# Searching for schools that are reasonable reaches based on SAT

What do you think of this method for estimating which schools are reasonable reaches based on SAT scores. I estimated the 5th, 10th, and 15th percentile SAT (CR + Math). The first number is an estimate of the 5th percentile which would mean you have 1 chance in 20 of being admitted. The second number is an estimate of the 10th percentile which would mean you have 2 chances in 20 of being admitted. The third number is an estimate of the 15th percentile which would mean you have 3 chances in 20 of being admitted. The fourth number is the 25th percentile (from IPEDS 2015) which means you have 5 chances in 20 of being admitted. (Yes, I know that other factors matter besides SAT. This is intended as an approximate guide.)

You can decide which number constitutes a âreasonableâ reach school.

I assumed that the bottom half of the SAT distribution for these top schools approximates a normal distribution. The upper half of the distribution would hit the SAT ceiling for some of the elite schools. I assumed that the standard deviation of SAT scores is about 125 and I used Z scores from an online normal distribution calculator. I used the most recent complete SAT scores available for schools that have become SAT optional.

I think prospective freshmen should attend the best school they can possibly afford. The âreasonable reachâ schools are the most important on your list. If you are applying to 10 schools, letâs say 5 should fall in the âreasonable reachâ category.

SAT CR + Math
5th, 10th, 15th percentile (estimates), 25th percentile (actual)

