. . . perhaps the most thorough exploration of guessing strategy ever visited on the Internet
If there’s one thing I get asked about more than anything else (apart from my credentials), it’s the issue of guessing on standardized tests.
There are many, many dimensions to this question, and in this post I’m going to do my best to cover all of them. I’ve broken it up into sections so you don’t have to slog through the whole thing if you’re not an obsessive testing geek like I am (and if you’re not, good for you ).
So first, let’s cut to the chase:
You should not guess on the SAT, or on any other test that penalizes you for putting down a wrong answer as opposed to leaving a question blank (that includes the SSAT, the PSAT, the SAT Subject Tests, the multiple-choice portions of the AP tests, and so on).
On tests like the ACT, the LSAT, and the ISEE, in which there is no penalty for being wrong, it’s okay to guess as a last resort, but guessing still shouldn’t be a major component of your approach.
For computerized tests like the current version of the GRE and the GMAT, guessing is sometimes inevitable but it still shouldn’t be something you plan to rely on.
If you’re familiar with the conventional wisdom in the test prep field, I probably sound like a raving lunatic for saying not to guess, especially on the SAT. Many tutors and students have taken time out from their busy lives to tell me so (I’ll get to that below).
But there’s solid reasoning behind my position, and I’ll lay it out now. After reading this, I think you’ll agree that guessing isn’t a reliable strategy if you want to do well on a standardized test.
First Things First: Guessing Defined
One thing I’ve learned over the years is that different people mean different things when they talk about guessing on a standardized test, and those different definitions can lead to confusion.
For the purpose of this article, when I talk about guessing on a test I’m talking about putting down an answer when you aren’t sure you’re right. If you’re looking at a reading comprehension question that asks what the author’s tone is in a particular passage and you think that two or three of the answer choices might all be good descriptions of that tone, then picking one of those choices and hoping for the best is the kind of guessing I’m talking about when I say that you shouldn’t guess.
I am NOT talking about putting down an answer that you know is correct even when you don’t understand why it’s correct.
Let’s imagine, for instance, that you’re looking at a math question that involves finding the distance from one point on a circle to another point on the circle. Assume that the question says the radius of the circle is 3 units. If 4 out of the 5 answer choices give distances greater than 6 units, then you know that the remaining answer choice must be the right one, because the distance from one point on a circle to another point can’t be greater than the diameter of the circle, which is 6 in this case. In this scenario, you should choose the only answer choice that can possibly be correct, even if you’re not sure how to find that distance mathematically, because you know that all of the other choices have to be wrong.
In a case like this hypothetical, you should answer the question, of course, because you can be positive you have the right answer even if you couldn’t have generated that answer on your own without the answer choices provided by the test. That’s not a guess, as far as I’m concerned; it’s marking an answer that you’re positive is correct.
So, again: When I refer to guessing, I’m only talking about putting down an answer when you aren’t sure it’s correct.
Now let’s take a look at the surrounding issues:
Wrong-Answer Penalties on Tests Like the SAT and PSAT
The whole guessing controversy arises in the first place because many popular standardized tests, like the SAT, PSAT, SSAT, SAT Subject Tests, and AP tests impose a penalty for wrong answers on multiple-choice questions.
They do this because they’re trying to counteract one of the weaknesses of the multiple-choice format, which is that multiple-choice questions necessarily place the correct answer to every single question in front of every single person, making it a lot easier, in theory, to guess the right answer on a multiple-choice question.
Testing companies like the College Board don’t want you guessing your way to higher scores than you ‘deserve,’ so this penalty for wrong answers is meant to counteract the impact of guessing.
If each correct answer counts for one raw point in your score, then each incorrect answer costs you a fraction of a raw point. That fraction is equal to 1/(the number of answer choices minus one). So if there are five answer choices per question, as there are for the SAT and PSAT, then the penalty is 1/4 of a raw point taken away for each wrong answer.
The idea behind this penalty is that it should exactly undo the effect of random guessing.
If we guess randomly on 5 SAT questions and each question has 5 answer choices, in theory we should expect to be right 1 time in 5, and wrong the other 4 times. The one time we’re right will net us 1 raw point, and the 4 times we’re wrong will each cost us 1/4 of a point, for a net change of zero points, or no impact from guessing whatsoever.
