Will Novak win the most?

Considering the recency effect of inevitability, practicing with base rates, and reducing the solution space.

In early 2022, the men’s career grand slam standing were tied at twenty wins each between Roger Federer (age 40), Rafael Nadal (35), and Novak Djokovic (34).

For tennis fans, the big question is: Who will end their career with the most? For a while it looked like Novak Djokovic who was the youngest and playing the best. Djokovic had also won three out of the four majors in 2021 and his dominance looked inevitable.

But few things in life are inevitable, no matter how they look in the moment. Sports provides an example for other parts of our life and the Wharton Moneyball crew (in the 1/26/2022 episode) provide a way to think through probabilistic, inevitable, and recency related issues that come in any part of life.

“I was convinced Djokovic was going to end up with the most majors,” Wharton professor Eric Bradlow begins, “but let’s talk about what’s happened in the last six months.” Novak lost the last tournament of 2021 and didn’t play in the first tournament of 2022. Without getting vaccinated, Novak will not play in the French Open (and maybe U.S. Open) either.

But Djokovic not playing also means that someone else, like Nadal can increase his total. Rafael made the semi-finals at WON the Australian and plays best at the French.

“Six months ago I would have said Djokovic would be the top of all time. Now it’s 50/50. I give Nadal a legitimate chance to have the most majors of all time,” Bradlow says.

Tap the brakes, host Cade Massey says, remind us of the base rates. That is, what’s the oldest that someone great tends to win these major tournaments. “Federer hasn’t won one since he was 37,” Eric explains.

Ah. Now we have something to work with. Let’s follow a page from Zeckhauser and simplify.

Djokovic and Nadal each have about 12 chances left. But Novak isn’t vaccinated so subtract the ’22 Australian, ’22 French, and ’22 U.S. Open. “You’ve gone from twelve good chances to nine. And you still have (to play) Nadal at the French!” Bradlow bellows. Plus, it’s not just Nadal and Djokovic but a field of players and like something is always happening, someone unexpected will win.

Rather than overreact to news, we found the base rate (oldest age to win a major) and opportunities left. Though men’s tennis is top heavy, there’s a lot that can happen.

But wait, that’s not all.

“I’m bummed for folks like him (Novak), like Kyrie Irving,” says Massey, “like any high profile athlete, that takes a no vax stance. There is so little room for changing your mind. Once you take that high profile a stance, with the politics of it, it really diminishes the chance of him shifting his position.”

Put another way, a strong public stance creates a restricted action section.

Who will end up with the most majors? We don’t know. But we do know that using base rates, avoiding recency bias, finding simple examples, and not reducing our solution space are all good processes.

For football fans, there’s a section of fervor about the Allen-Mahomes game that speaks to the inevitability and our reactions to recent events.

2021 predictions (graded)

Here are the 2021 predictions graded. My average Brier Score was 0.227 whereas a coin tosser Brier is 0.25. A perfectly accurate forecaster scores 0 and perfectly inaccurate forecaster is 1. The big misses will be in bold.

My guesses are blue, outcomes are red. The closer the blue is to the red the more accurate I was. This chart makes the predictions looks okay.

But when I bucket them it gets worse.

That looks terrible. Let’s see how.

Hurricanes. NOAA “An average season has 12 named storms, six hurricanes, and three major hurricanes.” Will there be more than 12 named storms? Yes, 90%. Will there be more than 30 named storms (the 2020 record)? Yes, 25% Will there be 3 or more major hurricanes (top winds of 111+mph)? Yes, 60% Will I lose power at my home in Central Florida for more than 3 days? Yes, 10%.

Overall there were 21 named storms and four of which were major and we didn’t lose power at all this summer. Mostly these were safe but relevant predictions. Hurricanes are one of those things I’d like to appreciate correctly. Like an alligator on the river bank, I want to know enough to take a good photo but also to keep my fingers.


Will this blog have more than 41,000 views in 2021 (41k is the 2020 number)? Yes, 15% Will this blog have more than 800 posts by year end? Yes, 30%

The blog had 29,000 views and 908 blog posts and a whopping 335,000 lifetime views (!!). What’s surprising was my inability to predict myself. As things go, I got into a great writing streak in the summer and fall of 2021 and the posts reflected that.


BTC will top 75,000 at any point in the year? Yes, 10% BTC will be under 30,000 at any point in the year (started 2020 at this point)? Yes, 20% ETH will top 5,000 at any point in the year? Yes 5% ETH will be under 130 at any point in the year (started 2020 at this point)? Yes, 20% BRKB will top 275 at any point in the year? Yes 10% BRKB will be under 234 at any point in the year (started 2020 at this point)? Yes, 30%

First, in hindsight this was cheating. ‘At any point in the year‘ is a case of something is always happening. To get better at predicting I need to ask better questions. The biggest paired misses of the year were my guesses about Berkshire Hathaway stock ($BRKB). I thought there was a 10% chance of the stock being under 234 and 30% being over 275 (and that’s with the generous ‘at any point’ language).

