The Base Rate Is A Hell of A Thing

Nick Maggiulli wrote a blog post a few weeks ago titled Respect the Base Rate , which opens with this wonderful story:

This is a companion discussion topic for the original entry at

Huh. On one hand I have never been an active investor, because getting (index fund + reinvested dividends + index survivor bias) returns for approximately zero effort has always felt like a great deal. On the other hand, as a regular buyer of assets, I look forward to the times when prices are down so I can buy at a discount.

It’s enough to make me wonder if I ought to experiment with a small active investment.

Oh dear, what have I done?

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This was a thought provoking post. I tried to apply some of the ideas discussed here to my own life, and discovered a few ideas that could be added to “respect the base rate” to help make better decisions

  1. Respect the base rate given your shots at goal
  2. Respect the base rate given the outcome payoff disparity
  3. Respect the base rate given the difference in reference classes

Respect the base rate given your shots at goal

If you only have one shot at goal (like Kahneman’s team did when writing a book for 7 years), it makes a lot of sense to respect the base rate. But when you have multiple shots at goal, you can see the compounding effects of the base rate. This is particularly true in cases where you can try, fail, and iterate quickly

For example, if you try something with a 20% chance of success but only have one shot at it, and requires a significant commitment to try — it may not be worth it. But if you have say, 10 shots at goal, the probability that you’ll fail in all 10 is only (1-0.2)^(10) = 10.7%

One can supercharge this process (i.e., have a higher chance of success in subsequent iterations) with the approach that Cedric had listed in his post about Better Trial and Error:

  1. Don’t blow up (avoid risk of ruin)
  2. Don’t select trials randomly or suboptimally. Iterate and learn from your failures. Instead, search for relevant approaches and fully reflect on your failures to figure out what to vary for future trials
  3. Don’t irrationally repeat the same trial over and over again, expecting different results
  4. Don’t think that solvable problems are unsolvable and stop prematurely
  5. Be efficient. Once you’ve figured out what works and generalized your approach, you can apply it to other similar scenarios and get to an optimal solution quicker

If one is more efficient with trial and error, they can increase the chances of success after every iteration. So one should respect the base rate, but always condition it on the number of shots on goal that one has

Respect the base rate, given the outcome payoff disparity

This is obvious, but worth stating in a checklist. If something that is likely to fail has a disproportionate payoff, such that the expected value of doing is positive, you should still do it.

When flipping a fair coin, getting 3 heads in a row is unlikely (12.5% probability). But if you’re given a game where you pay $1 to play the game, and will get $50 if you get 3 heads in a row, you should absolutely play the game (if losing the $1 won’t cause ruin for you)

Respect the base rate, given differences in reference classes

Cedric talked about this in the last bit of the blog, but this was worth putting as a separate point.

I have autoimmune issues (increase in eosinophils in response to specific food items) that are quite rare. If I take the advice that applies to most people (eat a wide variety of foods) – if will be catastrophic for me. My reference class in this case is indeed different from that of most people.

So instead of blindly looking at the base rate of an event x happening (P(x)), one should look at conditional probabilities that apply to them P(x|y). Where y is the set of attributes that applies to you.

If x and y are independent, one really doesn’t have to worry about this. Because in that scenario, P(x|y) will be equal to P(x). But in scenarios where they don’t, missing out the conditionally can be deadly.

Most people can’t be professional basketball players. If you’re a muscular 7”6’ with great cardio and coordination though…

Buffett puts this difference in reference classes really well when talking about how he evaluates opportunities

You should be like a basketball coach who runs into a seven-footer on the street. I mean, you’re interested to start with; now you have to find out if you can keep him in school, if he’s coordinated, and all that sort of thing


Fear not, Cedric. No temperament check is going to make me allergic to downside risk. :smile:

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