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  • Tom Birchard

Probabilistic Thinking

Updated: Feb 14

Probabilities are inherent in many decisions we make every day, and the ability to recognize this and do some quick mental math can be a superpower. Many people, myself included, just filled out an NCAA tournament basketball bracket (or several) and are enjoying watching the March Madness games. In the pool I’m in we were asked to pick the winners of the first 4 play-in games in addition to the remainder of the tournament. Glancing at the other brackets I noticed a few examples of picking the winners of those play-in games to advance another round and it dawned on me that despite picking other upsets, I had automatically decided not to consider picking the winners of those play-in games to advance any further. Why would that be? The answer is the multiplication rule in probability. Consider UCLA who tips off later this evening (as of the time of me writing this). UCLA has a 39% chance of beating BYU according to my ESPN app, not bad right? Well not exactly. The Bruins out of UCLA beat Michigan State to advance to play BYU, and let’s say their odds in that game, which went into overtime, were 50/50. Because of the multiplication rule in probability, their true chance to beat Michigan State AND to then advance past BYU would have been less than 20% (39% x 50%), not impossible but certainly handicapped from an odds standpoint due to having to compete in the play-in game.

When thinking about this post on probabilities, another recent sports example that came to mind was the Green Bay Packers decision to kick a late game field goal against the Tampa Bay Buccaneers in a game they ultimately lost (sorry to pour salt on a wound Packer fans). For those not familiar, the Packers were down 8 at the Bucs 8 yard line with a little less than 3 minutes left. It was 4th down and Green Bay opted to kick the field goal rather than try for the touchdown and 2 point conversion to tie the game. I can remember while watching the game it seemed like a foolish decision and the coach was heavily criticized. Once the dust settled though several articles were written such as this one (Link) breaking down the decision from a probabilistic standpoint. Arguments can clearly be made either way but what’s abundantly clear is the decision was far more complicated and nuanced than the typical human brain could accurately process in that moment.

In considering examples of probabilistic thinking, sports is an obvious place to look. However, where I think it gets really interesting is the many other areas of everyday life and decision making where probabilities are at play. Professional poker player Annie Duke wrote an excellent book about this exact topic called Thinking in Bets. Duke makes the argument that everything is a bet, even decisions that seem very binary or right vs. wrong. Decisions like what job to take, buying a house or where to live, even what you choose to eat has some sort of future probability distribution baked into it. There are many implications to this but I’ll touch on just a few…

· Acknowledge Uncertainty – It is totally ok, and probably a good thing, to say “I’m not sure” more often because the reality is, you don’t! Many people feel the need to have conviction even in the face of significant uncertainty. Next time someone asks whether now is a good time to invest in Stock XYZ, rather than simply saying yes or no, perhaps it’s better to talk through the pros and cons as well as assumptions, and express your opinion with a confidence level or simply say “I’m not sure”.

· Don’t Judge Based Solely on Outcomes – When you acknowledge that every decision has some degree of uncertainty and a future-looking probability distribution, you can start to separate outcomes and results from sound decision making. Over time, with the effect of compounding and the multiplication rule of compounding I mentioned earlier, the person who makes many sound decisions will probably find success. But in any specific situation, the best team doesn’t always win and the “right” decision doesn’t always lead to the expected outcome. Appreciate the role of luck and intrinsic uncertainty when judging past events and outcomes.

· Respect the Base Rate – Nick Maggiulli wrote an excellent Post on this. The base rate is essentially the probability of something without factoring in any other information. Maggiulli explains how he unknowingly doubled his chances of getting accepted into Stanford simply by applying early. Another base rate example would be that only 18% of active money managers beat their benchmarks over a 15 year period (Link). That certainly doesn’t mean you won’t find one that will, but you’d be wise to respect the base rate. Yet another base rate example would be smokers are 15 to 30 times more likely to develop lung cancer. We all probably know a lifelong smoker who’s perfectly healthy but once again…base rate. Read Nick’s post for a great example from the NBA where the base rate can quickly breakdown with a little additional information.

· Consider Both Risk and Reward – Adding in a variable and quantifiable reward to a probability distribution brings a new dynamic. Venture investing is a good example where the odds of picking a winner are low, and certainly far riskier in any single investment than an index fund or a stable, dividend-producing large company. That being said the potentially huge returns from picking the next Uber or Airbnb make it a still appealing field for a certain type of investor. Along these lines be on the lookout for the rare situations with asymmetric risk and reward where the downside is limited but the upside is considerable.

Can you think of any other effects of this way of thinking? If you’ve enjoyed reading this I’d encourage you to enter your email and subscribe at the bottom of the page. Remember to respect those probabilities when evaluating decision and enjoy the rest of the NCAA tournament!

Here are some recommendations from the last 2 weeks:

· Book - Three-Ring Circus: Kobe, Shaq, Phil, and the Crazy Years of the Lakers Dynasty – So this is a bit of a premature recommendation since I’m just getting started with the book, but I can already tell it’s going to extremely entertaining and fun to read. For NBA fans and especially a nostalgic Shaq/Lakers fan like myself, I think this is a must-read.

· Video - Jeff Booth Interview on Real Vision – If you’re interested at all in technology and the economy as well as trying to peer into the future, this is a very thought provoking and well done interview.

· Article - Addressing Climate Change in a Post-Pandemic World – If you’re interested in climate change (which we probably all should be at some level), this is a good breakdown of some of the implications of the current pandemic and some things that could be done at both a micro and macro level.

· Podcast Episode - Marissa King with Patrick O'Shaugnessy on Invest Like the Best – I feel like I’ve been recommending a lot of Patrick’s podcast episodes lately but he’s had some really insightful guests and just does a great job of displaying curiosity and asking excellent questions. This one is about social networks and three distinct networking styles and some of the pros/cons and implications of each.

· QuoteThe purpose of life, as far as I can tell… is to find a mode of being that's so meaningful that the fact that life is suffering is no longer relevant. by Jordan Peterson

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