“Welcome to Lake Wobegon, where all the women are strong, all the men are goodlooking, and all the children are above average." Garrison Keillor
More generally, illusory superiority is the tendency to overestimate one’s ability compared to others. For instance, it’s widely quoted that 80% of drivers think they are above average in driving skill, and we all poohpooh those other dumb people who erroneously think they can somehow defy simple math. However, there is a perfectly rational reason for this to be the case.
For something like height that is easy to measure and easy to compare, you would probably find that close to 50% of people think they are above average. But what about more complex skills like driving or intelligence or soccerplaying? There are multiple dimensions in each of those. Person A hasn’t been in an accident in 10 years. Person B easily maneuvers through city traffic and can merge onto a highway seamlessly. Person C would win a race around a closed course. In soccer, some players score goals, some pass the ball well, and some play defense. Who’s the best? Well, the mother of the soccer player who scores goals thinks that goalscoring is the most important skill, while the father of the defender thinks that defense wins championships, and the grandfather of the passer loves the beautiful game and wants to see the ball passed around. Who is best? “My kid!”
Let’s say that each player can accurately assess how good everyone is in each attribute. However, each of them thinks that the attribute they are best at is twice as important as the attribute they are secondbest at, and four times as important as the one they are worst at (so, a 4x2xx weighting). What happens now?
Here’s a simple example with three players. Each is really good at one skill, average in another, and terrible in the third, but is average if each skill is equally important. Fairly evaluating each skill (but not their importance to “soccer playing ability”), each player thinks that they are the best. Similarly, each player is considered by one of the others to be the worst.
Player

Scoring

Passing

Defending

Equal assessment

Scorer’s assessment

Passer’s assessment

Defender’s assessment

Scorer

9

5

1

5

6.7

4.4

3.9

Passer

1

9

5

5

3.9

6.7

4.4

Defender

5

1

9

5

4.4

3.9

6.7

What about the broader case? I did a simple simulation for this. I have 10 000 individuals whose skills in three attributes are independent and are uniformly distributed. As you would expect, 50% of them are above average on each attribute and on the average of the three attributes. However, each weights the importance of the skill in accordance with their ability in that skill. What happens now? As it turns out, 74% of these people are now above average! The median person is now in the 63^{rd} percentile.
Now let’s add in the illusory superiority bias and see where we get. Let’s assume each person overestimates their skill by a mere 5%, so if they are truly average, they think they are in the 55^{th} percentile. Now, 81% of the people are above average.
How about a reallife example? Who was the best hitter in the American League in 2017? I looked at three stats (batting average, home run rate, and strikeout avoidance) for all 78 qualifiers that year, and compared each player to the average qualifier in that stat. Using an equal weight for the three metrics, there were about an equal number of aboveaverage and belowaverage hitters, as we would expect. But what if each qualifier got to choose what stat was most important and which was least important, like in the hypothetical example above? Then, the average player was suddenly 12% better than average, and 57 of 79 (73%) are above average. Welcome to Lake Wobegon.
_{}^{}