The "league-table mentality", whose malign impact on schools and universities has been much discussed in the past few days, is an odd phenomenon. We all know - don't we? - that many, if not most, rankings make little or no sense, but the urge to compile them seems irresistible. It isn't a vice that solely afflicts the compilers of university rankings. The medieval papacy, raising money for assorted bad causes, sold indulgences that entitled purchasers to so many days' remission of their time in purgatory. The larger the sin, the higher the price. No doubt the costing was rough and ready, but it presupposed a rank order among the venial and the mortal sins that the faithful had committed and confessed to.

Ranking easily gets out of hand. We might find it easy to rank sins: kicking the cat is worse than sneering at the hamster, and murder is worse than speeding. But what about the greatest ages in art, the 60 greatest poems in the English language, the best seascapes in the British Isles, and all those other rankings and ratings that every newspaper is full of at the weekend? Is Charlie Parker better than Miles Davis; are they better than Paganini? Better as what? Better at what?

By the time this appears, either Chelsea or Manchester United will have won the Champions League final. It's a safe bet that the victory of whichever side wins will have no impact on the conviction of the losing side's supporters that their side was the better side and unlucky on the day. But better at what? Not better at winning the crucial game, since that question has been settled by the score at the end of the game. More entertaining, more imaginative, more innovative, more determined - or what?

The similarity between wrangling over football rankings and wrangling over university rankings doesn't stop there. The top handful of teams in all the European competitions are the top teams because they have vastly more resources than most of their competitors. What would the table look like if it ranked teams in terms of their ability to turn financial inputs into - well, into what? If it's entertainment, 90 minutes of Chelsea and Manchester United desperately trying to avoid the one mistake that will gift victory to the other side hardly looks like value for money. If it's winning enough games to secure a title, it'd be interesting to compile a cash-discounted effectiveness table.

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And that's the point about league tables. There is, in the abstract, no such thing as a "good" let alone a "top" university because there is no agreement on the one thing that a university is there to do; there are plenty of institutions that are "good at" one thing or another; in the same way, they are "good for" different sorts of people wanting different things. Whenever a table appears that puts the universities of Oxford or Cambridge at the top yet again, a predictable chorus goes up to the effect that it is pretty easy to be a good teacher at places whose students are already so well equipped to learn and so highly motivated. Surely it's unfair to praise the University of Oxford for excellent teaching when the truth is that such good students could - and certainly do - learn from teachers of a very wide range of competence.

That's perfectly true. It cuts a bit deeper than that, however, since it is dubious whether the great majority of university teachers, wherever they teach, is anything like as competent as the great majority of schoolteachers. And as for value added, primary schools beats the lot of us. If that were the point, we'd all face some embarrassment. Dig a bit deeper and it gets worse. All league tables give universities credit for being able to demand high A-level or International Baccalaureate grades from their would-be students. How, one may ask, is that a virtue of the university? It reflects two things. One is the difficulty of the courses on offer - no good doing maths at Imperial without the necessary prior education - and the other is the number of competent applicants you can expect. But we don't in fact set up league tables to rank courses for their capacity to induce terror and despair in their students - although mountaineers do it for how severely climbs will test their nerves and skills - so it's not clear why it's a merit.

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Oddly enough, the analogy with the Premiership has begun to worry American commentators. English football has become boring because we can predict the top four or five teams from the size of their managers' cheque-books, and Americans have begun to think the wealth of the Ivy League and Stanford University is beginning to have a deleterious effect on US higher education. They pay so well and offer such good facilities that they can hire away the best faculty from everyone else and they have become so rich that they can lure away the best students with enough bursaries, too. For anyone making less than ?70,000 a year, it's cheaper to have your child go to Harvard than to most state universities and much cheaper than sending him or her to a UK university.

But is that a cause for anxiety? Football really is built on contests between two teams that they cannot both win. Universities don't - though their vice-chancellors and PR flacks may - play against each other in that sense. The only analogy in the academy is research teams trying to be the first to crack the human genome or to find a viable vaccine against malaria, and they are the exceptional instances. Mostly, what we do is to build a collectively constructed intellectual edifice, borrowing one brick from here and another brick from there.

As to the students for whose benefits these league tables are supposedly compiled, they are being had for mugs if they take more than the most minimal notice of them. Only a sceptical reading of prospectuses and visits to watch the place in action will tell them anything worth knowing.