Percentages aren’t the same as random chance

This is a follow-up post to my More likely to die how? post from four years ago, because I still keep hearing people equating percentages with chance.

Look, people shouldn’t get flipped out about whether or not their marriage is going to fail or not. You don’t have a 50/50 chance of getting a divorce because 50% of marriages end in divorce. There are about 50% of married couples who have a 95% chance of getting divorced and about 50% of married couples who have a 95% chance of staying married. If you believe that marriage is about feelings and always being infatuated with each other, then your marriage is going to fail. If you believe that marriage is about commitment and staying together through thick and thin (or “for better or for worse,” as the vow typically goes), then your marriage is going to work.

Think about it another way. Let’s say your high school has a graduation rate of 75%. That means 1 out of every 4 students drops out, fails out, or gets kicked out before completing 12th grade (yes, I’m writing from an American context—I’m American, so humour me). It also means 3 out of every 4 students completes 12th grade and graduates. Does that mean every single student has a 1 in 4 chance of not graduating? Absolutely not. The kids in the honors classes who don’t suffer from extreme perfectionism or depression, who do their homework, and who don’t skip class have almost a 100% chance of graduating, assuming they don’t get hit by a bus the day before graduation. The kids who never complete assignments, skip school, and have chronic behavioral problems have almost 100% chance of not graduating.

Likewise, again I keep hearing about how planes are much safer to travel in than cars. Why are there variable insurance rates, depending on gender, age, how long you’ve been driving, etc.? If everyone has an equal chance of getting into a fatal car accident, wouldn’t insurance companies have the same rates for everybody? But they don’t. They know a 16-year-old male who just got his license is far more likely to get into an accident than a 36-year-old female who has been driving for twenty years. There are exceptions, of course. Some 16-year-old males are both skillful and cautious, and some people who have been driving for decades are both unskillful and reckless, despite their experience. If I get into an airplane, no matter how “skilled” I am as a passenger, I have the same chance of dying in a plane crash as all the other passengers, because we have no control over the plane’s operations, maintenance, pilot qualifications, etc. We have no control whatsoever. So whether you die in a plane crash or not is 100% up to chance. Whether you die in a car crash or not is only partially up to chance. If you’re skillful and cautious, you’re far less likely to get into a car accident. You can’t be 100% sure you’ll avoid all crashes. After all, someone may rear-end you. A drunk driver might run a red light and smash right into you. But you will avoid many accidents that other less skillful or more reckless drivers will still have to face.

Percentages are the same as chance only if you have no influence on the outcome. Your academic work influences your chances of graduating high school. Your commitment to marriage influences your chances of staying married. Your skill and caution in driving influences your chances of avoiding a car accident. There are some things you have control over and others you don’t, but either way, you may still end up with the same percentages. Percentages are not always chance.