The Math Behind the SSAT’s Wrong Answer Penalty
For many students preparing for the SSAT, there’s one aspect of the test that can seem especially daunting: The infamous wrong answer penalty.
Wrong answer penalties actually used to be the norm on most competitive standardized tests. Up until January of 2016, the SAT provided 5 answer choices per multiple-choice question and would deduct 1/4 point per wrong answer. Following the lead of Advanced Placement tests and the ACT, College Board got rid of the wrong-answer penalty and reduced the SAT’s per-question answer choices to four.
Students taking the Middle and Upper Level SSAT, however, must still contend with the wrong answer penalty, making split-second decisions between guessing on a question or skipping it entirely in order to maximize their score.
Or must they?
Here’s the oft-stated rule: “If you guess, try guessing only when you can eliminate one or more answer choices as wrong.”
But does this strategy make any mathematical sense?
Maybe not. And here’s the math as to why.
For example, let’s imagine a section with 20 questions, each with five answer choices and a quarter-point penalty for each wrong answer. Statistically, if you make a blind guess on every question, on average you will get 4 questions right and 16 questions wrong. You get 4 points for the correct questions, and then multiply 16 by -1/4 to get -4 points for the missed questions. Solve 4 – 4 to get 0 points, your expected value when you guess on all questions.
If you take the same 20 question section and skip all of those questions instead of guessing, you will also get 0 points (remember that you neither gain nor lose points for skipped questions).
Did you catch that? There is no statistical advantage to either guessing or not guessing on a question that you know nothing about. In reality, the wrong answer penalty negates any sort of advantage that a student would gain from guessing. On tests that don’t have a wrong answer penalty, like the ISEE and now the SAT, guessing is always a statistical advantage because you have a 1/4 chance of getting a point and no negative consequence for wrong answers.
So the popular strategy doesn’t really hold up: Obviously, if you can eliminate at least one answer, you increase your chance of choosing the correct one… if you can eliminate one answer choice, then you have a 1-in-4 chance rather than a 1-in-5 chance. You should always be trying to eliminate wrong answers on every question—that’s the whole point of this test! But you aren’t going to be adversely affected by guessing on a question, even when you can’t eliminate anything.
Finally, it’s easy to become fixated on this strategy and begin second-guessing yourself: “Am I really sure that I can eliminate this answer? Or could it be the correct one, and the test writers are trying to trick me?” This is absolutely the worst way to spend your time on a highly competitive test, and it can make test-taking even more stressful for students with test anxiety.
On a test where timing plays such an important role, the simpler the strategy, the better. Our recommendation is one that will get you the same number of points on average: Take a guess on any question you don’t know.
The one situation in which you should not go out of your way to guess is if you’re pressed for time at the end of the test. There’s no reason to spend your time randomly choosing answers for every remaining question instead of using that time to work your way through one or two of the problems.
Get started with your personalized SSAT preparation today!
Additional Reading:
G.L. Rowley & R.E. Traub: Formula Scoring, Number-Right Scoring, and Test-Taking Strategy.
D. Budescu & M. Bar-Hillel: A Decision-Theoretic View of Formula Scoring
Originally published on June 23 2016. Updated on January 22, 2025.