1380 1425 1455 1500 California Institute of Technology
1320 1365 1395 1440 University of Chicago
1310 1355 1385 1430 Yale University
1310 1355 1385 1430 Vanderbilt University
1310 1355 1385 1430 Massachusetts Institute of Technology
1280 1325 1355 1400 Harvard University
1280 1325 1355 1400 Harvey Mudd College
1280 1325 1355 1400 Northwestern University
1280 1325 1355 1400 Washington University in St Louis
1270 1315 1345 1390 Princeton University
1270 1315 1345 1390 Stanford University
1270 1315 1345 1390 Rice University
1260 1305 1335 1380 Columbia University in the City of New York
1260 1305 1335 1380 University of Pennsylvania
1250 1295 1325 1370 Brown University
1250 1295 1325 1370 Tufts University
1240 1285 1315 1360 Bowdoin College
1240 1285 1315 1360 Amherst College
1240 1285 1315 1360 Duke University
1240 1285 1315 1360 Carnegie Mellon University
1240 1285 1315 1360 Johns Hopkins University
1240 1285 1315 1360 Pomona College
1230 1275 1305 1350 University of Notre Dame
1220 1265 1295 1340 Claremont McKenna College
1220 1265 1295 1340 Swarthmore College
1220 1265 1295 1340 Northeastern University
1210 1255 1285 1330 Dartmouth College
1210 1255 1285 1330 Williams College
1210 1255 1285 1330 Cornell University
1210 1255 1285 1330 Vassar College
1200 1245 1275 1320 Haverford College
1200 1245 1275 1320 Carleton College
1200 1245 1275 1320 Georgetown University
1190 1235 1265 1310 Hamilton College
1190 1235 1265 1310 Georgia Institute of Technology-Main Campus
1190 1235 1265 1310 Washington and Lee University
1180 1225 1255 1300 Wesleyan University
1180 1225 1255 1300 Grinnell College
1180 1225 1255 1300 Case Western Reserve University
1170 1215 1245 1290 University of Michigan-Ann Arbor
1170 1215 1245 1290 Wellesley College
1170 1215 1245 1290 Reed College
1160 1205 1235 1280 Bates College
1160 1205 1235 1280 Rensselaer Polytechnic Institute
1160 1205 1235 1280 Scripps College
1150 1195 1225 1270 Middlebury College
1150 1195 1225 1270 University of Southern California
1150 1195 1225 1270 Emory University
1150 1195 1225 1270 University of Illinois at Urbana-Champaign
1150 1195 1225 1270 Colby College
1140 1185 1215 1260 Boston College
1140 1185 1215 1260 College of William and Mary
1140 1185 1215 1260 Barnard College
1140 1185 1215 1260 Oberlin College
1140 1185 1215 1260 Davidson College
1130 1175 1205 1250 University of Rochester
1130 1175 1205 1250 University of California-Berkeley
1130 1175 1205 1250 Brandeis University
1130 1175 1205 1250 New York University
1130 1175 1205 1250 University of Virginia-Main Campus
1130 1175 1205 1250 Colgate University
1130 1175 1205 1250 Colorado School of Mines
1120 1165 1195 1240 Connecticut College
1120 1165 1195 1240 Wake Forest University
1120 1165 1195 1240 Macalester College
1120 1165 1195 1240 Bryn Mawr College
1120 1165 1195 1240 Stevens Institute of Technology
1120 1165 1195 1240 Kenyon College
1120 1165 1195 1240 Tulane University of Louisiana
1110 1155 1185 1230 Franklin and Marshall College
1110 1155 1185 1230 Lehigh University
1110 1155 1185 1230 United States Air Force Academy
1110 1155 1185 1230 SUNY at Binghamton
1100 1145 1175 1220 Colorado College
1100 1145 1175 1220 Union College
1100 1145 1175 1220 University of California-San Diego
1100 1145 1175 1220 University of North Carolina at Chapel Hill
1100 1145 1175 1220 University of Richmond
1100 1145 1175 1220 Southern Methodist University
1090 1135 1165 1210 St Johnâs College
1090 1135 1165 1210 University of Maryland-College Park
1090 1135 1165 1210 Santa Clara University
1090 1135 1165 1210 Bucknell University
1080 1125 1155 1200 Gettysburg College
1080 1125 1155 1200 Whitman College
1080 1125 1155 1200 Boston University
1080 1125 1155 1200 Hillsdale College
1080 1125 1155 1200 Wheaton College
1080 1125 1155 1200 Villanova University
1080 1125 1155 1200 University of Miami
1080 1125 1155 1200 Lafayette College
1080 1125 1155 1200 Occidental College
1070 1115 1145 1190 Lawrence University
1070 1115 1145 1190 Worcester Polytechnic Institute
1070 1115 1145 1190 Pitzer College
1070 1115 1145 1190 Dickinson College
1070 1115 1145 1190 University of Wisconsin-Madison
1070 1115 1145 1190 Milwaukee School of Engineering
1070 1115 1145 1190 George Washington University
1070 1115 1145 1190 United States Military Academy
1070 1115 1145 1190 United States Merchant Marine Academy
1060 1105 1135 1180 Lewis & Clark College
1060 1105 1135 1180 University of California-Los Angeles
1060 1105 1135 1180 University of Minnesota-Twin Cities
1060 1105 1135 1180 Rhodes College
1060 1105 1135 1180 United States Naval Academy
1060 1105 1135 1180 Illinois Wesleyan University
1060 1105 1135 1180 United States Coast Guard Academy
1060 1105 1135 1180 University of Pittsburgh-Pittsburgh Campus
1050 1095 1125 1170 Smith College
1050 1095 1125 1170 The University of Texas at Austin
1050 1095 1125 1170 Ohio State University-Main Campus
1050 1095 1125 1170 New College of Florida
1050 1095 1125 1170 Fordham University
1050 1095 1125 1170 University of Florida

By the way, the 5th percentile would be 120 points below the 25th, the 10th would be 75 points below the 25th. and the 15th would be 45 points below the 25th (based on my assumptions). Is my method sound? Are my assumptions reasonable? Are my calculations accurate?

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Very interesting, but majority of the Ivy schools with around 6 percent admission rate, even with the perfect score majority of the applicants will get rejected. The 25% you mention may be applicable for someone with a strong hook, ie recruited athlete, multi million donor, âŠ

You say a student should attend the best college they can afford. But the school with the highest test scores may not be best.
Imo, applying to 5 schools where you fall at or below the 25th percentile, (unless you have a hook), would take too much time away from applications to schools where you actually do have a chance at acceptance.

There is so much wrong with this list, I donât know where to begin (but you did admit that you know there are other factors besides SAT that matter - so why bother creating this?)

Yep.

