The Math Behind the SSAT's Wrong Answer Penalty

  • Posted By: Geoff Dennis
  • June 23, 2016
  • 0 Comments

For many SSAT preppers, there is one test strategy that seems especially daunting: what to do about the infamous Wrong Answer Penalty.

The Wrong Answer Penalty (let’s call it the WAP) 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 one quarter point per wrong answer. Following the lead of Advanced Placement tests and the ACT, the College Board has gotten rid of the WAP 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 WAP, grappling with a complex mental equation for every question in order to maximize their scores.

Or must they?

Tutors and test prep companies have long preached one strategy that supposedly works best against the WAP. Google “SSAT wrong answer penalty” (go ahead, try it!) and you’ll find a lengthy lineup of articles with the same theme.

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.

Let’s take for example 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 -¼ 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. Really, the WAP just negates any sort of advantage that a student would gain from guessing. On tests that don’t have a WAP, like the ISEE and new SAT, guessing is always a statistical advantage because you have a ¼ 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 a 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. Of course you should 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.

And lastly, 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 any students with test anxiety.

On a test where timing plays such an important role, the simpler the strategy, the better. Our recommendation for a simpler strategy, and one that will get you the same number of points on average, is: 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 when 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.




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