Learning From the Boy Who Cried Wolf

False positive and false negative

Lots of us are paid to make decisions:

• Maybe you decide how to treat a patient
• Maybe you decide if a prisoner is guilty
• Maybe you decide how much soup to prepare
• Maybe you decide if a payment is fraudulent

Maybe, maybe, maybe. There are plenty of decisions to be made.

Making the wrong decision

If you make the right decision then everything goes swimmingly. Unfortunately if you make the wrong decision then things can get very expensive.

To make matters worse there is — usually — only one right decision and hundreds of wrong ones. What exactly is the best route for your delivery van?

Even with simple yes no decisions you can get them wrong in two different ways.  You can decide something is when it isn’t , or you can decide something isn’t when it is.  Confused?  Let me tell you a story.

The boy who cried wolf

There was a shepherd boy who spent his day looking after sheep on the side of a mountain near a big dark forest.  He was lonely and he was bored, so he came up with a plan to create a little excitement. 

At the top of his voice he started to shout “Wolf, Wolf, Wolf”.   The people in the village below heard the commotion and they ran up the hill to scare off the wolf and save the sheep.  But when they got to the pasture where the sheep were grazing there wasn’t a wolf to be seen. Obviously it had seen them charging up the hill and they had scared it off.  A few of the villagers stayed with the boy and kept him company, just incase the wolf returned. You can never be too sure with wolves…

This made the little shepherd boy so happy that a few days later he tried the same trick. Once again the villagers stormed up the hill to help him and once again there wasn’t a wolf in sight. The villagers started to grumble. Was there really a wolf or was the boy playing them for fools?

Later that week a pack of wolves really did come out of the forest.  The little boy was beside himself with fear and screamed out “Help Wolf, Help Wolf” even louder than before.

The villagers were heartily sick of running up the side of the hill. They had decided that the shepherd boy was an attention seeking little git and was making all the wolf rubbish up. So they carried on with their daily business.

And that, I am sorry to say, was the last that was ever heard of the sheep… or the little shepherd boy.

Aesop ~ give or take

Is when it isn’t and isn’t when it is

The villagers made two types of error; false positive and false negative.

• When the boy cried wolf and they ran up the hill the villagers made a false positive decision. They believed there was a wolf, but there wasn’t.
• When the villagers ignored the screaming boy they decided there wasn’t a wolf, but there was.  They made a false negative decision.

The available facts

Information is never perfect. When you make a decision you can only make it on the data that you have available to you.

When there was a wolf the boy would shout and make a lot of noise, but he never made exactly the same amount of noise. Nor did he shout the same thing. If the villagers had taken the time to collect some data they could have drawn a graph a little like this:

When the boy was just bored he may also have decided to shout, but his heart wouldn’t have been in it. His screams weren’t quite so loud.

The problem is that there was an overlap.  When the noise levels were in the middle the villagers listening to the boy could never be sure if there was a wolf or not.

Improving your decisions

There are two ways to improve your decisions:

1. Improve your test

The first is to improve the data you gather and the quality of the test you use.  The villagers could have bought the shepherd boy a pair of binoculars and a book on advanced wolf recognition techniques.  Alternatively they could have beaten him about a bit for being a pain in the neck.  If they had done that their test would have been better.

But still not perfect.

2. Define your cut off point

The second way to improve is to be clear about the cost of the decision.

If it was worse to run up the hill and have the shepherd boy smirking at them then the villagers should have set their tolerance to the right.  This would have resulted in fewer false positive decisions (unnecessarily sweaty villagers) but more false negatives (dead sheep).

If the sheep were the villagers entire livelihood they could have set their tolerance to the left. Then there would have been fewer dead sheep but more irate villagers.

Where should you set your tolerance?

It is wise to decide before you have to make decisions in anger.

Where you put your cut off depends on what is important to you. There is no magic answer other than to say it depends on whether you are a villager, a shepherd or a wolf.

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Photo by Neil Rosenstech on Unsplash