edit I noticed my reply was a bit long so put my preferences for university and me addressing your points on statistics in spoilers i suggest you look at the statistics spoiler (second spoiler) as you seem to be demonstrating a lack of understanding for statistics.
I dont get mad for people disagreeing with me that's how I learn if or when I am wrong, I just defend the position I believe to be right until I am given sufficient reason to believe otherwise.
In order to get this out the way crap/**** is a relative term I am sure compared to the world at large most of our universities are very good. its relative often when watching a sports game I might say player X is crap it is evident though that player X would absolutely destroy me on the court/pitch etc. I am talking in relative terms and for a uk university I consider the bottom half crap. Moving on.
I would be very concerned if what you are saying is correct. LSE are not so relevant to me because I want to do a maths degree they do a maths with economics degree and I don't want to spend half my time studying economics. So even if people said they were better then Cambridge I would not apply their. However Bristol have a very good reputation for maths and all things been well Would likely be one of my five on the UCAS form.
I have had a bad experience with university so far I completed a degree at poor standard university. They were actually considered fairly good for the subject but were ranked weak overall. Due to a number of factors long story I got by with a 6 hours of work outside of lectures and seminars a week and had only 8 hours a week of lectures and seminars. In total then my input was less then 14 hours a week. I came out with a 2:1. That should not be doable, a degree should be a full time job. There is something wrong with the course if I can coast through this easily for university exams I often learned entire modules from scratch not revised from scratch the night before the exam and still got a 2:1.
If I was an employer looking to employ graduates my concern would be the quality of the graduate I am getting how skilled how are they at maths/Engineering/topic X etc. The current impression I get and many would get is that A graduate from Bristol would be more competent then a graduate from Hull as a generic rule. EG if two candidates score exactly the same eg 2:1 with 65% average the candidate from Bristol would have completed a tougher degree and be more skilled in the area I wish to recruit for.
if you are actually telling me this in fact wrong and a candidate from Hull is more skilled then Bristol this is huge news, if this in fact true I need to know this to avoid making a mistake.
Now in the Olympics Bronze is an accomplishment however when there are three categories to be awarded and you get placed in one of these three regardless getting placed in the third tier is not good it is bad. I would consider universities in the bottom third in the UK bad for UK universities and I don't want to go somewhere considered bad.
I know that LSE graduates are very sought after by employers if they were less competent then their peers from other institutions to the extent that most universities provide better caliber graduates I would have thought this would have changed by now word would have got out. EG if I ran a small trading firm and employed a single graduate from LSE and found him to be a weak performer I would assume I got unlucky, If however I had a large trading firm and employed several hundred candidates from LSE over a period of years and had regularly noticed the majority of them seemed to be weak performers and the candidates I was getting from Hull were better overall I would start to seriously question the quality of the degree programs at LSE I certainly would not go on blindly saying LSE is a great university continue to employ from their regardless of what I see because league tables say so. Multiply this across the industry for Both LSE and Bristol and they just would not be targeted anymore. this relates to statistics and I will come back to that.
However for now for the reasons I just stated I find it hard to believe that the degree programs at LSE and Bristol as a generic average are not rigorous and or are producing weak caliber graduates. Is this what you are claiming? is a graduate from Hull better qualified on average then a graduate from LSE/Bristol? this is huge news if so.
I would have to assume your answer to that would be no, otherwise this is a major claim and I would require significant evidence of this if this is your claim then please correct me here.
I assume your claim has to relate to teaching as one could in theory have a very difficult degree program which is very rigorous and produces very higher caliber students but have poor teaching and relies on the students self teaching.
I have to assume this is your claim because this could be believable whilst the former would almost need a conspiracy to go have gone unnoticed by now. in that regard I think its highly contextual for example my subject in maths weaker students may need the lecturer to go slower and break down the stages whilst stronger students may have already seen the next several steps and the lecturer may well be able to skip over these. weaker students may need help going over many examples whilst stronger students may be able to be given problem sheets and work out practice most of these themselves. There are other things to debate and criteria etc but this is why teaching standards can be hard to assess and misleading.
in theory a university that admits students whom obtain CCC and gets them to graduate at the same standard or caliber of students at another university who admits students who achieve ABB would be better for teaching then the second university. This would be a clear measure and I am willing to accept there may be ways they can actually measure such things.
However if the second university was producing students of AAB caliber I would still choose this one in theory because whilst the teaching is poorer I would come out at a higher caliber.
I think rankings should be assessing the caliber standards and skills of graduates much more then anything else as this is what employers should and will be looking for.