Did you ever wonder why all the old buildings around you survived centuries whereas the modern houses seem nowhere near so sturdy? Maybe your conclusion was that ‘it was a different era when people built solid walls, not like today’. Well, maybe. But maybe you just don’t see all the other ancient buildings that didn’t make it and collapsed long before you were born.
US Navy story
Let’s talk about the Survivor’s bias. And before I spoil all the fun, you can test your logical reasoning skills on the following US Navy puzzle:
In the World War II, the US air forces were suffering big losses, because a significant number of their planes never returned back from the battle. The air forces concluded that they needed to strengthen the planes’ construction to make it more durable. The plan was to cover certain parts of the plane by an extra layer of armour.
But because the armour was heavy, the engineers had to use it sparsely and cover only the most critical parts of the plane. They noticed that the planes that had returned from the battles were most damaged on the wings, so they decided to cover the wings with the armour.
This was when the statistician Abraham Wald stepped in and argued that not the most-hit, but actually the least-hit parts of the planes must be covered in extra armour.
Abraham Wald was right. Can you explain his logic?
Puzzle solution
The above story is an example of a common reasoning fallacy called the Survivor’s bias. Even when we think that we make decisions completely rationally, based on the data, it may not be the case. The problem is that our dataset may not be complete and we didn’t get to see all the data points. Just as we didn’t get to see all the old buildings that were ever built but only those that persisted into our times.
Similarly, there were many US Navy planes that never returned from the battle. From the data that the US Navy could see, namely from all those planes that did return, Abraham Wald correctly noticed that even though these planes were heavily hit into certain parts, they were still able to fly to return from the battle. Hence, he deduced, it must be the other parts of the plane that are crucial, and susceptible to being hit. Being hit into a vulnerable spot would immediately cause the plane to crash and so, the plane would never return from the battle and the US Navy would never see that that was a vulnerable spot where the plane needs extra armour. Hence, the extra armour is needed at the least-hit parts of the planes that returned. Pretty counter-intuitive, right?
You can find more examples of the Survivor’s bias here, many of which happen in our everyday life. Can you identify an experience when you dealt with the Survivor’s bias in your own life?
If you are interested in trying more puzzles related to reasoning and rationality, you can check out the Grow Trails’ rationality trail.
Fun fact: old bridges are in fact better
When we already mentioned old buildings, let’s close up by also mentioning old bridges.
Did you know that the probability that an old bridge collapses exactly when you are crossing it is actually smaller than the probability that a newly built bridge collapses?
Isn’t that also pretty unintuitive? There’s a mathematical probability argument explaining it, but let’s discuss that one another time :).
Being a scientist and an educator, I love creating meaningful games for all those who are ready to trick their mind, experience adventure and discover more about themselves and the world around us.
I started Grow Trails, the interactive educational games for adults. Read my story.