(If you know a lot about stats you might be shaking your head at that, because a sample of 5 questions doesn’t guarantee any kind of predictable outcome. Let’s put that aside for the moment.)
So that’s the penalty. As you can tell, it’s supposed to make you think twice about putting down a wrong answer.
Instead, it’s lead to what I would call the Traditional Guessing Strategy, known and loved by mainstream SAT tutors since the days when Stanley Kaplan was making a quarter an hour.
The Traditional Guessing Strategy For The SAT, PSAT, and Similar Tests
The traditional guessing strategy for tests like the SAT is that you should guess all over the place, marking an answer for each question on the test. According to the traditional guessing strategy, when you guess you should try to rule out as many answer choices as possible first.
Here’s why . . .
The (Pretend) Math Behind The Guessing Strategy
The argument for the traditional guessing strategy is that you’re being penalized as though you were correct one time in 5, so guessing from fewer things should allow you to outpace the penalty.
In other words, if we guess from 10 questions with 5 answer choices each without eliminating, we’d expect to be right twice and wrong 8 times (ignoring some statistical principles about sample sizes), resulting in no change to the score. But if we can rule out 3 wrong answers for each of those 10 questions, so that we’re guessing from 2 things each time, then we’d expect to be right 5 times and wrong 5 times. We’d get 5 points added to our score for the right ones, and only lose 5/4 points for being wrong, amounting to a net gain in points.
The effect would be smaller if we could only eliminate one answer choice per question, but even that elimination should theoretically swing things in our favor.
And even if we can’t eliminate any answer choices, the guessing theory says we should still guess anyhow, because the penalty should still have us coming out even and we might just get lucky.
Here’s a very respected tutor laying out the argument for guessing in a private email:
No guessing? .. the math of the scoring system itself outright proves that guessing with even one answer choice crossed off is beneficial!
First of all, TOTALLY random guessing, with no eliminations at all, just blindly circling answers, works out mathematically THE SAME AS OMITTING! So how is elimination guessing not better, when it increases the probability of right answers . . .? How can we choose to omit on the basis that it is better, when math proves that it is NOT? This is math–and not differential calculus, this is basic arithmetic. It is not an opinion, not a debatable point!
(While this tutor is a very polite guy, you can tell from the rhetorical questions and the Paine-ian capitalization that he thinks I’m loony tunes. This is a common reaction, as I noted, but it doesn’t faze me, for reasons to follow below.)
Mathematically, the argument in favor of guessing seems like a pretty solid case. Indeed, anybody who would argue with the idea that you’re more likely to be right when you guess at random from fewer things would clearly have no idea what he was talking about.
But there’s one little issue that should maybe make us start questioning this logic . . .
So Where Are All The High-Scoring Guessers, Anyhow? (The Inductive Argument Against Guessing)
I can tell you with confidence that test-takers who make guessing a cornerstone of their approach to a standardized test almost never score high.
I’m saying “almost never” because I realize that there must be one extremely lucky test-taker somewhere out there in the universe who has christmas-treed his way to a perfect score on some standardized test, since there are millions of people who have taken millions of standardized tests. But I’ve never met such a person. I bet you haven’t, either.
What I really want to say is that it never works. As in it doesn’t work in well over 99% of cases. As in I’ve never, ever seen it work, nor have I met anybody who’s seen it work, and I bet you haven’t, either.
I was teaching a class once that was attended by a student who had already scored a perfect 800 on the SAT Math test (he was there because he wanted to bump his other section scores up to 800s from the low 700s).
A few minutes into the class, I brought up the idea of guessing to see what the class thought of it. Most of them were in favor of it. Without commenting on the issue myself, I asked Mr. 800 how many times he guessed on his perfect Math score, and what his SAT guessing strategy was.
He fidgeted a little, gave me an apologetic look, and said, “Actually, I didn’t guess at all on the Math section. I don’t believe in guessing on the SAT at all. I actually don’t think the normal SAT Guessing strategy is a good idea.” He was clearly concerned about disappointing me with that answer, because he thought I wanted to use him as an example of how to guess for the rest of the class.
Actually, though, I knew in advance that he would say he never guessed on the SAT, and I was planning to use his refusal to guess as an example for the others.
