# The Value of a College Degree

Is college worth its cost? A new study reported in the journal Science reiterates the long-standing conclusion that the clear answer is "yes." In case you're wondering why, below I'll give you an example in the same way I present it to students, adapted from my book Math for Life (Big Kid Science, 2014).

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Let's start with a multiple-choice question: Suppose you're soon to be a high school graduate and you think it would be nice to have an extra million bucks. Your best strategy for getting it is:

A. Wait for the lottery to have an unusually large prize, then buy a lot of tickets
B. Develop your athletic skills in hopes of becoming a professional athlete
C. Go to (and graduate from) college
D. Invest in the stock market
E. Get a restaurant job, in hopes that you can move up through the ranks to management

Let's go through the choices to see which one is correct. You might be surprised at how many people pick choice A. About half of all Americans play the lottery, and those who do spend an average of about \$500 per year on their lottery tickets. They are presumably enticed by ads showing the lucky winners of millions of dollars, but such luck is extremely rare. Here's an analogy: Suppose you are at a college football game in a full stadium, and the announcer comes on to say that if everyone is willing to ante up \$500 each, the college will pick one person at random to receive million-dollar prize. It's highly unlikely that anyone would agree to this deal, because when you look around at the huge crowd, it would not seem worth losing \$500 for your tiny chance of being a winner. But in fact, your odds in the stadium are better than your odds in playing the lottery. As I tell my students, "I can guarantee you that someone will win the lottery, but I can be more than 99.99 percent confident that it will not be you." So if you want a million dollars, the lottery is not the way to go.

Choice B may be more enticing if you happen to be a gifted athlete, but a few statistics should dampen your enthusiasm. In men's basketball, for example, the National Collegiate Athletic Association (NCAA) reports that only about 3 in 10,000 seniors on high school basketball teams will end up being drafted by a professional team. The odds for football are only a little better, at about 8 in 10,000. The chances of becoming a professional are even smaller for most other sports, including track, swimming, tennis, and golf. Overall, there are only about 10,000 professional athletes in the United States, or less than 1 in 30,000 of us, which means your odds of becoming one aren't much different from the abysmal odds of winning the lottery. For 99.997 percent of us, sports are for fun and health, not for money.

Skipping to Choice D, the gyrations we've all seen in the stock market should make it clear that this choice would entail a great deal of risk. While there are certainly investors who have become millionaires through stock market investments, the vast majority do no better than the overall market, and many who try to beat the market end up losing badly. Choice E might in principle work, but nearly all the good management jobs end up going to college graduates. So we are therefore left with Choice C. Can it really get you an extra million dollars?

I like to use this multiple choice question with students because it makes at least two important points. First, it shows one of the many reasons why math is so important: Without it, a simple analysis like we've done here would not be possible. Second, students are often looking for quick and easy paths to wealth, and they may devote vast amounts of time on endeavors with low probabilities of success. But in the end, the best use of their time is in investing in themselves by making sure they get the most out of their education. Education not only makes it far more likely not only that they'll lead a financially successful life, but also that they'll become happy and productive members of society.