I’m not quite sure what to think of this one. Robinhood and retail? The stock didn’t move more than 20-40 points in 2018 or 2019 and as a ‘value’ stock I expected tighter growth. Though mostly correct on crypto, with hindsight the range of outcomes is much wider.

Economic Recovery These will be graded per Bill McBride’s numbers on Calculate Risk. Any single day of the last week of the year will top 2M travelers (2019 was 2.0-2.5M)? Yes, 75% Open Table reservations will be down less than 10% YOY? Yes, 75% Open Table reservations will be positive YOY? Yes, 20% Any movie earns more than 250M on opening weekend during the year (highest grossing movies)? Yes, 5% Hotel occupancy tops 60% (graph)? Yes 80% Hotel occupancy tops 70%? Yes, 60%

Mostly got these correct and directionally too. Predicted 75, 75, 80, and 60% for events that all happened. Missed reservations being positive but grading it I can’t remember what this meant. Also missed on movie opening as Spider Man No Way Home earned 270M, partly from my two daughters and me.


As of year-end, Tom Brady averages +270 ypg? Yes, 30% The Lakers are NBA champions? Yes, 25%

Tom Brady continues to amaze averaging 313 yards per game. And our Aaron Rodgers saga comes to an end, with Rodgers just falling short by 1.5 touchdowns. This one is another head scratcher. Rodgers had two games with no touchdowns and missed a game due to Covid. Is this the variance that Plus EV noted or was it just luck?

By what conventions?

This episode dropped among a list of NFT episodes, but first the quote.

“In education there is a lot of incentive to fail with the pack rather than to take a risk away from the pack. For example, folks would teach the Prussian Lecture method. We all knew it was bad, we all did it together, and education failed but no one stood out. There were brave people who built flipped classrooms, but a lot of students didn’t like it and they would get bad teaching evaluations and sometimes lose tenure. If in football you play by the book, which isn’t really the book, it’s what everybody has historically done, and you fail then you are failing the same game the way everybody else fails. In a way you are failing in a more honorable space than somebody who does something differently and takes that chance.” – Eric Eager, The Science of Change, November 2021

Failing conventionally is an idea we’ve looked at before. But there are two additional points.
1. Conventions (‘the book’) change.
2. It’s the relative difference to these moving conventions that matter.

In football, for instance, going for it on fourth down is being normalized. If in next year’s season the convention is go for it on fourth and one in the opponent’s territory then the conventions have changed and coaches who go for in in their own territory will have less relative difference from the conventions.

What does any of this have to do with NFTs? NFTs are weird. They’re basically agreements. We all live under a collection of agreements: constitutions, laws, proposals, deals, partnerships, user agreements, contracts and so on. Some of these agreements are more explicit than others. The laws of physics notes Neil Degrasse Tyson are true whether you believe them or not. Contracts more solid agreements depending on the enforcement system. Relationships are toward the softer end of agreements and NFTs are digital agreements.

Like Eager’s flipped classroom and fourth down comments NFTs are novel conventions. And we should expect more weirdness.

Conventions used to be dictated by the physical space. We acted mostly like the people around us acted. Now, we hang out on the internet. The conventions are still dictated by the people around us but now it’s in the digital space. And as we are in the digital space more we will come up with new agreements there.

![Generative art](https://upload.wikimedia.org/wikipedia/commons/b/be/VeKings.png =200×200)

Digital art is an early development for these digital agreements because it’s easy. An NFT is basically a link to a file with an agreement attached. The file is stored in this server which is how website work, AND it is owned by so-and-so.

Our lives are full of agreements and conventions. If the things we do are online more the agreements and conventions in our lives will change. NFTs may be one such example.

Art NFT are a bit overhyped because the price is wrong. The floor on one ape was $200,000 but really the price was 50ETH. But there’s no way whoever buys this ape will pay for it when 200K=50ETH. Rather, part of the NFT craze is that a bunch of people have ETH at prices well below the fall 2021 levels.

Tailing Aaron Rodgers (part three)

It’s time to update two of our ongoing projects. First, to revisit the idea of Aaron Rodgers throwing less than 38.5 touchdowns. The point in parts one and two were to not think specifically about what might happen but think about the states of what could happen. We reasoned there were a lot more things that would influence Rodgers to throw fewer touchdowns rather than more.

Well, no one predicted this. Rodgers now has three games (with the snowy Seahawks showing) with zero touchdowns.

Another idea to update is ‘or the field?’ Are certain events more or less predictive than others? The Wharton Moneyball hosts note that the NCAA Men’s Basketball tournament odds are out.