How did I know he was going to say he didn’t like guessing on the SAT?
Because people who score high on standardized tests don’t rely on guessing.
I’m not saying there aren’t people who score an 800 on the SAT Math when they’ve guessed on one question and answered all the others with certainty. I’m sure that happens. I’m saying that people do not end up with 800′s (or even 650′s) after making ‘educated’ guesses on 20 SAT Math questions.
In other words, people do not guess their ways to scores that are significantly higher than where they would otherwise be.
Now why would that be, if the guessing strategy is mathematically sound and if the vast majority of test-takers use it?
Let’s take a look . . .
The (Gigantic) Logical Flaw in the Guessing Idea (The Deductive Argument)
As we discussed above, it seems pretty definite that you’re more likely to be correct when you guess at random from fewer things.
But, as I’ve just explained and as you may have noticed on your own, people who use the traditional guessing strategy tend not to do very well.
Which might seem puzzling, at first.
The reason the idea of guessing at random from fewer choices seems not to lead to higher scores lies in the phrase “at random.” It’s true that guessing randomly from two things is more likely to work out in your favor than guessing randomly from 5 things.
But test-takers don’t guess at random.
I’m going to say that again:
Test-takers don’t guess at random.
One more time, for good measure, with underlining and italics added so you know I really mean it:
Test-takers don’t guess at random.
Test-takers make their ‘educated’ guesses based on what they think they know about the question.
There’s one serious problem with that, though: The companies that design standardized tests are extremely good at writing questions so that students who can’t figure out the answer will be misled into liking a wrong answer.
The College Board, for instance, doesn’t just randomly generate wrong answers and then sit back and twiddle its evil institutional thumbs, hoping that you’ll do it a favor and pick one. It’s much too evil an institution for that, and, anyway, its thumbs are massive and really hard to twiddle.
Instead, the College Board (and every other testing company) knows that students like to use this guessing strategy (hell, the companies advocate this strategy themselves–I wonder why that might be?). So they go to a lot of trouble to anticipate the types of mistakes we might make, and then they position wrong answers to take advantage of those mistakes.
When you add in the fact that most test-takers aren’t thinking about the test the right way in the first place, you end up with a situation in which people guess like crazy and lose points like crazy, and end up with disappointing scores.
Every standardized test is designed so that each question has only one correct answer, and that correct answer always flows directly from the wording of the question itself. This design element is central to the nature of a standardized test; without it, the data from the tests would be inconsistent and the tests would serve no purpose.
So when we read a question and we’re not sure how to answer it, we have made a mistake somewhere. Period. From that point on, any attempt that we make to answer that question is very, very likely to result in a wrong answer, because (a) we misunderstood the question, and (b) the test has cunningly created wrong answers to appeal to people in this exact situation.
A Bonus Flaw In The Guessing Idea
There actually is a mathematical problem with the idea of guessing at random on a standardized test.
It doesn’t really matter for our purposes, since people who take standardized tests don’t guess at random, but for the sake of full exploration of the guessing idea I should point it out.
The problem has to do with a math idea called the “law of large numbers.”
Basically stated, this law says that when we’re dealing with a series of random selections, the distribution of the outcomes doesn’t necessarily approach the expected distribution until you’ve done the random selection a large number of times.
In everyday terms, if you flip a coin twice, most people would expect that it comes up heads once and tails once. But in real life, when you flip a coin twice you really can’t expect that result with any confidence. There’s a decent chance that you get two matching outcomes on your two flips. On the other hand, if you flip 10,000 coins, you can be almost certain that roughly 5,000 of them will come up heads.
So the confidence you can expect to have in achieving the predicted outcome increases significantly as you accumulate more and more randomized choices.
(This, by the way, is basically how a casino stays in business. On any given bet it might lose a tremendous amount of money, but it has so much money in reserve and handles so many bets at once that it can rely on the odds working out in its favor in the long run.)
Here’s why all of this matters for the guessing discussion: The number of questions on a standardized test isn’t big enough to give us much confidence in the overall outcome of the randomized guesses we might make. So there’s still a pretty decent chance that randomized guessing would lead to an outcome that was markedly better or markedly worse than what pure probability might predict.
