Can you predict chances accurately?

Furthermore, probability is not predictability. Knowing that that the probability that a fair coin will land on heads is 50%, you in no way can accurately predict the next flip. Maybe you can predict on average how many flips out of 100 will be heads, but you won't be able to predict the next flip with any certainty.

towardsdatascience.com - Probability is not Predictability | by Barry Leybovich

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Probability is not Predictability

Weather Forecasts, Cancer Diagnoses, Coin Tosses

Suppose you are watching the nightly news (or more likely your phone just tells you) that tomorrow there is a 30% chance of rain. Tomorrow, do you carry an umbrella?

It’s a seemingly benign question, but the way we interpret probabilities has real ramifications for how we make decisions and business and in life. It In the following, we’ll break down what probabilities and statistics like this mean at their core, and how we make decisions around this uncertainty.

When Statistics Become Probabilities

Let’s use the same example — tomorrow there is a 30% chance of rain. Generally, statements like these are using inferential statistics: they look at the frequency an event has occurred in the past and using an inference to apply it to the future. Suppose that in the past 100 times a particular weather pattern has occurred, 30 of the times it has rained the next day. If today a meteorologist sees that pattern, he or she may say: “30% of the times I have seen this pattern, it rained the next day. So there is a 30% chance it will rain tomorrow.”

- Some meteorologist, somewhere

However, that’s not quite what the probability (note: statistics are historical frequencies, probabilities are future likelihoods) means. What it actually means is roughly: Based on the fact that 30 out of the past 100 times I’ve seen this pattern, it rained the next day, I am inferring that out of the next 100 times I see this pattern, it will rain on the day following 30 times. Given that I see the pattern today, there is a 30% chance that this is one of the days when I see the pattern and it rains the next day.

- No meteorologist, anywhere

We see right away that this is a much more involved statement. Importantly, we see how the historical observations (i.e. statistics) are translating into forward-looking probabilities. Unfortunately we don’t know if tomorrow will be one of the days it will rain — knowing the probability doesn’t help us predict whether or not to bring an umbrella tomorrow. After all, tomorrow isn’t happening 100 times, it’s happening once.

Probabilities and Discrete Events

Weather is something that happens every day, and so it may be appropriate to use probabilities to characterize weather in the long run. Let’s look at something discrete: a patient receiving a cancer diagnosis. When a patient is diagnosed with cancer, something that they may commonly ask (or be told by their physician) is “what are my chances?” This is frequently used to help patients assess the seriousness of the diagnosis. Intuitively, we understand that “80% of similar patients survive after 10 years” is a better prognosis than “8% chance to make it to 10 years”. However, we ought to unpack this further to really try to understand what these mean.

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