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. 😬

Machiavellian framing

“The thing that makes The Prince such a timeless and scandalous work,” explained Stacy Vanek Smith, “is the same exact thing, Machiavelli removes morality from the situation.”

Smith is out to talk about her book, Machiavelli for Women and the book’s seed came about when Smith was stuck on her salary. Rather, her salary disparity. In her first job out of college, Smith and two classmates both ended up at the same organization in roughly the same jobs. But, not with the same pay. Rather than plead her case, pound the table, and present data, “I was in an emotional spiral of unjustness and upset and I never asked for a raise.” Smith needed some unemotional advice.

“What Machiavelli does is remove all that. He would probably look at (the salary disparity) as great information to use. Now what’s the best way to go about getting a raise? What’s the best way to ask? What do I do now? That’s why it is timeless, because it’s so smart.” – Stacy Vanek Smith, September 2021

Good framing is a design choice that affects behavior. We can frame self talk by having multiple ‘jobs’. We can frame vaccines as better than being bulletproof. We can frame decisions by asking, would I want this even if it were free? Each prompt changes the reference point and possibly the behavior.

As needed then, maybe some people should be Machiavelli Bayesians. Be slightly more princely, if that works do it again until it doesn’t.

Being (even more) Bayesian

Bayesianism has become my favorite math-idea-that-doesn’t-involve-math. It’s three simple steps. Step 1: have an idea about a thing. Step 2: observe the thing. Step 3: have a new idea based on the observation. (repeat)

There are two tricks to make this work for you. The first is how much to update. Being Bayesian means changing your mind in proportion to the change. Try the expression, “I’m slightly more sympathetic to X,” for example. Saying this acknowledges the new information and massages the ego.

The second trick is where to start (Step one), and we have to start somewhere.

“By not taking advantage of the accumulated knowledge that we have as a scientific community, we are artificially leveling the playing field. We are giving theories with no basis in scientific fact too great of a chance to prove themselves through the data.” – Aubry Clayton, The Conversation, August 2021

Clayton’s context is Covid19, but he touches on a larger point too. How much coordination and decentralized command a system allows.

A decentralized command iterates quickly. From the front lines of fast food to fashion to fights. If an organization wants to move fast, the decentralized command structure works better than coordination.

But while individual agents may be fast, the whole may be slow. Why? No coordination. The scientists in a medical research lab will do more experiments with no oversight or collaboration but they may not make more progress.

Coordination and decentralized command apply to both knowledge and people. Having accurate base rates and priors means coordinating our existing knowledge with the accumulated.


Bayesians even frame things beautifully. It’s not “changing your mind” bur rather it is “updating your beliefs”.

3 prompts to being Bayesian

How much should new information matter? Or, is this time different? Because sometimes it’s not.

“Merlin (Heidemanns) said that essentially the polls gain more weight. It’s not that we construct a model and weight the polls. We don’t take a weighted average of the polls, we estimate latent parameters and the polls are data. That said, you can roughly approximate the estimate as a weighted average.”

Andrew Gelman

According to Gelman, priors like “the economy, stupid” never exit the model. According to Nate Silver, the final poll removes all prior data.

In college sports priors matter more than Gelman allows for politics. Nearly two-thirds of college basketball teams who start a season ranked in the top-25, finish in the top-25. College football is the same.

How much new information should matter is a tricky question, but it’s helpful and why the Wharton Moneyball co-hosts encourage each other to become more Bayesian.

At the start of a football season we can guess (or hope) on a team’s chances. With more information, each play, game, and season, we update our idea. Eventually our guess at the start of the year gives way to the information of the year.

It’s hard to do though because we don’t know is this time different. Most of the time it’s not different enough, and base rates work best. But there are three general frameworks which might help us become more Bayesian.

First is to ask a Marc Andreessen like question: is software eating the world? How has the system changed and what does that mean? From FAANG to Testa joining the S&P, it seems like a systemic shift toward technology. Ditto for passing in football.

Second is to ask the Michael Mauboussin question: how much of this was luck? There’s a lot more luck in a single football play than an entire football game. It’s always a mix of skill and luck, but in what ratio?

Third is to consider our identity: am I attached to a position for unacknowledged reasons? This category includes biases like sunk cost and personal influences like ego or status.

The 2021 vaccine rollout is a good instance of practicing Bayesianism. Start with the base rate for vaccines. Watch for evidence. Adjust accordingly.