many have grown at 15% a year? Zero.

Another example is (large, but maybe all) construction. The “base rate” is not good, fast, and cheap but overpromised, over-budget, and underwhelming. You cannot compare this to that people protest. Boloney says Bent Flyvbjerg, the cost overruns and benefit shortfalls are so consistent they are comical.

So starting with the base rate can help. What else?

On Wharton Moneyball the hosts discussed the 2020 Olympics and noted that the United States (men especially) have underperformed compared to years past. Is it culture? Training? Commitment?

“Is the U.S. doing badly or are other countries proportionally better?” – Shane Jensen, Wharton Moneyball, August 2021

Yes, says cohost Cade Massey, “Give Shane credit for the most parsimonious explanation we suggest for most any situation, try regression to the mean on for size and see if that can explain it.”

The idea behind regression to the mean is that performance varies up and down. There are many causal explanations for why this happens, think about talking heads for sports or stocks, but sometimes the mechanism is just old fashioned randomness.

But, ugh, we do no like this. Give me a reason man. So we assign reasons, which may be more comfortable than they are accurate.

We can make easier decisions. Easy decisions are designed. What designing a decision does is it shifts the information people use. Simple starter explanations like, the base rate or mean reversion, both create a decision making structure that will often help people get pointed in the right direction first. Start in the ballpark or base rates and then move towards your unique situation. Start with mean reversion as the mechanism and the adjust for other factors.

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Mean reversion, said Cliff Aeneas (Bloomberg) is basically value investing, “they’re almost synonymous.”