80% of All Statistics

Many years ago, I was introduced to the snarky statistic that 80% of drivers believe they are above average. This annoyed me from the start. Initially, I thought it was just another useless statistic; its snarky meaning had to be explained to me, “You see—idiot—only 50% of drivers can be above average; so at least 30% of the people are fooling themselves!”

The statistic has the feel of an urban legend. It seems reasonable—but then such stories always do. In fact, it appeals to my prejudice (very common among the kind of people who would pass on such information) that people over-estimate their own skills and under-value those of others. Just like an urban legend. And, of course, there is no real reference, and one has to wonder who would pay to find out how many people think their driving is better than it really is. (It turns out that a number of people would; see the caveat at the end.)

The biggest problem is that the snarky aspect of this “fact” is incorrect. It is quite possible for 80% of a population to be above the average (mean). Just imagine if driver quality were rated on a scale of 0 to 100. Further, imagine that there were ten drivers with the following ratings: 0, 100, 100, 100, 100, 100, 100, 100, 100, 100. Clearly, the average would be less than 100 and so 90% of the population would be “above average”. (I’m slow, not stupid.) This is hardly a normal distribution, however. And you would think that driver ability would be a normal distribution, or something like it. (But maybe not; my father thinks that the road is filled with “idiots” and him.)

At this point, the worst case scenario is that someone comes forward with an actual study that shows, more precisely: 80% of drivers believe they drive better than the median. On its face, this cannot be factually true: 50% of a population must be above the median and 50% must be below; this is the definition of “median”. However, this too is a ridiculous claim and leads me to the whole point of this article.

What does it mean to be a good driver? We must know this before we can know if one driver is better than another. For one person, a good driver might be one who can control his car at high speeds. For another, it may be one who always drives the speed limit. Given that most people are rather good at the kind of driving they value—and thus practice regularly—it is surprising to me that only 80% consider themselves “above average”. [caveat]

People are foolish. And at least in political matters, people tend to under-estimate others. For example, Americans consistantly over-estimate how racist their neighbors are: almost always rating them as more racist than they rate themselves. But this is exactly the appeal of this little statistic: “I am not one of those silly people who think that their driving is better than it really is.” My driving, however, definitely is above average.

[Caveat: Illusory Superiority]

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