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:
Graphically

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.

Favorites or the field?


The top five S&P companies account for 22% of the index’s earnings and a similar percent of the market cap.

“To me that is an interesting market question right now. If you were a betting man would you take the other 495? Would you take the field or would you take the Lakers with LeBron, a healthy Anthony Davis, James Harden and Kevin Durant on the team too?” – Carl Kawaja, Invest Like the Best, July 2021

One way to improve decision making is to understand the mechanics of a system. The physics system for example is relatively stable and that’s why, with great work, engineers can land the Perseverance rover in a Martian area twice as wide and one-third as long as Manhattan. Other systems, like social systems, follow the rules of network effects like the friendship paradox.

Sometimes analogies help to understand the type of system. One sporting analogy is to take the favorites or the field. When Kawaja’s episode was released, the Chiefs and Bucs had a cumulative 33% chance to win the NFL big game. Sports vary though. In January 2020, three NFL favorites had cumulative odds of about 30%. Meanwhile the top three NCAAF football favorites had odds of about 75%. Three tennis players at the French Open get a bettor to better than ninety-five percent. Want to bet the PGA Master favorites? The top seven golfers only get you better than a coin flip.

Odds in January 2020

One reason to take the field is that more can go wrong than go right. Something is always happening and it’s more likely to be a “negative tail” event than a positive one. During the 2020-21 NFL season we guessed that Tom Brady would not hit the over on passing yards (he did) by guessing that injury, Covid, and new teammates had a much larger downside area. Kawaja recognizes this too, noting “guys get injured”.

It’s not that the field or the favorite is better, but which is cheaper relative to the expected returns. During the Big Game for instance, things happening (safety, two-point conversation, etc.) are priced higher because people like to bet more on something happening. Successful betting and investing isn’t about finding the best, but finding the best odds. Yes, the Chiefs and Apple are great teams but is there value in the high prices?


Physics systems or social systems are wonderfully illuminated in Nassim Taleb’s book Antifragile.

How to complete next year’s NCAA Men’s Basketball bracket

A quarantine activity in my sister-in-law’s family is buying stocks. Stonks. Gamestonks? Each week, each kid, gets five dollars. They invest in whatever they want.

The best returns, to date, are from my niece. She’s 8. Her name begins with ‘T’ so her stock choices begin with ‘T’. She owns Tesla.

My three nieces and nephews aren’t competing but they do demonstrate that in small groups the best way to outperform others is ‘be chalky.’ Picking favorites is called chalky because in the days of horse racing, tracks wrote the lines on chalkboards with chalk. Even then, people liked betting favorites, so those odds were updated more often and had fresher chalk marks. Hence, ‘betting chalk’.

The same structure works for winning in any small group. To outperform, bet chalk. **However in a large group, choose variance.** Be different, and be right. We know that something will happen. We just don’t know which something.

One way to think through this approach is to consider the sum of the NCAAM final four team’s ranks. This question was posed on Wharton Moneyball and we have an answer: 11. On average, two number one seeds make it to the final four each year. Only in 1993 did all one seeds make it to the FF.

Yeah, but Covid!

That’s what I thought too. When Cade Massey proposed that it might be a more variable season I thought, base rates be dammed it’s going over. But that’s probably wrong (Narrator: It was not).

What I missed what something Daniel Kahneman wrote about in TFaS: substitution.

Rather than answer the question: Will the sum of the ranks of the final four teams be larger than average this year? I substituted the question: Will there be more variance this year?

What I missed was the idea behind hurdle technologies. In food preservation there’s not just one way that keeps food safe to eat, but a bunch. Food might be too acidic and be cooled and be sealed. It’s the combination of things, a series of obstacles, which limits bacteria.

That same idea applies in a bracket. Oral Roberts (#15) beat Ohio State (#2) and Florida (#7) but had to face Arkansas (#3) too, who won.

Ultimately the final four seeds totaled 15 (1,1,2,11). My direction was right. My reasoning was wrong.

Gambling with Votes

Thirty days of September and October PredictIt markets.

Like Gambling with Covid19, betting markets can demonstrate probabilistic thinking. In that post we considered an idea from Matt (+EV) about Tom Brady’s potential passing yards.

In April Brady’s over-under yardage was 4,256, nicely inline with previous years of 4057, 4355, 4577, and 3554. However, Matt noted, there’s a lot more room under 4,256 than over it. Brady could get injured, retire mid-year, have a worse system, lose teammates and so on.

On Wharton Moneyball Cade Massey noted that the same idea can apply to modeling voting and prediction markets. In the FiveThirtyEight simulation (40,000 runs), Joe Biden wins eighty-seven times out of one hundred.

What’s the gap between 87 and 66?

  • Potential polling errors. 538 is an aggregation. Put another way, the level of awareness while driving one hour twelve times is not the same as driving twelve hours one time.
  • The Brady effect. There’s just more room for ‘something to happen‘ in one direction instead of another.
  • Matt’s Twitter handle +EV gives an idea too. It could be that Donald Trump’s odds to wins are less than a coin flip just not as bad as a single number on a roll of the dice. That middle area is the market.
  • People like betting favorites, public teams, and for the safety.

A neighbor invited me to a watch party on November third. Another challenges himself to go as long as possible without finding out the news (in 2016 he made it three days). I follow things loosely but thinking about it this way does feel sharp.

As Howard Marks says, it’s not so much what you buy as what you pay. Brady, for those interested, is on pace to go over.