No numbers. I promise. No formulas, no tables, and certainly no proofs. You do not need a pencil or graph paper to enjoy this essay. Yes, I am a math teacher in recovery and I suppose I have been known to stop people on the street, hand them a calculator, and ask them to “pick a three-digit number…” like a desperate magician who is off their meds, but probability and statistics is not what this column is about. And I certainly won’t do any of that “think of a number” stuff that has caused some of my neighbors to lock their door when they see me walking toward their homes.
Imagine playing dice with a buddy. Your friend rolls a seven. You give them a dollar. Your friend rolls another seven. You give them another dollar. Your friend keeps rolling sevens. You keep giving them a dollar. At some point you say, “hey, let me look at those dice.” Because some number of consecutive sevens seems reasonable. But too many sevens in a row makes you think that maybe the dice are crooked and you are being scammed.
That’s it. We’re done. Move along. Nothing to see here. An undergraduate statistics course can be summed up as “when is it time to say, ‘I think there is something funny going on with those dice.’” Mathematicians use some scary words including “inferential,” “statistically significant,” and “null hypothesis.” All of which can be safely ignored. No need to run and hide. A few sevens seems lucky; too many sevens is unreasonable. At some point we have to reject the idea that the dice are legit and consider that someone wants your dollars more than your friendship.
Which brings us back to “Anna.” Top of her class at an intensely academic high school; impressive, long-range, meaningful extra-curriculars; high 90-something-ith percentiles on her SAT. She got her AP results back a few weeks ago: Government, 5; English Literature, 5; French, 5; Calculus, 5. Lovely, motivated, pleasant kid. Intellectually curious. Loves books. The worst thing anyone could say about her is that she suffers from a little anxiety about where she will be admitted to college next year. And where does this angst about being turned down at Duke come from? Her counselor. Who told Anna this week: “our school has bad luck at Duke, there’s no reason for you to even apply.”
Which brings us back to elementary stats. Duke admits five percent of its applicants lately. Anna has as good a chance as anyone, better than most. The counselor would need so many more dice rolls than she has—hundreds of applicants over dozens of generations to make the inference “our school has bad luck at Duke.”
The counselor has no more insight into whether Anna will be admitted to Duke than I know what the price of a gallon of gas will be in 2034.
Why is the counselor so thoroughly negative? How could it possibly harm Anna to kick in a $75 application fee?
Does the counselor want to show off her awareness of what five percent means?
Our job as counselors—and what are we as parents if not our children’s first and best counselors?—is to encourage our beloved children to take reasonable chances. And to minimize the knocks to their sense of themselves when they fall. Fail better next time is good advice. As is you miss all the shots you don’t take.
The expected value theorem tells us our likely return: Mutual funds probably good; roulette wheel unquestionably not. Seventy-five dollars is a rounding error when compared to the impending cost of Anna’s undergraduate application. What can possibly be gained by not throwing the dice at Duke?
Put on your big-girl pants is reasonable guidance. Duke rejects a lot of awesome students just like you is also judicious. So is you are still the academic star you were yesterday before you got the rejection email. But don’t apply because our school has had bad luck at Duke flies in the face of good counseling and good mathematics.
C’mon, come out from behind that locked door and let’s talk more about the numbers. But first let’s encourage Anna to fill in an application for Duke.