The SAT Curve and How to Beat It


You may have the right résumé and grades for your top-choice college, but one hurdle yet remains: The SAT Exam. What scores do you need for the SAT, and how hard is it to improve your score? Is there a right test date to sit for? The SAT curve is not as mysterious as you think. Read on to understand the numbers and intent behind the College Board’s grading process.

The SAT score distribution

As shown in the Class of 2018 Report, The College Board uses a lot of complicated statistical measures to analyze the scores of the millions of students who take the SAT each year. One of the most useful metrics for parents and students is the official 2018 percentiles table, which ranks the total and section scores on the SAT. By comparing your score with the “SAT User” percentiles in the table, you can tell where you stand against your competition. A score of 1200, for example, puts you in the 76th percentile of SAT users, meaning that you scored higher than 76% of students.

What is a good SAT test score?

Consider the following distribution of the 2018 test scores:

Normal Distribution of the SAT Bell-curve
SAT 2018 Score Distribution

 

When SAT scores (horizontal axis) are plotted against the number of students who attain each score, a normal distribution forms whereby the average score of 1070 (as indicated by the dotted line) is halfway between the lowest possible score of 400 and a perfect score of 1600.

Within such a distribution, the majority of students score close to the average – 68% of them score anywhere between 860 and 1280, and 95% obtain scores between 700 and 1460. Of the remaining 5% of test takers, half of them score above 1460. As implied by the distribution, the competition increases drastically at the higher end of the spectrum, resulting in only a small percentage of students achieving the most competitive scores.

How difficult is it to achieve your target score?

Many schools in the US release data on their most recent class of admitted students. Take Harvard’s class of 2022, for example, where the 25th percentile for admitted students is about 1470, and the 75th percentile is about 1570. At the national level, these scores correspond to the 98th and 99th percentiles of all students who have taken the SAT — the 100-point difference is only a single percentile point!

In general, with every ten points that you earn above the median score, the corresponding increase in your percentile ranking decreases – you get ahead of fewer students with each score improvement – and, as exemplified by the distribution of scores among Harvard students, the highest scores are achieved by a small and competitive group of students. This scoring process is further complicated by a mechanism called equating.

What is equating?

Since a different test is given every time the SAT is administered, the difficulty of each test varies slightly. The College Board has to ensure that the score for a test taken on a certain date “equates” to the same score earned on any other administration of the test, and they achieve this by penalizing students less on harder exams and more on easier ones. Depending on how much an exam is equated, a student aiming for a perfect score may have zero room for error. In summary:

There is no way of predicting the difficulty of an upcoming test, and the equating process removes any advantage that might come from taking an easier test. The only way to guarantee a score of 1600 is to get all 154 questions right! 

How does equating work?

To see how the wrong-answer penalty varies on each test, let us compare the math section scales from three different SAT exams:

 

How hard is it to get a perfect score on the SAT?
SAT Math Score by Number of Wrong Answers

 

The SAT Math section has 58 questions. If you were to make four mistakes, for instance, you would attain the following scores on each of the three tests:

May 2018 -760

April 2018 -780

April 2017 – 750

As you can see, the math section on the April 2018 SAT (in gray) is the most difficult of the three since four incorrect answers are not penalized as harshly as on the other two tests. Comparing the scales of the April 2017 (in orange) and April 2018 tests, we can see that the penalty for four mistakes (20 points) on the 2018 test is incurred by making two mistakes on the 2017 test. It is only after eight mistakes are made on the 2018 test that the difference in section scores between the tests decreases. Both scales finally converge once a student makes 16 mistakes.

The equating process may vary between tests, but we see the same general trend in both the math and verbal sections of every test: the number of points lost per mistake is greater at higher scores than at the median. When you are aiming for higher scores, each mistake becomes costlier.

So what can you do now?

It is difficult (and highly improbable) to attain a perfect score of 1600. As a student aiming to improve your score, you will have to contend with increasing competition in the student pool, College Board’s equating process, and decreasing room for error, obstacles that become harder to surmount as you move further up the distribution.

The best advice I can give you is to start your preparation early! Improvement is a gradual process, and most students take the official SAT exam more than once before attaining their target scores. The last possible SAT test for regular decision candidates is in December, but Early Decision candidates may have to complete testing as early as October. To find out more about applying early, check this blog post out!

Although this blog dissects the SAT scores, the ACT exam uses a similar equating process. To find out the differences between the SAT and ACT, check out this post.

To find out where you stand right now, sign up for a free SAT practice test today! Reserve your spot here!

Joel Lai is test prep instructor and a graduate of The University of Richmond





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