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It came to me in a flash.

“You appear to be saying that the Premier League would be fairer if we didn’t have points,” a friend of mine said. And all of a sudden, just like that, I realised that this was precisely what I was saying.

I want to make the case for a simple, radical reform of the league table. In one stroke I think we can make football fairer and more exciting. Although I am more confident about the fairer bit.

Let me start with a thought experiment. If there were two teams who scored the same number of points in a season, who would you judge to have been the better — the one with a positive goal difference of 40 or the one with a goal difference of 60? You would probably agree that the latter team were the better. Now think why. It is because, while the first team have proceeded with a bit of luck, the second have more cleanly gained their points.

The scheme I want to suggest is a simple extension from this. I want the Premier League to be decided on goal difference entirely.

The title should be won by the best team, with the table being, as close as possible, a measure of quality. So how good a measure are points? Dr Mark Latham, Dr Ian Graham and Dr Henry Stott have been investigating.

If points are a good, consistent measure of quality, one would expect that points scored in one season would be a reasonably good predictor of the number of points scored the next season. And so it proves. On a scale of 0 to 1, the predictiveness of points in one season for points in the next is 0.6.

But is it possible to do better? It is. How well does goal difference in one season predict points in the next? It scores 0.65 on the predictiveness scale. This suggests that, by using goal difference, we are eliminating a bit of the luck, we are getting less noise and more signal about quality. And if you use goal difference to predict goal difference, you score 0.68.

It is not hard to see why this should be so. Take Michael Owen’s goal against Manchester City last weekend. Match of the Day 2 claimed that he scored it one second after the game should have been over. The cut-off point for the match was as important in settling the destination of the points as the quality of the combatants. This is inevitable unless games are going to go on for ever. But it does mean that a lumpy amount of points can be allocated because of the good fortune of a goal coming just before or just after the cut-off point.

The goal-difference scheme smooths things. It means that luck makes a smaller impact. It is a better measure of quality. The graphic shows what would have happened if it had been in force for the past few seasons.

What about making the game more exciting? Arsène Wenger, the Arsenal manager, favours adding points for goal difference to make teams attack. And certainly the style of play would have changed (which is why the graphic is only a bit of fun, because teams would have had different strategies). Teams might attack more in games against poor opponents, rather than sitting back after scoring a couple of goals.

On the other hand, in tight games against roughly equal opponents, the price of a big defeat might be terrible. So teams might sit on a 1-0 deficit and try simply to avoid any more goals, rather than countering.

So that’s my scheme. What do you think?