“We need to do our calculation, how many teams do we have to go down until the odds get to about fifty percent? You probably have to go down six or seven teams, I think I’m still taking the field. I’ll give you Gonzaga, Michigan, Kentucky, Texas, UCLA, and Duke and I’ll take everyone else.” – Eric Bradlow, Wharton Moneyball, November 2021

Well, here’s how the different sports stack up.

November field update

In the EPL and Men’s tennis the top three favorites have a larger cumulative expected odds than NCAA Football and the NBA which have larger cumulative odds than MLB, NFL, or NHL while NCAA basketball seems to be the most unpredictable. The larger the favorites, the thinking goes, the more predictable the skill and the less influential the luck.

Tom Brady continues to chug along contra to the Rodgers reasoning, needing to average 180 passing yards in his remaining games or even just 240 if he misses two. One explanation here is that positive early variance (four games over 375 yards passing) changes things a lot. Prior to this year, Brady only had 23 games with that many yards or more.

Filters for thought

The best way to make decisions is to collect information most related to the system at hand. Touch a hot stove. Drop a pen. Kiss a lover. Each of these offers a direct action-feedback-action loop.

But these aren’t the interesting parts of life. The interesting parts of life are multiple people functioning at different times towards a goal that’s only shared in the sense of each person’s understanding.

Life is messy.

But we know that. Like driving across Interstate 80 with the prospect of a blizzard, we can plan accordingly. In talking with Cleveland Browns General Manager Andrew Berry, Annie Duke noted how difficult the decisions are within a team. Teams are messy! There are sunk costs, biases, entrenched interests as well as the alignment (or not) of stakeholders . But Berry knows this.

“There’s a couple things we try to do. Number one is to do the hardcore analysis removed from the emotion of the season, the player, the decision maker….

“The second part is getting a number of independent perspectives and letting them state their case. It’s easy as the decision maker to be in your own cocoon and only consider your viewpoint on a player…And the last thing we try to do is have a third-party perspective. There are a couple of things we use that aren’t in our building. As much as you try to weed out every type of bias with your internal evaluation methods, it’s to some degree impossible.” – Andrew Berry, The Alliance for Decision Making podcast, July 2021

That’s a lot of specific, helpful, in-practice advice but it is really just one thing: distance.

Distance is the idea behind base rates. It’s switching to “the outside view“. Distance is the idea behind sleeping on it. If the input to good decision making is the best information, then distance changes the information.

Berry recognizes, first, that he alone won’t make the best choice. Berry recognizes that his team will make better choices with training. Berry recognizes that no matter how much work he puts into himself and his team that they’ll still use some suboptimal information, so they get outside information too.

A friend went to a wedding and proudly said he wasn’t hungover because he alternated drinks of beer and water. That’s good design. Berry probably has good design too, don’t evaluate players within one week of a season. Maybe they do it like the Olympics, and throw out the best and worst scores. Whatever the Cleveland Browns system is, they definitely have a system for making good decisions.

Life is messy is one of Brent Beshore’s expressions and it’s a wonderful “default”. If our thinking is framed by the starting state then to start with the idea that life is messy makes a lot of other parts less so.

Tailing Rodgers (part two)

For each thing that happens there is a field of potential things which could happen. Those potential events fill out a distribution where some events are more likely than others. A daughter’s height for instance, could be between four and eight feet but it’s very very likely that her height will be between her mother’s and father’s heights.

Thinking about these distributions of potential outcomes can be helpful because the areas which are not compact, like daughter’s height, are interesting.

Our annual NFL example (last year was Tom Brady passing yards) is Aaron Rodgers over/under 38.5 touchdowns. Here’s how we visualized it in September 2021:

Rodgers chart

The thinking then, as now, was that Rodgers would throw between twenty and fifty touchdowns but not with equal odds. The number of touchdowns would be asymmetrical. It was much more likely Rodgers threw half of 38.5 than double it.

Five games into the season offers a chance to be Bayesians and update our forecast. In addition to the preseason line of 38.5, his career average is 33.4, and his current pace is 32. Mix in the chance of injury, and he could also finish the year with the ten touchdowns he’s tossed thus far.

Let’s tack this on to the 2021 predictions:
– +10 TD, 90%
– +20 TD, 85%
– +30 TD, 50%
– +38.5 TD, 10%

I wanted to go lower on the 38.5 percentage, but one lesson from Cade Massey is to be less certain about extreme events. So in the same way that online doesn’t equate to real life and we should adjust for that, I will adjust my percentages as well.

Daughter height is top of mind because I have eleven and thirteen year old daughters. 😬

Does the bundle explain it?

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.

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.”