(At this point, you might notice that what I just said leaves open the possibility of people doing “markedly better” than what we might expect if they guessed randomly. So where, you might ask, are all those people who should have ended up getting much better scores through a combination of randomized guessing and dumb luck? They don’t exist, because, as I mentioned above, test-takers don’t guess randomly, almost as a rule. They guess based on misunderstanding the questions they’re working on, and they end up losing a lot of points.)
“So You’re Saying Not To Guess At All?!?! What, We Just Leave Questions Blank If We Can’t Answer Them?”
People are often surprised to hear that I’m in favor leaving questions blank if we don’t know the answer and we’ll be penalized for being wrong.
But that’s exactly that I’m suggesting. Well, it’s part of what I’m suggesting, anyway.
When you don’t know the answer to a question on a standardized test, you don’t understand the question. And when you don’t understand a standardized test question but you try to answer it anyway, you are very, very, very likely to be wrong–way more likely than probability would suggest, because probability doesn’t take into account that the test is designed to attract people to wrong answers if they don’t know how to find the right one.
Given this scenario, skipping (which costs zero points) is preferable to guessing (which usually costs more than zero points).
It might seem counter-intuitive, but it’s not just a coincidence that the people who score high on the SAT and the people who use the Traditional SAT Guessing strategy aren’t the same people.
And that leads me to my next important topic on this overly thorough explanation of basic standardized testing theory . . .
The Hidden Damage of SAT Guessing
At this point, you might begin to suspect that the reason I hate guessing on standardized tests so much is that it leads to a lot of wrong answers when people don’t understand the questions they’re guessing on.
And that’s definitely a large part of why I don’t like guessing.
But there’s a much bigger reason, actually: The idea of guessing on a standardized test is basically the intellectual equivalent of throwing your hands up in despair and surrendering. I hate that in general, and I really hate it when we’re talking about a standardized test, because there’s no reason to do it.
The guessing strategy flows very naturally out of the most people’s test-taking attitude, which is that standardized tests must be nearly impossible because they’re weird and because so few people do well on them.
That attitude is one I reject completely. I recommend you reject it, too.
Standardized tests aren’t actually hard at all. They’re very easy, once you know how to look at them, because the standardization means they have to do the same things over and over. They are predictable and beatable, if you see them as they are instead of buying into the widespread hysteria that surrounds them.
A test-taker who has been correctly prepared for a test knows what to do at all times. When he comes to a question that seems difficult or abnormal, he immediately realizes that he must have made a mistake somewhere, and he checks through the likely causes of that mistake to correct himself and find the right answer; if he still can’t find the source of his mistake, he realizes that he must still be overlooking or misundestanding something–so he skips the question and forgets about it, ready to tackle the next one.
But the traditional guessing strategy will keep you from reaching that state of full preparedness, because it assumes that there are sometimes questions that nobody could figure out with certainty. Most people who use the traditional SAT guessing strategy (which, again, is most test-takers) go all the way through an entire test without ever once feeling certain of what they’re doing. They might feel 95% sure on one question, 20% sure on another, 45% on another, and so on, and they just stumble through the test hoping they’re guessing correctly.
It’s a poisonous way to look at the test. There are better options out there.
So I’m not just suggesting that you never guess. I’m also suggesting that you start looking at your test in the right way, so that you can answer questions with certainty.
Which leads me to my next issue . . .
Why Guessing Still Isn’t A Great Idea on Tests That Don’t Penalize
Some tests, like the ACT, LSAT, and ISEE, don’t penalize you for being wrong. For this reason, students frequently think that they can rely on guessing to help them in those tests.
But guessing is still pretty unlikely to help you in these situations.
Tests that choose not to penalize you make that decision not because they don’t care about the validity of their data, but because they realize two things:
(1) guessing is unlikely to help anyway, since students base their guesses on misunderstanding the question, and
(2) standardized tests exist to rank students against one another, not against an objective measurement, so giving all students the same “advantage” doesn’t change the overall distribution of test scores
So, in other words, the decision not to penalize for a wrong answer doesn’t actually make a test any easier from a guessing perspective, because scoring well on that test is still going to require getting a lot of questions right, and people don’t guess their way to high scores on standardized tests.
