When I showed different people the graphic I made comparing my salary with that of Albert Pujols over the next ten years, I noticed they tended to overestimate the amount of money I earned by a good margin. In fact, I earn less per year than the average male, 25-34 years old, with a bachelor’s degree or more.
I attribute the reason for this over-estimation to the fact that I used the areas of circles to represent the two salaries, and in my experience people (myself included) are just generally bad at discerning relative areas. While making the graphic, I had to triple check my arithmetic because the picture I saw didn’t match intuitively with the numbers I had in mind.
So here’s another take. The area of each figure still represents the salaries of myself and Albert Pujols, but now the figures are rectangles, and each rectangle has the same width. Therefore, to compare relative sizes, you only need to compare a single dimension (the height) rather than two.
Albert Pujols recently signed a $254 million dollar contract over the next ten years with the Los Angeles Angels. Here’s how that looks next to what I expect to make over the next ten years.
Baseball. I should’ve gone into that.
The St. Louis Cardinals won the world series last night. I wish I had some emotional interest in either team as there was some great baseball played, and the two teams needed seven games to decide the final winner.
In that spirit, John Allen Paulos (the author of Innumeracy) tweeted earlier this week an interesting probability question:
Well, my intuition was stuck in the mud with this question so I did do some calculating. And like any good stats teacher with a frequentist view of probability, I simulated the World Series one million times with the following Python script:
trials = 1000000
games = [0,0,0,0]
for n in range(0,trials):
play = True
a,b = 0,0
a = a + 1
b = b + 1
if a == 4 or b == 4:
g = a + b
games[g-4] = games[g-4] + 1
play = False
for i in range(0,len(games)):
print i+4, "games:", games[i]/float(trials)
4 games: 0.125343
5 games: 0.249538
6 games: 0.312847
7 games: 0.312272
So there’s definitely no reason to believe the chances are not equal.
Of course, there’s something to be said for using some simple reasoning: