SAT Test Taking Strategies: The Science of Guessing

Matt Larriva
Oct 10, 2021
Home » Blog » SAT Test Taking Strategies: The Science of Guessing

Guessing is one of the most important SAT test-taking strategies.

But are you doing it right?

In a simpler world, you would be able to guess on every SAT question you couldn’t solve, or didn’t have time for.

But the ETS (makers of the SAT) know this and built a so-called “guessing penalty” into the test.

That’s right: ETS deducts .25 points for every incorrect answer, which really turns the “guessing penalty” into error punishment. To refresh you: on the SAT you receive one point for every correct answer, zero for blank answers, and -.25 for every incorrect answer. The only exception is the Mathematical Grid In Section where there is no “guessing penalty.”

With this scoring mechanism, it is clearly advisable to leave blank any question which you do not have time to look at. Old wisdom suggests that you should guess when you can eliminate one or more answers. This is proved using E(V), and by assigning all questions the same worth.

This article will prove why that logic is incorrect, and then show how to better guess on the SAT by segmenting the sections into levels of difficulty, and then using that to calculate how many answers you must eliminate on each question before guessing.

student taking act sat test

The Old Way of Guessing

Now, if you have grown up around the chorus of people recanting the adage, “guess if you can eliminate more than 1 answer choice” then this new strategy will strike your ear wrong.

Let’s examine the math behind the old adage and then prove why the new is preferable. Both methods rely on a statistical concept called Expected Value, abbreviated E(V). Expected Value tells you the approximate result of a probability event whose outcomes each have an assigned value—like the SAT. E(V) is calculated as the sum of the values times the probabilities of the values.

For example, to calculate the E(V) of a coin toss in which you make $1 for every Heads and lose $2 for every Tails would be expressed E(V) = ($1 x .5) + (-$2 x .5) = -1. Notice the negative sign (-) in front of the $2 telling us that we lose $2 for every Tails.

Now on the SAT we gain 1 point for every right answer and lose -.25 for each incorrect one. So on any random SAT question where we don’t know the answer we have a one-in-five chance of guessing correctly, so E(V) = (1 point x .2)+(-.25 points x .8) = 0.

This is to say that if you guessed on 5 questions, you would get 4 wrong and get 1 right which would be -.25 times 4 incorrect answers plus 1 point for the correct answer, which equals zero.  So every time you can eliminate one incorrect answer, your E(V) is >0. Every additional wrong answer you can eliminate increases your E(V).

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Will you get accepted?

Find out how likely you are to get accepted based on your GPA, test scores, and even extracurricular activities. Then, get custom recommendations for how to improve your odds – completely for free on CollegeVine.

The Old Way Is Wrong:

The old method works from a mathematical standpoint, because it encourages you to only guess when you can create a positive E(V).

But this method fails from three standpoints:

the model fails to recognize the fact that the SAT is a timed test, and the time needs to be modeled in. For example, if I spent a minute on one question, before deciding that I couldn’t eliminate any wrong answers, then left it blank, I would supposedly still have an E(V) of zero. But this is incorrect; in truth, I would have wasted 1 minute that I could have used to increase my chances of accuracy on other questions. A more accurate formula for E(V) considers the time.

whereas the model is correct in saying all questions are worth the same points, it is incorrect in that it doesn’t recognize that questions have different difficulties. Questions should be grouped into 5 sections of varying difficulty. Each section of the SAT increases in difficulty from low to high.

Average Score:
the average score on the SAT math is 510 which is equivalent to a raw score of 26. A raw score is the sum of the points correct minus the sum of error penalties. So if the old method of guessing were accurate, it should bring you closer to the average when you employed it—you would hope. However, that method actually brings you further from the average. You actually need to have a 60% chance of guessing correctly (not a 25% chance, which you have when you can only eliminate 1 wrong answer) to score a 510. So anytime you do not have a 60% chance of accuracy you’re bringing yourself further away from the average score, and closer to a poor score.

international student studying for ivy league acceptance

The New Way of Guessing

Divide the test: you know that there are 54 math questions which distribute in the following way: 10 level 1s, 16 level 2s, 14 level 3s, 10 level 4s, and 4 level 5s. Approximately this is 20%, 30%, 25%, 20%, 5% respectively. So divide each math section in terms of the level of questions.

The first math section has 20 questions, so the first 20% (4) will be level 1, the next 30% (5-10) will be level 2, and so on. On level 1 questions you should be 100% accurate, on level 2 questions you should be at least 50% accurate (able to eliminate 3 wrong answers), on level 3 questions you should be 33% accurate (able to eliminate  2 wrong answers) on level 4 questions you should be 25% accurate (able to eliminate 1 wrong answer), and on level 5 questions it’s a pure guess at 20% accurate (able to eliminate no wrong answers).

The time distribution is also theoretically, on a 25 question section, as follows: 1 minute per L1, 1.2 minutes per L2, 1.3 minutes per L3, 1.5 minutes per L4, and 2 minutes per L5. The E(V) of this strategy has a raw score of 18.96 compared to a raw score of 3.375 with the old strategy.

Therefore, divide each section into the 5 levels and guess when you can eliminate (5-Level) answers. On a level 3 question, guess if you can eliminate more than 2 answers (5-3=2) otherwise leave it blank.

Compared to other SAT test-taking strategies, this new method ensures you a much higher E(V), takes into consideration the timing of the test, the average score, and the difficulty of eliminating wrong answers on different questions.