Insurance is about covering risk and not a certainty. For instance, a young and healthy person faces the risk of untimely death due to an accident or sudden illness, but for an ailing person who does not have age on his side, the possibility of death is more immediate. Death will no longer be an untimely event.
For an insurer, the probability of the risk actually becoming a reality is important. So the probability of death for an old and ailing person is higher compared with a young and healthy person. To get their numbers right and predict risk more accurately, insurers need a large pool of people facing the same risk. Here, the law of large numbers comes into play.
What is law of large numbers?
The law of large numbers is one of the laws of the probability theorem. This law states that the average of the results obtained from a large number of trials will inch closer to the expected result as more and more trials are performed. Let’s explain this through a popular example. When you flip a coin, the chances of it landing head upwards are 50% since the coin has two sides and it could either show head or tail. By this logic, a person flipping a coin six times should get a tail at least three times, but when a coin is flipped just six times, the person may get five tails in a row. But flip that coin 60 times and the number of tails would be closer to the half mark. As you increase the number of trials of the same event, the chance of that event happening gets closer and closer to the average chance of the event taking place.
Why do insurers apply this law?
An insurer can predict the chances of a defined risk taking place more accurately through this law. For example, as the number of people in a group wanting an insurance cover against a common risk (say risk of car theft) increases, the real life cases of that disaster comes close to the expected average of that event occurring. In other words, the deviation of the actual event from the expected average will reduce as the number of people in the pool increases.
So larger the sample size, the greater is the predictability for insurance when doing their premium rating. If, according to the past track record, one in 10 cars get stolen in a locality in a year, then the probability is 10%. If 1,000 cars are insured, the actual number of cars getting stolen will be around 100. But if there were 100,000 cars in the pool, the actual number of cars getting stolen will be close to 10,000. By having a larger pool, the insurer can accurately predict the probability of an event and price the policy accordingly.