Arguing that sport can learn from philosophy sounds improbable. Superficially, sport and philosophy have little in common: one is allegedly purely physical, the other (according to cliché) a matter of thinking about thinking.

But professional sport, casting its net ever wider in the search for competitive advantage, has embraced many new disciplines. Several sciences - and quite a few quasi-sciences - find themselves contributing not only ideas but also employees to professional sport. Mathematics, statistics, physiology, nutrition and psychology have all influenced sport. Almost every top professional side has access to data analysts, physiotherapists, strength and conditioning coaches, nutritionists and psychologists. Step forward the philosophers?

After all, sport's new vogue disciplines do not always rely on proof and practicality. The greatest beneficiary of all has been the least scientifically tested: managerialism. The biggest growth industry inside sport is the management class and the language it invented for its own purposes. Words and phrases that never used to impinge on sport at all are now commonplace: "reporting to", "mission statements", "line managers", "accountability", "job descriptions", "clearly defined roles". We forget that these things are relatively new and that leaders used to exercise power without them. Instead, we got by with decisions, judgements and authority.

I realised that professional sport was being swamped with managerial jargon when I witnessed a hard-living, straight-talking and usually no-nonsense team-mate complain after being fired out by a bad lbw decision. Back in the dressing room, he started throwing his kit around. But his rant was phrased in a peculiar way: "No ******* accountability, these umpires!" With such unhelpful concepts buzzing around inside his mind, no wonder he got hit on the front pad.

It sounds pretentious, almost preposterous, to argue that sport's management class would be better off to ditch the mission statements and corporate jargon, and to read some (select) philosophy instead - but I think it's true.

Sport is always desperate to empower people who can give them information - statistics, diet sheets or training programmes - as though information is the only form of advantage. But it isn't. The greatest competitive advantage is the ability to use existing information better than the opposition, to be trained in critical thinking. This, of course, belongs to a much longer-standing tradition: philosophy.

TS Eliot's classic lines - "Where is the wisdom we have lost in knowledge? Where is the knowledge we have lost in information?" - is even more relevant in the internet age. Everyone has got opinions; anyone can gather facts. It's using them better that's the real opportunity. At a time when information is so vastly available and cheap to gather, the long-term advantage derives not only from how much coaches "know", but how well they can "read" sport. And it's not only the coaches. Reading the game is also at the heart of playing sport and central to experiencing a fuller enjoyment as a spectator.

So here goes, the case for using thinking to rethink sport. One of the things that led me to think about this subject is A Philosophy of Sport, a superb book by the Cambridge academic Steven Connor that deserves to be far better known by serious sports fans and practitioners.

First, we should be cautious about believing that sport delivers justice, that the "right" team or player wins. Yes, sport is structured to deliver a final judgement. Like a trial (or the trial's medieval precursor, the "ordeal") sport ends in an answer - yes or no, win or lose. The scoreboard, we might say, is the jury. A decision must be reached, and sport's drama derives from artificially orchestrating a situation (the clock) where time is always running out. But that doesn't mean that we - as players, fans or coaches - must accept the infallibility of the decision reached.

"I often wish that the energy and debate devoted to obsessing about "winning" could be reconfigured as interest in improving performance. I think players would play a lot better as a result"

Sport's default position is to overestimate the extent to which the score reflects performance. Here is a trivial example drawn from life as a spectator rather than a player. The other day, as I watched Arsenal play football with a friend (we are both fans, though he is an instinctive pessimist) he suggested that Arsenal ought to change tactics because they were totally dominant yet still hadn't scored. My reply: "Given that they are obviously trying to score, can you think of a better way of achieving it than being totally dominant? How about more of the same?"

How many good plans are abandoned before they come good because the score does not reflect underlying reality? And how many bad plans survive too long because the scoreline is misleadingly positive?

The same point applies in retrospect. First-level thinking is: "We won - we were better" and "We lost - we were worse." Second-level thinking is: "We won - perhaps we were better" and "We lost - perhaps we were worse." Winning and losing are certainly evidence; but they are not the only evidence. People who think that winning is the only thing are less likely to help teams to win more often. Obviously you have to play to win at the time; that is a simple function of necessary competitiveness. Yet I often wish that as if by magic, the energy and debate devoted to obsessing about "winning" could be reconfigured as interest in improving performance. What would happen? I think players would play a lot better.

A connected idea (and I would agree with this, wouldn't I?) is that believing in luck is not unscientific, or slack or, as many people think, an "excuse." Luck is simply a fact of sport, built into its hardware, an inevitably huge factor over the short term. Sport misleads us doubly on the question of luck. First, because sport delivers a final judgement, acknowledging luck seems to undermine the whole spectacle from an emotional point of view. Secondly, the final result, after the fact, takes on the aura of being predestined - so we tend to forget how explicitly uncertain it was all along.

Think carefully the next time you say: it was always going to end that way. Are you sure it couldn't have ended the opposite way just as easily, had the bounce of the ball been different?

In sport, we exercise and train the body to make it more flexible and adaptive, so it is able to do what it could not do previously. The aim is to increase and improve capacity, opening up the possibility of solving problems that haven't yet materialised. Now substitute the mind for the body: we "exercise" the mind, training ourselves to think better, by way of philosophy. Many of the best sportsmen, of course, do this naturally, without ever thinking of themselves as "intellectual", still less "philosophical" - though they are, in fact, both. But they have to get there on their own, without much outside encouragement. The idea that sportsmen should try to become better at thinking and decision-making, every bit as much as they do in movement or strength, has almost never been part of mainstream sporting education.

Finally - for the purposes of the column, though certainly not the subject - we have sport in the wrong category. In particular, we misread sport's relationship with "real life" (shorthand: serious, grown-up living). "Real life" is cast as something sturdy, solid and verifiable, whereas sport is assumed to be ephemeral and lightweight, only useful as a symbol or an allegory for something more real and determinate in the real world. This may be the wrong way around. Sports may not "matter", in the sense of life and death, but they are unusually and explicitly real. Events in sport definitely happened. Unlike real life, which, as Connor puts it, "despite its upright reputation, is plainly a treacherous fogbank of delusions and deceptions".

When I wrote editorials (that's the serious bits, not the sporty bits) for a newspaper, I sometimes wondered if papers should experiment with putting the back pages at the front and the front pages at the back. Typical back-page story: "He shoots, he scores." Typical front-page story: "An anonymous source close to the prime minister confirms…" Now tell me, which one is hard news?

Sport is both more serious and less serious than you thought, a subject deserving of more philosophical attention and a discipline that would benefit from it.