I see what you are trying to accomplish here but using SATs alone to determine what might constitute a reasonable reach is over simplified, IMO. I donât think that you can extrapolate that if a school accepts X percentile of applicants with a given SAT score that any given applicant will have a 1 in whatever chance of receiving an acceptance. As noted above, a disproportionate number of the sub 25th percentile acceptances will come from hooked students. For the average excellent student, one with good grades and a rigorous course load but no hooks, a reasonable reach might be something in the 25th percentile to 35th percentile range. The same might be true of a student who tests in the 75th percentile but has an otherwise less impressive academic record. There are just too many variables.

You use an interesting term of âreasonable reachesâ. But then it seems like you are suggesting a reasonable reach is a school where you scores fall in the 5-25 range. To me, that is more like a lightning strike. A reasonable reach is more like a school where your scores fall at the 75th percentile or above, but the admit rate is fairly low. So itâs a school you are very qualified for and where lots of students with similar stats get accepted, but because of low acceptance rates, itâs a tough place to get admitted.

The table is useful if an applicantâs goal is to apply to schools with specific SAT stats. âI want to apply to schools where the students are at a [higher, similar, lower] thinking level as I am.â

@collegehelp These stats seem to be from 2014, slot of these schools have increased scores by 50 points, some by 100.

Bates accurate?

The table is interesting, but you cannot draw any conclusions from it regarding admit rates. Most of the colleges on the top half of the list have admit rates at or far below ~25% for all students, so implying that being at the 25% range corresponds to a 25% admit rate is just flat out implausible.

For instance, take a look at Amherstâs profile: https://www.amherst.edu/media/view/669797 Even those scoring at 750-800 on a section or a 34-36 ACT never go higher than a 25% admit rate.

Great idea but I think your SAT estimates are overly optimistic for the top end schools. Brownâs own admissions facts says they accept approximately 25% of applicants with perfect test scores. However, your estimate says that an applicant with a 1370 SAT has a 25% chance of being admitted.

https://www.brown.edu/admission/undergraduate/explore/admission-facts

Since SAT scores are far from the only thing that matters in admission to highly selective colleges, the list is much less useful than purported.

In some cases, the listed SAT scores do not at all factor into whether the school is a reach or safety. Example: University of Texas - Austin.

I do not think admit rate is a useful index of selectivity. The correlation between admit rate and SAT scores is only about -.28. Admit rate tells you little about how good the student body is. Admit rate depends on who applies. Some schools attract better applicants than others. Ultimately, it is the SAT that best tells the story about how hard it is to get in.

The 25th percentile SAT for Brown is what Brown reported to the US Dept of Ed. It 25% of the freshmen at Brown did, in fact, have SATs of 1370 or below.

I think the importance of having a âhookâ is overblown. Other things almost equal, the student with an exceptional achievement might be given preference.

When I say âbestâ school, I am talking about quality. I know that the definition of âqualityâ differs from one person to another but, by most objective measures, SATs are highly correlated with indicators of quality such as graduation and retention rates.

The 25th percentile for Bates appears to be accurate. Their 25th percentile CR + Math was 1280 in 2002, the last year they reported to US Dept of Ed.

Thanks for the helpful comments. Good discussion.

No, it does not. Most colleges weight high school record (including GPA, rank, and/or course rigor) as much as or more than SAT scores.

âI think the importance of having a âhookâ is overblown.â

All the hooks and categories together leave little room for the unhooked at selective schools.

Could somebody post a list of median or average SATs of same list of schools (not good with stats, sorry, not sure which is more useful)âŠ

Itâs just that unhooked kids might get false hopes since as others have pointed out if acceptance rates are really low 25%percentile might not be as pertinent to their situation.

@collegehelp, are you saying that you are using data from 2002? In picking two points to confirm accuracy, I find that Bates reports an 1150 and Hamilton a 1300 as bottom 25%, respectively, in the 2016-2017 Common Data Set so the table appears to be flawed.

Regarding correlation, I donât see the support as I just went through the process with twin DDâs that both had 35 ACTâs and the results over 16 schools each didnât match your assumption at either universities or LACâs ranked 1-10 by USNWR.