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

Tailing Aaron Rodgers

First, the New England Patriots pre-season win totals…

“If you forced me to make a play I’m circling the under at 9.5 (wins) at -120. I think there is a longer tail to the under here; if they stick with Cam Newton a little too long, if Mac Jones is a little farther away than people realize, if there are injuries in this relatively aging defense, if the offensive line isn’t quite as good, if the offensive weapons don’t really make a contribution. There are a lot of ifs that are potentially negatives for the Patriots and I am perfectly fine playing the win total under.” – Drew Dinsick, Deep Dive Podcast, July 2021

During the 20/21 NFL season we ‘Tracked Tom‘ to see if Tom Brady would hit the over on his passing yards for the year. The theory at the time was the same that Drew describes: more can go wrong than go right. The question wasn’t about how well Brady played, per se, but rather what big events might happen and which way would they break? For Tom, everything was terrific and he hit the over.

It’s Plus EV Analytics who thinks this way, in part from reading Nassim Taleb. And from him we’ve got another for the 21/22 NFL season!

There’s a chance Aaron Rodgers says chuck-it, and goes on to host a game show and he throws 0 touchdowns, a 100% decrease from the line of 38.5. There is no chance he Proves them All Wrong™️ and has a 100% increase to 77 touchdowns (the league record is fifty-five, only three players have thrown more than fifty).

Visually the idea looks like this:

Take the under on Rodgers.

But not all systems are like this. Sports can be under on the idea of injury alone. Financials can be under too. Cryptocurrencies, for instance, can be hacked, regulated, or fall out of fashion. If someone put the over/under line of Bitcoin at $38,500 at the end of the NFL season, a similar set of arguments and conclusions flow.

To a point.

Unlike Rodgers, Bitcoin could double. It’s a different system. Businesses are more like Bitcoin than NFL lines. Most of the Amazon services started out as bets: will this thing work? Amazon’s wager was the outlay in resources but Amazon’s winnings, unlike Aaron’s TDs, could easily double, triple or more. Here’s how Jeff Bezos put it.

“We all know that if you swing for the fences, you’re going to strike out a lot, but you’re also going to hit some home runs. The difference between baseball and business, however, is that baseball has a truncated outcome distribution. When you swing, no matter how well you connect with the ball, the most runs you can get is four. In business, every once in a while, when you step up to the plate, you can score 1,000 runs. This long-tailed distribution of returns is why it’s important to be bold. Big winners pay for so many experiments.” – Jeff Bezos, Invent and Wander

Fat bottom tails make the complex world go ’round and a basic understanding of distributions, curves, and areas helps.

Football ’21 favorites or field?

“Between the Chiefs, Bucs, Packers and Bills there’s a fifty percent chance of one of those four teams winning the Super Bowl. In other words, you can have those four teams or the other twenty-eight in the league.” – Cade Massey, Wharton Moneyball, August 2021

Take the other twenty-eight! This idea holds in both sports and investing.

One potential bit of mental muck is what we can call Visibility. It is easy to imagine a specific thing happening rather than a range of things happening. Visibility is part-of-the-reason counterfactuals and postmortems are difficult to conduct. That three of the four quarterbacks have in fact won a Super Bowl makes this effect more so. I can ‘see’ one of these quarterbacks winning the big one, but that doesn’t provide helpful information.

Not so fast though.

What is ‘the field’? As Tim Harford wrote, it is as often the words as the numbers which cause confusion (life expectancy for instance). In the case of the NFL, it’s the twenty-eight other teams that might win the Super Bowl.

But is that right? Can every other team win the Super Bowl? While on “any given Sunday” any team might win, stringing together a group of wins to be champion is far less likely.

The central point to Zeckhauser’s Maxims is that reframing a situation may cause our conclusions to change. We used this framework to ask: Was the Ohio Vaccine Lotta a Good Idea? What if we reframe the question around Super Bowl favorites then?

Roughly speaking there are three groups: the Favorites (4 teams), the Chasers (X), and the No Chancers (Y). Now how many Chasers and No Chancers there are is questionable, but the framing changes our thinking. If this is the structure then the relevant idea isn’t the field but a subset of the field: the Chasers. If there are 4 Favorites, 4 Chasers, and 24 No Chancers then the choice changes. Take the favorites. What if there are 4 Favorites, 8 Chasers, and 20 No Chancers? The top twelve preseason favorites have won 85% of the previous 20 Super Bowls.

There’s no definite answer to this Favorites, Chasers, and No Chancers structure but the framing does change how we think about it.

Another mental model is the same mindset we used “Tracking Tom“. The idea there was that there’s more downward variance than upward variance. The same idea holds for the Bucs, Chiefs, Bills, and Packers: those teams are more likely to underachieve. Put another way, it’s more likely that something goes wrong (someone’s quarterback underperforms) than right. The Chiefs and Bills, for instance, both notably outperformed their 2020 Pythagorean figures.
“Uncertainty is generally underestimated,” said Adi Wyner, “and that means that the field collectively have a little bit more probability than you might assign to four teams.” The data agrees. Take the field.