Doing well on the ACT or the LSAT, just like on the SAT or the GMAT, is going to require understanding the mechanics of the test and learning to recognize right answers and wrong answers with certainty.
So you shouldn’t count on guessing to help you too much here, either, especially because it promotes a toxic, defeatist attitude toward the test, as noted above.
One small caveat, though: Since you won’t be penalized for a wrong answer on these tests, you should still answer every single question, even if you’re not sure what the answer is. Just don’t expect it to help too much–it’s only very, very, very slightly better than leaving the question blank in most cases, and your best bet is still to spend a little time learning how the test actually works so you don’t want to guess as much.
As with many strategic decisions, the strategic decision not to guess frequently on a standardized test has certain exceptions for certain very limited situations. There are two exceptions I can think of, and they only apply to a very small percentage of test-takers: the situation of the perfect score-seeker and the situation of some scholarship athletes.
In some cases, a highly recruited scholarship athlete only needs to clear a certain minimal score on the SAT or ACT in order to be eligible for admission. Such a student may be justified in guessing, and guessing a lot, in order to clear that minimum threshold. If a student needs SAT sub-scores in the low 400′s, for instance, his most efficient strategy might just be to take the test a dozen times with no preparation at all and guess randomly each time; on at least one of those trials he might well clear the threshold. Of course, most test-takers don’t find themselves in this kind of position. (By the way, in choosing this example I certainly don’t mean to suggest that athletes are less intelligent than the general population. I’m an athlete myself, and most of the more intelligent people I’ve ever met have been athletes, as well. I chose this situation because the only time this minimal threshold situation seems to come up is when a student needs to clear it in order to be eligible for the NCAA.)
Just as some test-takers only care about clearing a minimal score, some test-takers only care about achieving a perfect score. Generally, the people who would only be satisfied with a perfect score are professional tutors and teachers like me, but there are also some students who want a perfect score for the prestige they think it might bring them in the admissions process. If you absolutely must have a perfect score in order to reach some goal, and if a score that’s even one notch down from perfect would be utterly valueless for you, then you should plan to answer every question on most sections of most tests, no matter what.
As you can see, these two exceptions to the no-guessing rule only apply to very small fractions of the testing population. If your goal is just to get the highest score that you possibly can, then you don’t want guessing to be a cornerstone of your approach to the test.
Coda: so How Many Should I Answer?
Some students still want to know a specific number of questions they should answer in order to maximize their chances of getting a high score.
I realize that people feel uncomfortable leaving things blank and don’t want to do it too many times. But the question “How many test questions should I leave blank?” comes from a misunderstanding of the math and the strategy involved: I’m saying that every single time you guess, you’re very likely to be throwing away points that you didn’t have to throw away. Skipping is always better than losing points, no matter how many times you have to make the decision.
And the other side of all of this, of course, is that we need to learn how to look at the test correctly, so that there are fewer times when we feel like we need to skip something.
If you’re doing a practice test and you’re still pretty far from your goal and you skipped 20 questions, guessing on those 20 questions won’t get you to your goal. In fact, it will probably only put you even further back. What will get you to your goal is improving your understanding of the way the test is designed, so that you don’t end up in testing situations that tempt you to guess in the first place.
Think of it in football terms: A Hail Mary pass is a desperate act that rarely results in success, much like a guess on a standardized test question. If your football team keeps losing games but doesn’t resort to any Hail Mary passes, the solution is not to start doing Hail Maries on every play, because Hail Maries are very ineffective; the solution is to improve the team’s fundamentals so that it knows how to play the game better, eliminating the desperate situations that give rise to Hail Maries in the first place.
The team that wins the Super Bowl each year isn’t the team that gets really good at Hail Maries, but the team that plays solidly throughout the year and cuts down on its mistakes and misunderstandings. Similarly, the test-taker who learns how to appreciate the fundamentals of a particular test and approach questions correctly over and over again will be the test-taker who does very well on the test.
So, in a nutshell: Don’t rely on guessing Standardized tests like the SAT, ACT, LSAT, GRE, ISEE, and SSAT are all designed too intelligently for guessing to be an effective strategy. Get better at test-taking instead, and you won’t even want to guess, because you’ll know how to answer the questions you encounter.