The last two years of David Anderson’s life have been harrowing. The 23 year-old has survived two of the most publicized mass shootings in recent memory.
First, in October 2017, he was a concert-goer in the Las Vegas shooting that killed 58. Second, about a year later he attended Borderline Bar, where a deranged gunman shot down 12.
Upon hearing these horrors, the first thoughts of many are, “what are the odds of witnessing two mass shootings?”
Well, thanks to Google we can figure it out.
Source: Business Insider
The odds of being in a mass shooting in your lifetime are 1 in 11,125.
That means the odds of being in two are 1 in 123.8 million.
Math time
If the odds of getting heads by coin flip are 1 in 2, what are the odds of getting two heads in a row?
Well, it’s (1 in 2) * (1 in 2) = 1 in 4
Same goes for David Anderson’s probabilities.
(1 in 11,125) * (1 in 11,125) = 1 in 123.8 million
When news stories like Mr. Andersons’ break, our first reaction is fear. We see these stories plastered all over TV and the front page. This plays on our availability bias, the human tendency to think examples of things that come readily to mind are more representative than is actually the case.
To illustrate why this is a problem, let’s use an example.
Unsurprisingly, after a publicized plane crash, many people will give up flying for driving if their destination can reasonably be reached by car.
But this ignores a key fact.
If you gave the above chart a good look-through, you may have noticed that the odds of dying by plane crash are 1 in 2,499 whereas the dying in a car, van or truck accident is 5x more likely at 1 in 491 (apologies for the morbidity).
So think about that. People are increasing their odds of death by five times because of availability bias. Since, right after a publicized plane crash, we can easily remember the horror, we tend to ignore the data, leading to a suboptimal decision.
Another name for this data is a ‘base rate.’
Base rates are probabilistic starting points for us to make better decisions. Because availability bias and a plethora of others can cloud our judgment, base rates are a helpful tool to give us a frame of reference.
But before diving in too much, we need to clear up a couple things.
A Few Biases
First, there is an inside view and an outside view. The inside view is your own view on a particular subject and the outside view is a collection of similar examples.
Obviously, because we know our own view, we weight that more heavily.
Daniel Kahneman and Amos Tversky, the famous Israeli psychologists addressed this issue in a paper. Using project management as an example, the duo said that people would be better off starting with the question, “How long do such projects last?” versus the more typical approach of, “How long will this project last?”
The difference may seem trivial but it’s getting at the fact that we are overconfident in our own predictions. To strengthen these, we need to look at the base rates of similar projects to inform our reasoning.
Second, we love stories. We do a beautiful job painting our inside-view narratives. Dr. Sanjay Bakshi summarizes this wonderfully,
“When you evaluate whether smoking is good for you or not, if you look at the average experience of 1,000 smokers and compare them with a 1,000 non-smokers, you’ll see what happens. People don’t do that. They get influenced by individual stories like a smoker who lived till he was 95. Such a smoker will force many people to ignore base rates, and to focus on his story, to fool themselves into believing that smoking can’t be all that bad for them.”
Third, the more luck that is involved in your task, the more you should weight the outside view. On the other hand, if a task is all skill, taking the inside view makes more sense. For instance, if you’re playing Blackjack, base rates would make more sense in the long run for your decision-making than because you’re wearing your lucky underwear.
So with those in mind, we can begin to form a defense system to these biases. Importantly, base rates can also be used in a positive sense as well (it’s not just death stuff).
For instance, there is a researcher named Michael Mauboussin, who went back and figured out the base rates for a bunch of metrics to see how many companies could sustain superior performance.
Source: Michael Mauboussin
This chart represents what proportion of companies achieved different sales growth numbers between 1950-2015. So in context, 15.1% of companies with revenues under $325 million grew over 45% on a one-year basis.
But if we look at the ten-year basis, just 2.1% of companies grew over 45%. This makes sense. Competition, rapidly changing industries, the Law of Large Numbers all contribute to slowing sales growth. Put another way, performance usually reverts to the mean.
Notice I said ‘usually.’ There are those special companies that can sustain superior growth for a long time. But using sales growth base rates suggests these are rare. By grounding our expectations in averages we can form realistic opinions, which helps protect us from the above-mentioned biases.
That is not to say we shouldn’t try, as investors, to seek out the great companies, but rather we should not delude ourselves to the reality of how hard it is for companies to grow quickly for a long time.
To End
Using base rates will improve your ability to predict the future. Rather than being tricked by recency, overconfidence and stories, your viewpoint will be grounded in data.
Here’s to another tool in your tool-belt for making better decisions!
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