Haverford was ranked 12 last year to answer a couple questions above. But keep in mind there are a LOT of ties in the rankings. So this year the ranks jump from 12 to 18 because of a 6-way tie for 12, so by that measure Haverford only dropped one slot. If you flatten all the ties (i.e. counted the next one below a tie as the next sequential number), Haverford could be ranked 8.
Within this narrow margin, these rankings are basically all within a margin of error. Meaning there is little statistical different between most of the ones in the top 20. Also, note that every ranking chooses to emphasize different statistical measures so there is no magic to the rankings – it’s not like some definitive experts of what makes a great college did this ranking, it’s a formula that is tweaked a bit every year.
Bottom line, the rankings are useful to a point but you can’t obsess on them to the smallest number.
I have no dog in this fight – no kids at Haverford and not an alum; toured once and that’s it. But my eldest focused deeply on LAC’s and my second is leaning that way too. So I’ve spent the last 3 years pretty deeply invested in researching them. I would say, if anything, Haverford would be a slight step above the “prestige” of those you mentioned in the first part of your sentence (Hamilton, Colby, Colgate) and on par with those in the second part (Bowdoin, Middlebury).
It is harder to gain admission for what it’s worth than those on the first part of your list. My kids considered Haverford a low reach but Colgate and Hamilton matches. Their high school has extensive Naivance data going back years (every student is required to participate). Mileage will vary school-to-school but for perspective the average SAT (new 1600 scale) of an accepted student from their high school to Haverford was 1516 with a weighted GPA of 4.24 (this scale would only be meaningful to their high school so only including it for comparison to other schools stats from their high school). Keep in mind these averages have to factor in recruited varsity athletes and legacies, so if you have no hook the likely required stats would be higher than these. Also, Haverford (and most of the others you listed) rely extensively on Early Decision to fill about half their classes. So there’s a major difference in admission stats between ED and regular decision – these stats are an average of the two.
Now for comparison, Colgate’s stats are 1450/4.06 (meaningfully lower ave GPA than Haverford). Hamilton stats are 1477/4.14. And Colby’s are 1474/4.09. Again, don’t assume these numbers have any relevance to other schools. But they are comparatively relevant to each other from the same school.
Yet another measure would be endowment size. The larger the endowment, the more they can spend on students whether through aid or capital programs or general resources. It’s also used by some ranking schemes as indicative of alumni success since most of these endowment funds come from alumni giving. When ranked by size of the endowment per student, of those schools you listed, Bowdoin is ranked 16 (of all colleges in the US), Hamilton is 34, Haverford 44, Middlebury 49, Colby 50 and Colgate 57. Putting Haverford in the middle of the pack.
Admission difficulty, like rankings, is not the be-al-end-all either. So I’m not sharing the stats to make a case that it makes one of these schools better than the other. Just sharing the data to counter the OP’s daughter’s perception that Haverford is some tier lower than those other schools. The bottom line is all these schools are so close together than you should basically consider them a tie. Which means you shouldn’t rule any in or out based on rank or admission stats and instead focus on what makes them unique.
Does your daughter want an urban setting, a suburban setting (i.e. proximity to urban) or truly rural? Haverford is nominally suburban but very close and convenient to Philadelphia and very close to a major airport and train station that could get students to NYC in a couple hours. By comparison, Colgate (really pretty campus BTW) is literally in the middle of nowhere, as rural as it gets for an LAC on the Eastern seaboard. Hamilton (another pretty campus – less uniform that Colgate due to historically having been two schools) is less rural but not much. All LAC’s are small schools, but there’s still a meaningful difference between Colgate with about 3,000 students and Haverford with 1,100. Some people love the idea of that smaller student body. Others want more students. What Haverford does have that none of the others you listed do is that they are part of the tri-college consortium (does sound a lot like the Harry Potter tri-wizard tournament). That means you can take classes, do activities, etc. at Bryn Mawr and Swarthmore and there’s shuttles between them daily. Bryn Mawr is super convenient – 5 minutes way. Swarthmore is less so, pragmatically more like 20. All three schools also have a relationship with UPenn for engineering classes. There are some other schools with consortiums (all the Claremont schools in particular), but most don’t.
Good luck in any event with your process.